task_url stringlengths 30 116 | task_name stringlengths 2 86 | task_description stringlengths 0 14.4k | language_url stringlengths 2 53 | language_name stringlengths 1 52 | code stringlengths 0 61.9k |
|---|---|---|---|---|---|
http://rosettacode.org/wiki/Multi-dimensional_array | Multi-dimensional array | For the purposes of this task, the actual memory layout or access method of this data structure is not mandated.
It is enough to:
State the number and extent of each index to the array.
Provide specific, ordered, integer indices for all dimensions of the array together with a new value to update the indexed value.
Provide specific, ordered, numeric indices for all dimensions of the array to obtain the arrays value at that indexed position.
Task
State if the language supports multi-dimensional arrays in its syntax and usual implementation.
State whether the language uses row-major or column major order for multi-dimensional array storage, or any other relevant kind of storage.
Show how to create a four dimensional array in your language and set, access, set to another value; and access the new value of an integer-indexed item of the array.
The idiomatic method for the language is preferred.
The array should allow a range of five, four, three and two (or two three four five if convenient), in each of the indices, in order. (For example, if indexing starts at zero for the first index then a range of 0..4 inclusive would suffice).
State if memory allocation is optimised for the array - especially if contiguous memory is likely to be allocated.
If the language has exceptional native multi-dimensional array support such as optional bounds checking, reshaping, or being able to state both the lower and upper bounds of index ranges, then this is the task to mention them.
Show all output here, (but you may judiciously use ellipses to shorten repetitive output text).
| #Python | Python | >>> from pprint import pprint as pp # Pretty printer
>>> from itertools import product
>>>
>>> def dict_as_mdarray(dimensions=(2, 3), init=0.0):
... return {indices: init for indices in product(*(range(i) for i in dimensions))}
...
>>>
>>> mdarray = dict_as_mdarray((2, 3, 4, 5))
>>> pp(mdarray)
{(0, 0, 0, 0): 0.0,
(0, 0, 0, 1): 0.0,
(0, 0, 0, 2): 0.0,
(0, 0, 0, 3): 0.0,
(0, 0, 0, 4): 0.0,
(0, 0, 1, 0): 0.0,
...
(1, 2, 3, 0): 0.0,
(1, 2, 3, 1): 0.0,
(1, 2, 3, 2): 0.0,
(1, 2, 3, 3): 0.0,
(1, 2, 3, 4): 0.0}
>>> mdarray[(0, 1, 2, 3)]
0.0
>>> mdarray[(0, 1, 2, 3)] = 6.78
>>> mdarray[(0, 1, 2, 3)]
6.78
>>> mdarray[(0, 1, 2, 3)] = 5.4321
>>> mdarray[(0, 1, 2, 3)]
5.4321
>>> pp(mdarray)
{(0, 0, 0, 0): 0.0,
(0, 0, 0, 1): 0.0,
(0, 0, 0, 2): 0.0,
...
(0, 1, 2, 2): 0.0,
(0, 1, 2, 3): 5.4321,
(0, 1, 2, 4): 0.0,
...
(1, 2, 3, 3): 0.0,
(1, 2, 3, 4): 0.0}
>>> |
http://rosettacode.org/wiki/Multiplication_tables | Multiplication tables | Task
Produce a formatted 12×12 multiplication table of the kind memorized by rote when in primary (or elementary) school.
Only print the top half triangle of products.
| #ALGOL_W | ALGOL W | begin
% print a school style multiplication table %
i_w := 3; s_w := 0; % set output formating %
write( " " );
for i := 1 until 12 do writeon( " ", i );
write( " +" );
for i := 1 until 12 do writeon( "----" );
for i := 1 until 12 do begin
write( i, "|" );
for j := 1 until i - 1 do writeon( " " );
for j := i until 12 do writeon( " ", i * j );
end;
end. |
http://rosettacode.org/wiki/Multiple_regression | Multiple regression | Task
Given a set of data vectors in the following format:
y
=
{
y
1
,
y
2
,
.
.
.
,
y
n
}
{\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
X
i
=
{
x
i
1
,
x
i
2
,
.
.
.
,
x
i
n
}
,
i
∈
1..
k
{\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
Compute the vector
β
=
{
β
1
,
β
2
,
.
.
.
,
β
k
}
{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}
using ordinary least squares regression using the following equation:
y
j
=
Σ
i
β
i
⋅
x
i
j
,
j
∈
1..
n
{\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
You can assume y is given to you as a vector (a one-dimensional array), and X is given to you as a two-dimensional array (i.e. matrix).
| #PARI.2FGP | PARI/GP | pseudoinv(M)=my(sz=matsize(M),T=conj(M))~;if(sz[1]<sz[2],T/(M*T),(T*M)^-1*T)
addhelp(pseudoinv, "pseudoinv(M): Moore pseudoinverse of the matrix M.");
y*pseudoinv(X) |
http://rosettacode.org/wiki/Multifactorial | Multifactorial | The factorial of a number, written as
n
!
{\displaystyle n!}
, is defined as
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
.
Multifactorials generalize factorials as follows:
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.
{\displaystyle n!!=n(n-2)(n-4)...}
n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.
{\displaystyle n!!!=n(n-3)(n-6)...}
n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.
{\displaystyle n!!!!=n(n-4)(n-8)...}
n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.
{\displaystyle n!!!!!=n(n-5)(n-10)...}
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
| #Factor | Factor | USING: formatting io kernel math math.ranges prettyprint
sequences ;
IN: rosetta-code.multifactorial
: multifactorial ( n degree -- m )
neg 1 swap <range> product ;
: mf-row ( degree -- )
dup "Degree %d: " printf
10 [1,b] [ swap multifactorial pprint bl ] with each ;
: main ( -- )
5 [1,b] [ mf-row nl ] each ;
MAIN: main |
http://rosettacode.org/wiki/Multifactorial | Multifactorial | The factorial of a number, written as
n
!
{\displaystyle n!}
, is defined as
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
.
Multifactorials generalize factorials as follows:
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.
{\displaystyle n!!=n(n-2)(n-4)...}
n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.
{\displaystyle n!!!=n(n-3)(n-6)...}
n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.
{\displaystyle n!!!!=n(n-4)(n-8)...}
n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.
{\displaystyle n!!!!!=n(n-5)(n-10)...}
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
| #Forth | Forth | : !n negate swap 1 dup rot do i * over +loop nip ;
: test cr 6 1 ?do 11 1 ?do i j !n . loop cr loop ; |
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #Lingo | Lingo | put _mouse.mouseLoc
-- point(310, 199) |
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #xTalk | xTalk |
-- Method 1:
-- this script in either the stack script or the card script to get position relative to the current stack window
on mouseMove pMouseH,pMouseV
put pMouseH,pMouse
end mouseMove
-- Method 2:
-- this script can go anywhere to get current position relative to the current stack window
put mouseLoc()
-- Method 3:
-- this script can go anywhere to get current position relative to the current stack window
put the mouseLoc
-- Method 4:
-- this script can go anywhere to get current position relative to the current window
put the mouseH &","& the mouseV
To get the mousePosition relative to the current screen instead of relative to the current stack window use the screenMouseLoc keyword
example results:
117,394 -- relative to current window
117,394 -- relative to current window
117,394 -- relative to current window
148,521 -- relative to current screen
|
http://rosettacode.org/wiki/N-queens_problem | N-queens problem |
Solve the eight queens puzzle.
You can extend the problem to solve the puzzle with a board of size NxN.
For the number of solutions for small values of N, see OEIS: A000170.
Related tasks
A* search algorithm
Solve a Hidato puzzle
Solve a Holy Knight's tour
Knight's tour
Peaceful chess queen armies
Solve a Hopido puzzle
Solve a Numbrix puzzle
Solve the no connection puzzle
| #Groovy | Groovy | def listOrder = { a, b ->
def k = [a.size(), b.size()].min()
def i = (0..<k).find { a[it] != b[it] }
(i != null) ? a[i] <=> b[i] : a.size() <=> b.size()
}
def orderedPermutations = { list ->
def n = list.size()
(0..<n).permutations().sort(listOrder)
}
def diagonalSafe = { list ->
def n = list.size()
n == 1 || (0..<(n-1)).every{ i ->
((i+1)..<n).every{ j ->
!([list[i]+j-i, list[i]+i-j].contains(list[j]))
}
}
}
def queensDistinctSolutions = { n ->
// each permutation is an N-Rooks solution
orderedPermutations((0..<n)).findAll (diagonalSafe)
} |
http://rosettacode.org/wiki/Nth_root | Nth root | Task
Implement the algorithm to compute the principal nth root
A
n
{\displaystyle {\sqrt[{n}]{A}}}
of a positive real number A, as explained at the Wikipedia page.
| #VBA | VBA | Private Function nth_root(y As Double, n As Double)
Dim eps As Double: eps = 0.00000000000001 '-- relative accuracy
Dim x As Variant: x = 1
Do While True
d = (y / x ^ (n - 1) - x) / n
x = x + d
e = eps * x '-- absolute accuracy
If d > -e And d < e Then
Exit Do
End If
Loop
Debug.Print y; n; x; y ^ (1 / n)
End Function
Public Sub main()
nth_root 1024, 10
nth_root 27, 3
nth_root 2, 2
nth_root 5642, 125
nth_root 7, 0.5
nth_root 4913, 3
nth_root 8, 3
nth_root 16, 2
nth_root 16, 4
nth_root 125, 3
nth_root 1000000000, 3
nth_root 1000000000, 9
End Sub |
http://rosettacode.org/wiki/N%27th | N'th | Write a function/method/subroutine/... that when given an integer greater than or equal to zero returns a string of the number followed by an apostrophe then the ordinal suffix.
Example
Returns would include 1'st 2'nd 3'rd 11'th 111'th 1001'st 1012'th
Task
Use your routine to show here the output for at least the following (inclusive) ranges of integer inputs:
0..25, 250..265, 1000..1025
Note: apostrophes are now optional to allow correct apostrophe-less English.
| #Oforth | Oforth | : nth(n)
| r |
n "th" over 10 mod ->r
r 1 == ifTrue: [ n 100 mod 11 == ifFalse: [ drop "st" ] ]
r 2 == ifTrue: [ n 100 mod 12 == ifFalse: [ drop "nd" ] ]
r 3 == ifTrue: [ n 100 mod 13 == ifFalse: [ drop "rd" ] ]
+ ; |
http://rosettacode.org/wiki/Munchausen_numbers | Munchausen numbers | A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.
(Munchausen is also spelled: Münchhausen.)
For instance: 3435 = 33 + 44 + 33 + 55
Task
Find all Munchausen numbers between 1 and 5000.
Also see
The OEIS entry: A046253
The Wikipedia entry: Perfect digit-to-digit invariant, redirected from Munchausen Number
| #PHP | PHP |
<?php
$pwr = array_fill(0, 10, 0);
function isMunchhausen($n)
{
global $pwr;
$sm = 0;
$temp = $n;
while ($temp) {
$sm= $sm + $pwr[($temp % 10)];
$temp = (int)($temp / 10);
}
return $sm == $n;
}
for ($i = 0; $i < 10; $i++) {
$pwr[$i] = pow((float)($i), (float)($i));
}
for ($i = 1; $i < 5000 + 1; $i++) {
if (isMunchhausen($i)) {
echo $i . PHP_EOL;
}
} |
http://rosettacode.org/wiki/Mutual_recursion | Mutual recursion | Two functions are said to be mutually recursive if the first calls the second,
and in turn the second calls the first.
Write two mutually recursive functions that compute members of the Hofstadter Female and Male sequences defined as:
F
(
0
)
=
1
;
M
(
0
)
=
0
F
(
n
)
=
n
−
M
(
F
(
n
−
1
)
)
,
n
>
0
M
(
n
)
=
n
−
F
(
M
(
n
−
1
)
)
,
n
>
0.
{\displaystyle {\begin{aligned}F(0)&=1\ ;\ M(0)=0\\F(n)&=n-M(F(n-1)),\quad n>0\\M(n)&=n-F(M(n-1)),\quad n>0.\end{aligned}}}
(If a language does not allow for a solution using mutually recursive functions
then state this rather than give a solution by other means).
| #Java | Java |
import java.util.HashMap;
import java.util.Map;
public class MutualRecursion {
public static void main(final String args[]) {
int max = 20;
System.out.printf("First %d values of the Female sequence: %n", max);
for (int i = 0; i < max; i++) {
System.out.printf(" f(%d) = %d%n", i, f(i));
}
System.out.printf("First %d values of the Male sequence: %n", max);
for (int i = 0; i < 20; i++) {
System.out.printf(" m(%d) = %d%n", i, m(i));
}
}
private static Map<Integer,Integer> F_MAP = new HashMap<>();
private static int f(final int n) {
if ( F_MAP.containsKey(n) ) {
return F_MAP.get(n);
}
int fn = n == 0 ? 1 : n - m(f(n - 1));
F_MAP.put(n, fn);
return fn;
}
private static Map<Integer,Integer> M_MAP = new HashMap<>();
private static int m(final int n) {
if ( M_MAP.containsKey(n) ) {
return M_MAP.get(n);
}
int mn = n == 0 ? 0 : n - f(m(n - 1));
M_MAP.put(n, mn);
return mn;
}
}
|
http://rosettacode.org/wiki/Multiple_distinct_objects | Multiple distinct objects | Create a sequence (array, list, whatever) consisting of n distinct, initialized items of the same type. n should be determined at runtime.
By distinct we mean that if they are mutable, changes to one do not affect all others; if there is an appropriate equality operator they are considered unequal; etc. The code need not specify a particular kind of distinction, but do not use e.g. a numeric-range generator which does not generalize.
By initialized we mean that each item must be in a well-defined state appropriate for its type, rather than e.g. arbitrary previous memory contents in an array allocation. Do not show only an initialization technique which initializes only to "zero" values (e.g. calloc() or int a[n] = {}; in C), unless user-defined types can provide definitions of "zero" for that type.
This task was inspired by the common error of intending to do this, but instead creating a sequence of n references to the same mutable object; it might be informative to show the way to do that as well, both as a negative example and as how to do it when that's all that's actually necessary.
This task is most relevant to languages operating in the pass-references-by-value style (most object-oriented, garbage-collected, and/or 'dynamic' languages).
See also: Closures/Value capture
| #zkl | zkl | n:=3;
n.pump(List) //-->L(0,1,2)
n.pump(List,List) //-->L(0,1,2), not expected
because the second list can be used to describe a calculation
n.pump(List,List(Void,List)) //--> L(L(),L(),L()) all same
List(Void,List) means returns List, which is a "known" value
n.pump(List,List.fpM("-")) //--> L(L(),L(),L()) all distinct
fpM is partial application: call List.create()
n.pump(List,(0.0).random.fp(1)) //--> 3 [0,1) randoms
L(0.902645,0.799657,0.0753809)
n.pump(String) //-->"012", default action is id function
class C{ var n; fcn init(x){n=x} }
n.pump(List,C) //--> L(C,C,C)
n.pump(List,C).apply("n") //-->L(0,1,2) ie all classes distinct |
http://rosettacode.org/wiki/Monads/Maybe_monad | Monads/Maybe monad | Demonstrate in your programming language the following:
Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
Compose the two functions with bind
A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.
A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.
| #F.23 | F# |
// We can use Some as return, Option.bind and the pipeline operator in order to have a very concise code
let f1 (v:int) = Some v // int -> Option<int>
let f2 (v:int) = Some(string v) // int -> Option<sting>
f1 4 |> Option.bind f2 |> printfn "Value is %A" // bind when option (maybe) has data
None |> Option.bind f2 |> printfn "Value is %A" // bind when option (maybe) does not have data
|
http://rosettacode.org/wiki/Monads/Maybe_monad | Monads/Maybe monad | Demonstrate in your programming language the following:
Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
Compose the two functions with bind
A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.
A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.
| #Factor | Factor | USING: monads ;
FROM: monads => do ;
! Prints "T{ just { value 7 } }"
3 maybe-monad return >>= [ 2 * maybe-monad return ] swap call
>>= [ 1 + maybe-monad return ] swap call .
! Prints "nothing"
nothing >>= [ 2 * maybe-monad return ] swap call
>>= [ 1 + maybe-monad return ] swap call . |
http://rosettacode.org/wiki/Monte_Carlo_methods | Monte Carlo methods | A Monte Carlo Simulation is a way of approximating the value of a function
where calculating the actual value is difficult or impossible.
It uses random sampling to define constraints on the value
and then makes a sort of "best guess."
A simple Monte Carlo Simulation can be used to calculate the value for
π
{\displaystyle \pi }
.
If you had a circle and a square where the length of a side of the square
was the same as the diameter of the circle, the ratio of the area of the circle
to the area of the square would be
π
/
4
{\displaystyle \pi /4}
.
So, if you put this circle inside the square and select many random points
inside the square, the number of points inside the circle
divided by the number of points inside the square and the circle
would be approximately
π
/
4
{\displaystyle \pi /4}
.
Task
Write a function to run a simulation like this, with a variable number of random points to select.
Also, show the results of a few different sample sizes.
For software where the number
π
{\displaystyle \pi }
is not built-in,
we give
π
{\displaystyle \pi }
as a number of digits:
3.141592653589793238462643383280
| #Arturo | Arturo | Pi: function [throws][
inside: new 0.0
do.times: throws [
if 1 > hypot random 0 1.0 random 0 1.0 -> inc 'inside
]
return 4 * inside / throws
]
loop [100 1000 10000 100000 1000000] 'n ->
print [pad to :string n 8 "=>" Pi n] |
http://rosettacode.org/wiki/Monte_Carlo_methods | Monte Carlo methods | A Monte Carlo Simulation is a way of approximating the value of a function
where calculating the actual value is difficult or impossible.
It uses random sampling to define constraints on the value
and then makes a sort of "best guess."
A simple Monte Carlo Simulation can be used to calculate the value for
π
{\displaystyle \pi }
.
If you had a circle and a square where the length of a side of the square
was the same as the diameter of the circle, the ratio of the area of the circle
to the area of the square would be
π
/
4
{\displaystyle \pi /4}
.
So, if you put this circle inside the square and select many random points
inside the square, the number of points inside the circle
divided by the number of points inside the square and the circle
would be approximately
π
/
4
{\displaystyle \pi /4}
.
Task
Write a function to run a simulation like this, with a variable number of random points to select.
Also, show the results of a few different sample sizes.
For software where the number
π
{\displaystyle \pi }
is not built-in,
we give
π
{\displaystyle \pi }
as a number of digits:
3.141592653589793238462643383280
| #AutoHotkey | AutoHotkey |
MsgBox % MontePi(10000) ; 3.154400
MsgBox % MontePi(100000) ; 3.142040
MsgBox % MontePi(1000000) ; 3.142096
MontePi(n) {
Loop %n% {
Random x, -1, 1.0
Random y, -1, 1.0
p += x*x+y*y < 1
}
Return 4*p/n
}
|
http://rosettacode.org/wiki/Move-to-front_algorithm | Move-to-front algorithm | Given a symbol table of a zero-indexed array of all possible input symbols
this algorithm reversibly transforms a sequence
of input symbols into an array of output numbers (indices).
The transform in many cases acts to give frequently repeated input symbols
lower indices which is useful in some compression algorithms.
Encoding algorithm
for each symbol of the input sequence:
output the index of the symbol in the symbol table
move that symbol to the front of the symbol table
Decoding algorithm
# Using the same starting symbol table
for each index of the input sequence:
output the symbol at that index of the symbol table
move that symbol to the front of the symbol table
Example
Encoding the string of character symbols 'broood' using a symbol table of the lowercase characters a-to-z
Input
Output
SymbolTable
broood
1
'abcdefghijklmnopqrstuvwxyz'
broood
1 17
'bacdefghijklmnopqrstuvwxyz'
broood
1 17 15
'rbacdefghijklmnopqstuvwxyz'
broood
1 17 15 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0 5
'orbacdefghijklmnpqstuvwxyz'
Decoding the indices back to the original symbol order:
Input
Output
SymbolTable
1 17 15 0 0 5
b
'abcdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
br
'bacdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
bro
'rbacdefghijklmnopqstuvwxyz'
1 17 15 0 0 5
broo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
brooo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
broood
'orbacdefghijklmnpqstuvwxyz'
Task
Encode and decode the following three strings of characters using the symbol table of the lowercase characters a-to-z as above.
Show the strings and their encoding here.
Add a check to ensure that the decoded string is the same as the original.
The strings are:
broood
bananaaa
hiphophiphop
(Note the misspellings in the above strings.)
| #jq | jq | # Input is the string to be encoded, st is the initial symbol table (an array)
# Output: the encoded string (an array)
def m2f_encode(st):
reduce explode[] as $ch
( [ [], st]; # state: [ans, st]
(.[1]|index($ch)) as $ix
| .[1] as $st
| [ (.[0] + [ $ix ]), [$st[$ix]] + $st[0:$ix] + $st[$ix+1:] ] )
| .[0];
# Input should be the encoded string (an array)
# and st should be the initial symbol table (an array)
def m2f_decode(st):
reduce .[] as $ix
( [ [], st]; # state: [ans, st]
.[1] as $st
| [ (.[0] + [ $st[$ix] ]), [$st[$ix]] + $st[0:$ix] + $st[$ix+1:] ] )
| .[0]
| implode; |
http://rosettacode.org/wiki/Move-to-front_algorithm | Move-to-front algorithm | Given a symbol table of a zero-indexed array of all possible input symbols
this algorithm reversibly transforms a sequence
of input symbols into an array of output numbers (indices).
The transform in many cases acts to give frequently repeated input symbols
lower indices which is useful in some compression algorithms.
Encoding algorithm
for each symbol of the input sequence:
output the index of the symbol in the symbol table
move that symbol to the front of the symbol table
Decoding algorithm
# Using the same starting symbol table
for each index of the input sequence:
output the symbol at that index of the symbol table
move that symbol to the front of the symbol table
Example
Encoding the string of character symbols 'broood' using a symbol table of the lowercase characters a-to-z
Input
Output
SymbolTable
broood
1
'abcdefghijklmnopqrstuvwxyz'
broood
1 17
'bacdefghijklmnopqrstuvwxyz'
broood
1 17 15
'rbacdefghijklmnopqstuvwxyz'
broood
1 17 15 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0 5
'orbacdefghijklmnpqstuvwxyz'
Decoding the indices back to the original symbol order:
Input
Output
SymbolTable
1 17 15 0 0 5
b
'abcdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
br
'bacdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
bro
'rbacdefghijklmnopqstuvwxyz'
1 17 15 0 0 5
broo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
brooo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
broood
'orbacdefghijklmnpqstuvwxyz'
Task
Encode and decode the following three strings of characters using the symbol table of the lowercase characters a-to-z as above.
Show the strings and their encoding here.
Add a check to ensure that the decoded string is the same as the original.
The strings are:
broood
bananaaa
hiphophiphop
(Note the misspellings in the above strings.)
| #Julia | Julia | function encodeMTF(str::AbstractString, symtable::Vector{Char}=collect('a':'z'))
function encode(ch::Char)
r = findfirst(symtable, ch)
deleteat!(symtable, r)
prepend!(symtable, ch)
return r
end
collect(encode(ch) for ch in str)
end
function decodeMTF(arr::Vector{Int}, symtable::Vector{Char}=collect('a':'z'))
function decode(i::Int)
r = symtable[i]
deleteat!(symtable, i)
prepend!(symtable, r)
return r
end
join(decode(i) for i in arr)
end
testset = ["broood", "bananaaa", "hiphophiphop"]
encoded = encodeMTF.(testset)
decoded = decodeMTF.(encoded)
for (str, enc, dec) in zip(testset, encoded, decoded)
println("Test string: $str\n -> Encoded: $enc\n -> Decoded: $dec")
end
using Base.Test
@testset "Decoded string equal to original" begin
for (str, dec) in zip(testset, decoded)
@test str == dec
end
end |
http://rosettacode.org/wiki/Morse_code | Morse code | Morse code
It has been in use for more than 175 years — longer than any other electronic encoding system.
Task
Send a string as audible Morse code to an audio device (e.g., the PC speaker).
As the standard Morse code does not contain all possible characters,
you may either ignore unknown characters in the file,
or indicate them somehow (e.g. with a different pitch).
| #Ada | Ada | package Morse is
type Symbols is (Nul, '-', '.', ' ');
-- Nul is the letter separator, space the word separator;
Dash : constant Symbols := '-';
Dot : constant Symbols := '.';
type Morse_Str is array (Positive range <>) of Symbols;
pragma Pack (Morse_Str);
function Convert (Input : String) return Morse_Str;
procedure Morsebeep (Input : Morse_Str);
private
subtype Reschars is Character range ' ' .. 'Z';
-- restricted set of characters from 16#20# to 16#60#
subtype Length is Natural range 1 .. 5;
subtype Codes is Morse_Str (Length);
-- using the current ITU standard with 5 signs
-- only alphanumeric characters are taken into consideration
type Codings is record
L : Length;
Code : Codes;
end record;
Table : constant array (Reschars) of Codings :=
('A' => (2, ".- "), 'B' => (4, "-... "), 'C' => (4, "-.-. "),
'D' => (3, "-.. "), 'E' => (1, ". "), 'F' => (4, "..-. "),
'G' => (3, "--. "), 'H' => (4, ".... "), 'I' => (2, ".. "),
'J' => (4, ".--- "), 'K' => (3, "-.- "), 'L' => (4, ".-.. "),
'M' => (2, "-- "), 'N' => (2, "-. "), 'O' => (3, "--- "),
'P' => (4, ".--. "), 'Q' => (4, "--.- "), 'R' => (3, ".-. "),
'S' => (3, "... "), 'T' => (1, "- "), 'U' => (3, "..- "),
'V' => (4, "...- "), 'W' => (3, ".-- "), 'X' => (4, "-..- "),
'Y' => (4, "-.-- "), 'Z' => (4, "--.. "), '1' => (5, ".----"),
'2' => (5, "..---"), '3' => (5, "...--"), '4' => (5, "....-"),
'5' => (5, "....."), '6' => (5, "-...."), '7' => (5, "--..."),
'8' => (5, "---.."), '9' => (5, "----."), '0' => (5, "-----"),
others => (1, " ")); -- Dummy => Other characters do not need code.
end Morse; |
http://rosettacode.org/wiki/Monty_Hall_problem | Monty Hall problem |
Suppose you're on a game show and you're given the choice of three doors.
Behind one door is a car; behind the others, goats.
The car and the goats were placed randomly behind the doors before the show.
Rules of the game
After you have chosen a door, the door remains closed for the time being.
The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it.
If both remaining doors have goats behind them, he chooses one randomly.
After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door.
Imagine that you chose Door 1 and the host opens Door 3, which has a goat.
He then asks you "Do you want to switch to Door Number 2?"
The question
Is it to your advantage to change your choice?
Note
The player may initially choose any of the three doors (not just Door 1), that the host opens a different door revealing a goat (not necessarily Door 3), and that he gives the player a second choice between the two remaining unopened doors.
Task
Run random simulations of the Monty Hall game. Show the effects of a strategy of the contestant always keeping his first guess so it can be contrasted with the strategy of the contestant always switching his guess.
Simulate at least a thousand games using three doors for each strategy and show the results in such a way as to make it easy to compare the effects of each strategy.
References
Stefan Krauss, X. T. Wang, "The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser.", Journal of Experimental Psychology: General, Vol 132(1), Mar 2003, 3-22 DOI: 10.1037/0096-3445.132.1.3
A YouTube video: Monty Hall Problem - Numberphile.
| #Ada | Ada | -- Monty Hall Game
with Ada.Text_Io; use Ada.Text_Io;
with Ada.Float_Text_Io; use Ada.Float_Text_Io;
with ada.Numerics.Discrete_Random;
procedure Monty_Stats is
Num_Iterations : Positive := 100000;
type Action_Type is (Stay, Switch);
type Prize_Type is (Goat, Pig, Car);
type Door_Index is range 1..3;
package Random_Prize is new Ada.Numerics.Discrete_Random(Door_Index);
use Random_Prize;
Seed : Generator;
Doors : array(Door_Index) of Prize_Type;
procedure Set_Prizes is
Prize_Index : Door_Index;
Booby_Prize : Prize_Type := Goat;
begin
Reset(Seed);
Prize_Index := Random(Seed);
Doors(Prize_Index) := Car;
for I in Doors'range loop
if I /= Prize_Index then
Doors(I) := Booby_Prize;
Booby_Prize := Prize_Type'Succ(Booby_Prize);
end if;
end loop;
end Set_Prizes;
function Play(Action : Action_Type) return Prize_Type is
Chosen : Door_Index := Random(Seed);
Monty : Door_Index;
begin
Set_Prizes;
for I in Doors'range loop
if I /= Chosen and Doors(I) /= Car then
Monty := I;
end if;
end loop;
if Action = Switch then
for I in Doors'range loop
if I /= Monty and I /= Chosen then
Chosen := I;
exit;
end if;
end loop;
end if;
return Doors(Chosen);
end Play;
Winners : Natural;
Pct : Float;
begin
Winners := 0;
for I in 1..Num_Iterations loop
if Play(Stay) = Car then
Winners := Winners + 1;
end if;
end loop;
Put("Stay : count" & Natural'Image(Winners) & " = ");
Pct := Float(Winners * 100) / Float(Num_Iterations);
Put(Item => Pct, Aft => 2, Exp => 0);
Put_Line("%");
Winners := 0;
for I in 1..Num_Iterations loop
if Play(Switch) = Car then
Winners := Winners + 1;
end if;
end loop;
Put("Switch : count" & Natural'Image(Winners) & " = ");
Pct := Float(Winners * 100) / Float(Num_Iterations);
Put(Item => Pct, Aft => 2, Exp => 0);
Put_Line("%");
end Monty_Stats; |
http://rosettacode.org/wiki/Modular_inverse | Modular inverse | From Wikipedia:
In modular arithmetic, the modular multiplicative inverse of an integer a modulo m is an integer x such that
a
x
≡
1
(
mod
m
)
.
{\displaystyle a\,x\equiv 1{\pmod {m}}.}
Or in other words, such that:
∃
k
∈
Z
,
a
x
=
1
+
k
m
{\displaystyle \exists k\in \mathbb {Z} ,\qquad a\,x=1+k\,m}
It can be shown that such an inverse exists if and only if a and m are coprime, but we will ignore this for this task.
Task
Either by implementing the algorithm, by using a dedicated library or by using a built-in function in
your language, compute the modular inverse of 42 modulo 2017.
| #Batch_File | Batch File | @echo off
setlocal enabledelayedexpansion
%== Calls the "function" ==%
call :ModInv 42 2017 result
echo !result!
call :ModInv 40 1 result
echo !result!
call :ModInv 52 -217 result
echo !result!
call :ModInv -486 217 result
echo !result!
call :ModInv 40 2018 result
echo !result!
pause>nul
exit /b 0
%== The "function" ==%
:ModInv
set a=%1
set b=%2
if !b! lss 0 (set /a b=-b)
if !a! lss 0 (set /a a=b - ^(-a %% b^))
set t=0&set nt=1&set r=!b!&set /a nr=a%%b
:while_loop
if !nr! neq 0 (
set /a q=r/nr
set /a tmp=nt
set /a nt=t - ^(q*nt^)
set /a t=tmp
set /a tmp=nr
set /a nr=r - ^(q*nr^)
set /a r=tmp
goto while_loop
)
if !r! gtr 1 (set %3=-1&goto :EOF)
if !t! lss 0 set /a t+=b
set %3=!t!
goto :EOF |
http://rosettacode.org/wiki/Monads/Writer_monad | Monads/Writer monad | The Writer monad is a programming design pattern which makes it possible to compose functions which return their result values paired with a log string. The final result of a composed function yields both a value, and a concatenation of the logs from each component function application.
Demonstrate in your programming language the following:
Construct a Writer monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that monad (or just use what the language already provides)
Write three simple functions: root, addOne, and half
Derive Writer monad versions of each of these functions
Apply a composition of the Writer versions of root, addOne, and half to the integer 5, deriving both a value for the Golden Ratio φ, and a concatenated log of the function applications (starting with the initial value, and followed by the application of root, etc.) | #Phix | Phix | with javascript_semantics
function bind(object m, integer f)
return f(m)
end function
function unit(object m)
return m
end function
function root(sequence al)
{atom a, string lg} = al
atom res = sqrt(a)
return {res,lg&sprintf("took root: %f -> %f\n",{a,res})}
end function
function addOne(sequence al)
{atom a, string lg} = al
atom res = a + 1
return {res,lg&sprintf("added one: %f -> %f\n",{a,res})}
end function
function half(sequence al)
{atom a, string lg} = al
atom res = a / 2
return {res,lg&sprintf("halved it: %f -> %f\n",{a,res})}
end function
printf(1,"%f obtained by\n%s", bind(bind(bind({5,""},root),addOne),half))
|
http://rosettacode.org/wiki/Monads/List_monad | Monads/List monad | A Monad is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as eta and mu, but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of concat and map, which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
Construct a List Monad by writing the 'bind' function and the 'pure' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
Compose the two functions with bind | #Perl | Perl | use strict;
use feature 'say';
use Data::Monad::List;
# Cartesian product to 'count' in binary
my @cartesian = [(
list_flat_map_multi { scalar_list(join '', @_) }
scalar_list(0..1),
scalar_list(0..1),
scalar_list(0..1)
)->scalars];
say join "\n", @{shift @cartesian};
say '';
# Pythagorean triples
my @triples = [(
list_flat_map_multi { scalar_list(
{ $_[0] < $_[1] && $_[0]**2+$_[1]**2 == $_[2]**2 ? join(',',@_) : () }
) }
scalar_list(1..10),
scalar_list(1..10),
scalar_list(1..10)
)->scalars];
for (@{shift @triples}) {
say keys %$_ if keys %$_;
} |
http://rosettacode.org/wiki/Multi-dimensional_array | Multi-dimensional array | For the purposes of this task, the actual memory layout or access method of this data structure is not mandated.
It is enough to:
State the number and extent of each index to the array.
Provide specific, ordered, integer indices for all dimensions of the array together with a new value to update the indexed value.
Provide specific, ordered, numeric indices for all dimensions of the array to obtain the arrays value at that indexed position.
Task
State if the language supports multi-dimensional arrays in its syntax and usual implementation.
State whether the language uses row-major or column major order for multi-dimensional array storage, or any other relevant kind of storage.
Show how to create a four dimensional array in your language and set, access, set to another value; and access the new value of an integer-indexed item of the array.
The idiomatic method for the language is preferred.
The array should allow a range of five, four, three and two (or two three four five if convenient), in each of the indices, in order. (For example, if indexing starts at zero for the first index then a range of 0..4 inclusive would suffice).
State if memory allocation is optimised for the array - especially if contiguous memory is likely to be allocated.
If the language has exceptional native multi-dimensional array support such as optional bounds checking, reshaping, or being able to state both the lower and upper bounds of index ranges, then this is the task to mention them.
Show all output here, (but you may judiciously use ellipses to shorten repetitive output text).
| #Racket | Racket | # Raku supports multi dimension arrays natively. There are no arbitrary limits on the number of dimensions or maximum indices. Theoretically, you could have an infinite number of dimensions of infinite length, though in practice more than a few dozen dimensions gets unwieldy. An infinite maximum index is a fairly common idiom though. You can assign an infinite lazy list to an array and it will only produce the values when they are accessed.
my @integers = 1 .. Inf; # an infinite array containing all positive integers
say @integers[100000]; #100001 (arrays are zero indexed.)
# Multi dimension arrays may be predeclared which constrains the indices to the declared size:
my @dim5[3,3,3,3,3];
#Creates a preallocated 5 dimensional array where each branch has 3 storage slots and constrains the size to the declared size.
#It can then be accessed like so:
@dim5[0;1;2;1;0] = 'Raku';
say @dim5[0;1;2;1;0]; # prints 'Raku'
#@dim5[0;1;2;1;4] = 'error'; # runtime error: Index 4 for dimension 5 out of range (must be 0..2)
# Note that the dimensions do not _need_ to be predeclared / allocated. Raku will auto-vivify the necessary storage slots on first access.
my @a2;
@a2[0;1;2;1;0] = 'Raku';
@a2[0;1;2;1;4] = 'not an error';
# It is easy to access array "slices" in Raku.
my @b = map { [$_ X~ 1..5] }, <a b c d>;
.say for @b;
# [a1 a2 a3 a4 a5]
# [b1 b2 b3 b4 b5]
# [c1 c2 c3 c4 c5]
# [d1 d2 d3 d4 d5]
say @b[*;2]; # Get the all of the values in the third "column"
# (a3 b3 c3 d3)
# By default, Raku can store any object in an array, and it is not very compact. You can constrain the type of values that may be stored which can allow the optimizer to store them much more efficiently.
my @c = 1 .. 10; # Stores integers, but not very compactly since there are no constraints on what the values _may_ be
my uint16 @d = 1 .. 10 # Since there are and only can be unsigned 16 bit integers, the optimizer will use a much more compact memory layout.
# Indices must be a positive integer. Negative indices are not permitted, fractional indices will be truncated to an integer. |
http://rosettacode.org/wiki/Multiplication_tables | Multiplication tables | Task
Produce a formatted 12×12 multiplication table of the kind memorized by rote when in primary (or elementary) school.
Only print the top half triangle of products.
| #AppleScript | AppleScript | set n to 12 -- Size of table.
repeat with x from 0 to n
if x = 0 then set {table, x} to {{return}, -1}
repeat with y from 0 to n
if y's contents = 0 then
if x > 0 then set row to {f(x)}
if x = -1 then set {row, x} to {{f("x")}, 1}
else
if y ≥ x then set end of row to f(x * y)
if y < x then set end of row to f("")
end if
end repeat
set end of table to row & return
end repeat
return table as string
-- Handler/Function for formatting fixed width integer string.
on f(x)
set text item delimiters to ""
return (characters -4 thru -1 of (" " & x)) as string
end f |
http://rosettacode.org/wiki/Multiple_regression | Multiple regression | Task
Given a set of data vectors in the following format:
y
=
{
y
1
,
y
2
,
.
.
.
,
y
n
}
{\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
X
i
=
{
x
i
1
,
x
i
2
,
.
.
.
,
x
i
n
}
,
i
∈
1..
k
{\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
Compute the vector
β
=
{
β
1
,
β
2
,
.
.
.
,
β
k
}
{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}
using ordinary least squares regression using the following equation:
y
j
=
Σ
i
β
i
⋅
x
i
j
,
j
∈
1..
n
{\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
You can assume y is given to you as a vector (a one-dimensional array), and X is given to you as a two-dimensional array (i.e. matrix).
| #Perl | Perl | use strict;
use warnings;
use Statistics::Regression;
my @y = (52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46);
my @x = ( 1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83);
my @model = ('const', 'X', 'X**2');
my $reg = Statistics::Regression->new( '', [@model] );
$reg->include( $y[$_], [ 1.0, $x[$_], $x[$_]**2 ]) for 0..@y-1;
my @coeff = $reg->theta();
printf "%-6s %8.3f\n", $model[$_], $coeff[$_] for 0..@model-1; |
http://rosettacode.org/wiki/Multifactorial | Multifactorial | The factorial of a number, written as
n
!
{\displaystyle n!}
, is defined as
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
.
Multifactorials generalize factorials as follows:
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.
{\displaystyle n!!=n(n-2)(n-4)...}
n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.
{\displaystyle n!!!=n(n-3)(n-6)...}
n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.
{\displaystyle n!!!!=n(n-4)(n-8)...}
n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.
{\displaystyle n!!!!!=n(n-5)(n-10)...}
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
| #Fortran | Fortran | program test
implicit none
integer :: i, j, n
do i = 1, 5
write(*, "(a, i0, a)", advance = "no") "Degree ", i, ": "
do j = 1, 10
n = multifactorial(j, i)
write(*, "(i0, 1x)", advance = "no") n
end do
write(*,*)
end do
contains
function multifactorial (range, degree)
integer :: multifactorial, range, degree
integer :: k
multifactorial = product((/(k, k=range, 1, -degree)/))
end function multifactorial
end program test |
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #LiveCode_Builder | LiveCode Builder |
LiveCode Builder (LCB) is a slightly lower level, strictly typed variant of LiveCode Script (LCS) used for making add-on extensions to LiveCode Script
-- results will be a point array struct like [117.0000,394.0000] relative to the current widget's view port
use com.livecode.widget -- include the required module
--- in your handler:
variable tPosition as Point -- type declaration, tPosition is a point array struct
put the mouse position into tPosition
variable tRect as Rectangle -- type declaration, tRect is a rect array struct, something like [0,1024,0,768]
put my bounds into tRect
if tPosition is within tRect then
log "mouse position is within the widget bounds"
end if
|
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #Logo | Logo | show mousepos ; [-250 250] |
http://rosettacode.org/wiki/N-queens_problem | N-queens problem |
Solve the eight queens puzzle.
You can extend the problem to solve the puzzle with a board of size NxN.
For the number of solutions for small values of N, see OEIS: A000170.
Related tasks
A* search algorithm
Solve a Hidato puzzle
Solve a Holy Knight's tour
Knight's tour
Peaceful chess queen armies
Solve a Hopido puzzle
Solve a Numbrix puzzle
Solve the no connection puzzle
| #Haskell | Haskell | import Control.Monad
import Data.List
-- given n, "queens n" solves the n-queens problem, returning a list of all the
-- safe arrangements. each solution is a list of the columns where the queens are
-- located for each row
queens :: Int -> [[Int]]
queens n = map fst $ foldM oneMoreQueen ([],[1..n]) [1..n] where
-- foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
-- foldM folds (from left to right) in the list monad, which is convenient for
-- "nondeterminstically" finding "all possible solutions" of something. the
-- initial value [] corresponds to the only safe arrangement of queens in 0 rows
-- given a safe arrangement y of queens in the first i rows, and a list of
-- possible choices, "oneMoreQueen y _" returns a list of all the safe
-- arrangements of queens in the first (i+1) rows along with remaining choices
oneMoreQueen (y,d) _ = [(x:y, delete x d) | x <- d, safe x] where
-- "safe x" tests whether a queen at column x is safe from previous queens
safe x = and [x /= c + n && x /= c - n | (n,c) <- zip [1..] y]
-- prints what the board looks like for a solution; with an extra newline
printSolution y = do
let n = length y
mapM_ (\x -> putStrLn [if z == x then 'Q' else '.' | z <- [1..n]]) y
putStrLn ""
-- prints all the solutions for 6 queens
main = mapM_ printSolution $ queens 6 |
http://rosettacode.org/wiki/Nth_root | Nth root | Task
Implement the algorithm to compute the principal nth root
A
n
{\displaystyle {\sqrt[{n}]{A}}}
of a positive real number A, as explained at the Wikipedia page.
| #Wren | Wren | var nthRoot = Fn.new { |x, n|
if (n < 2) Fiber.abort("n must be more than 1")
if (x <= 0) Fiber.abort("x must be positive")
var np = n - 1
var iter = Fn.new { |g| (np*g + x/g.pow(np))/n }
var g1 = x
var g2 = iter.call(g1)
while (g1 != g2) {
g1 = iter.call(g1)
g2 = iter.call(iter.call(g2))
}
return g1
}
var trios = [ [1728, 3, 2], [1024, 10, 1], [2, 2, 5] ]
for (trio in trios) {
System.print("%(trio[0]) ^ 1/%(trio[1])%(" "*trio[2]) = %(nthRoot.call(trio[0], trio[1]))")
} |
http://rosettacode.org/wiki/N%27th | N'th | Write a function/method/subroutine/... that when given an integer greater than or equal to zero returns a string of the number followed by an apostrophe then the ordinal suffix.
Example
Returns would include 1'st 2'nd 3'rd 11'th 111'th 1001'st 1012'th
Task
Use your routine to show here the output for at least the following (inclusive) ranges of integer inputs:
0..25, 250..265, 1000..1025
Note: apostrophes are now optional to allow correct apostrophe-less English.
| #PARI.2FGP | PARI/GP | ordinal(n)=my(k=n%10,m=n%100); Str(n,if(m<21&&m>3,"th",k==1,"st",k==2,"nd",k==3,"rd","th"));
apply(ordinal, [0..25])
apply(ordinal, [250..265])
apply(ordinal, [1000..1025])
apply(ordinal, [111, 1012]) |
http://rosettacode.org/wiki/Munchausen_numbers | Munchausen numbers | A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.
(Munchausen is also spelled: Münchhausen.)
For instance: 3435 = 33 + 44 + 33 + 55
Task
Find all Munchausen numbers between 1 and 5000.
Also see
The OEIS entry: A046253
The Wikipedia entry: Perfect digit-to-digit invariant, redirected from Munchausen Number
| #Picat | Picat | go =>
println([N : N in 1..5000, munchhausen_number(N)]).
munchhausen_number(N) =>
N == sum([T : I in N.to_string(),II = I.to_int(), T = II**II]). |
http://rosettacode.org/wiki/Mutual_recursion | Mutual recursion | Two functions are said to be mutually recursive if the first calls the second,
and in turn the second calls the first.
Write two mutually recursive functions that compute members of the Hofstadter Female and Male sequences defined as:
F
(
0
)
=
1
;
M
(
0
)
=
0
F
(
n
)
=
n
−
M
(
F
(
n
−
1
)
)
,
n
>
0
M
(
n
)
=
n
−
F
(
M
(
n
−
1
)
)
,
n
>
0.
{\displaystyle {\begin{aligned}F(0)&=1\ ;\ M(0)=0\\F(n)&=n-M(F(n-1)),\quad n>0\\M(n)&=n-F(M(n-1)),\quad n>0.\end{aligned}}}
(If a language does not allow for a solution using mutually recursive functions
then state this rather than give a solution by other means).
| #JavaScript | JavaScript | function f(num) {
return (num === 0) ? 1 : num - m(f(num - 1));
}
function m(num) {
return (num === 0) ? 0 : num - f(m(num - 1));
}
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map(
function (x, i) { return m + i; }
);
}
var a = range(0, 19);
//return a new array of the results and join with commas to print
console.log(a.map(function (n) { return f(n); }).join(', '));
console.log(a.map(function (n) { return m(n); }).join(', ')); |
http://rosettacode.org/wiki/Monads/Maybe_monad | Monads/Maybe monad | Demonstrate in your programming language the following:
Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
Compose the two functions with bind
A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.
A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.
| #Go | Go | package main
import (
"fmt"
"strconv"
)
type maybe struct{ value *int }
func (m maybe) bind(f func(p *int) maybe) maybe {
return f(m.value)
}
func unit(p *int) maybe {
return maybe{p}
}
func decrement(p *int) maybe {
if p == nil {
return unit(nil)
} else {
q := *p - 1
return unit(&q)
}
}
func triple(p *int) maybe {
if p == nil {
return unit(nil)
} else {
q := (*p) * 3
return unit(&q)
}
}
func main() {
i, j, k := 3, 4, 5
for _, p := range []*int{&i, &j, nil, &k} {
m1 := unit(p)
m2 := m1.bind(decrement).bind(triple)
var s1, s2 string = "none", "none"
if m1.value != nil {
s1 = strconv.Itoa(*m1.value)
}
if m2.value != nil {
s2 = strconv.Itoa(*m2.value)
}
fmt.Printf("%4s -> %s\n", s1, s2)
}
} |
http://rosettacode.org/wiki/Monte_Carlo_methods | Monte Carlo methods | A Monte Carlo Simulation is a way of approximating the value of a function
where calculating the actual value is difficult or impossible.
It uses random sampling to define constraints on the value
and then makes a sort of "best guess."
A simple Monte Carlo Simulation can be used to calculate the value for
π
{\displaystyle \pi }
.
If you had a circle and a square where the length of a side of the square
was the same as the diameter of the circle, the ratio of the area of the circle
to the area of the square would be
π
/
4
{\displaystyle \pi /4}
.
So, if you put this circle inside the square and select many random points
inside the square, the number of points inside the circle
divided by the number of points inside the square and the circle
would be approximately
π
/
4
{\displaystyle \pi /4}
.
Task
Write a function to run a simulation like this, with a variable number of random points to select.
Also, show the results of a few different sample sizes.
For software where the number
π
{\displaystyle \pi }
is not built-in,
we give
π
{\displaystyle \pi }
as a number of digits:
3.141592653589793238462643383280
| #AWK | AWK |
# --- with command line argument "throws" ---
BEGIN{ th=ARGV[1];
for(i=0; i<th; i++) cin += (rand()^2 + rand()^2) < 1
printf("Pi = %8.5f\n",4*cin/th)
}
usage: awk -f pi 2300
Pi = 3.14333
|
http://rosettacode.org/wiki/Move-to-front_algorithm | Move-to-front algorithm | Given a symbol table of a zero-indexed array of all possible input symbols
this algorithm reversibly transforms a sequence
of input symbols into an array of output numbers (indices).
The transform in many cases acts to give frequently repeated input symbols
lower indices which is useful in some compression algorithms.
Encoding algorithm
for each symbol of the input sequence:
output the index of the symbol in the symbol table
move that symbol to the front of the symbol table
Decoding algorithm
# Using the same starting symbol table
for each index of the input sequence:
output the symbol at that index of the symbol table
move that symbol to the front of the symbol table
Example
Encoding the string of character symbols 'broood' using a symbol table of the lowercase characters a-to-z
Input
Output
SymbolTable
broood
1
'abcdefghijklmnopqrstuvwxyz'
broood
1 17
'bacdefghijklmnopqrstuvwxyz'
broood
1 17 15
'rbacdefghijklmnopqstuvwxyz'
broood
1 17 15 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0 5
'orbacdefghijklmnpqstuvwxyz'
Decoding the indices back to the original symbol order:
Input
Output
SymbolTable
1 17 15 0 0 5
b
'abcdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
br
'bacdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
bro
'rbacdefghijklmnopqstuvwxyz'
1 17 15 0 0 5
broo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
brooo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
broood
'orbacdefghijklmnpqstuvwxyz'
Task
Encode and decode the following three strings of characters using the symbol table of the lowercase characters a-to-z as above.
Show the strings and their encoding here.
Add a check to ensure that the decoded string is the same as the original.
The strings are:
broood
bananaaa
hiphophiphop
(Note the misspellings in the above strings.)
| #Kotlin | Kotlin | // version 1.1.2
fun encode(s: String): IntArray {
if (s.isEmpty()) return intArrayOf()
val symbols = "abcdefghijklmnopqrstuvwxyz".toCharArray()
val result = IntArray(s.length)
for ((i, c) in s.withIndex()) {
val index = symbols.indexOf(c)
if (index == -1)
throw IllegalArgumentException("$s contains a non-alphabetic character")
result[i] = index
if (index == 0) continue
for (j in index - 1 downTo 0) symbols[j + 1] = symbols[j]
symbols[0] = c
}
return result
}
fun decode(a: IntArray): String {
if (a.isEmpty()) return ""
val symbols = "abcdefghijklmnopqrstuvwxyz".toCharArray()
val result = CharArray(a.size)
for ((i, n) in a.withIndex()) {
if (n !in 0..25)
throw IllegalArgumentException("${a.contentToString()} contains an invalid number")
result[i] = symbols[n]
if (n == 0) continue
for (j in n - 1 downTo 0) symbols[j + 1] = symbols[j]
symbols[0] = result[i]
}
return result.joinToString("")
}
fun main(args: Array<String>) {
val strings = arrayOf("broood", "bananaaa", "hiphophiphop")
val encoded = Array<IntArray?>(strings.size) { null }
for ((i, s) in strings.withIndex()) {
encoded[i] = encode(s)
println("${s.padEnd(12)} -> ${encoded[i]!!.contentToString()}")
}
println()
val decoded = Array<String?>(encoded.size) { null }
for ((i, a) in encoded.withIndex()) {
decoded[i] = decode(a!!)
print("${a.contentToString().padEnd(38)} -> ${decoded[i]!!.padEnd(12)}")
println(" -> ${if (decoded[i] == strings[i]) "correct" else "incorrect"}")
}
} |
http://rosettacode.org/wiki/Morse_code | Morse code | Morse code
It has been in use for more than 175 years — longer than any other electronic encoding system.
Task
Send a string as audible Morse code to an audio device (e.g., the PC speaker).
As the standard Morse code does not contain all possible characters,
you may either ignore unknown characters in the file,
or indicate them somehow (e.g. with a different pitch).
| #AppleScript | AppleScript | use AppleScript version "2.4" -- OS X 10.10 (Yosemite) or later
use framework "Foundation"
use framework "AppKit"
on morseCode(msg)
script morse
-- Unit duration in seconds and sounds used.
property units : 0.075
property morseSound : current application's class "NSSound"'s soundNamed:("Glass")
property unknownCharacterSound : current application's class "NSSound"'s soundNamed:("Frog")
-- Unicode IDs of in-range but uncatered-for punctuation characters.
property unrecognisedPunctuation : {35, 37, 42, 60, 62, 91, 92, 93, 94}
-- Dits and dahs for recognised characters, in units.
property letters : {{1, 3}, {3, 1, 1, 1}, {3, 1, 3, 1}, {3, 1, 1}, {1}, {1, 1, 3, 1}, {3, 3, 1}, {1, 1, 1, 1}, {1, 1}, ¬
{1, 3, 3, 3}, {3, 1, 3}, {1, 3, 1, 1}, {3, 3}, {3, 1}, {3, 3, 3}, {1, 3, 3, 1}, {3, 3, 1, 3}, {1, 3, 1}, {1, 1, 1}, ¬
{3}, {1, 1, 3}, {1, 1, 1, 3}, {1, 3, 3}, {3, 1, 1, 3}, {3, 1, 3, 3}, {3, 3, 1, 1}}
property underscore : {1, 1, 3, 3, 1, 3}
property digitsAndPunctuation : {{3, 3, 3, 3, 3}, {1, 3, 3, 3, 3}, {1, 1, 3, 3, 3}, {1, 1, 1, 3, 3}, ¬
{1, 1, 1, 1, 3}, {1, 1, 1, 1, 1}, {3, 1, 1, 1, 1}, {3, 3, 1, 1, 1}, {3, 3, 3, 1, 1}, {3, 3, 3, 3, 1}, ¬
{3, 3, 3, 1, 1, 1}, {3, 1, 3, 1, 3, 1}, missing value, {3, 1, 1, 1, 3}, missing value, ¬
{1, 1, 3, 3, 1, 1}, {1, 3, 3, 1, 3, 1}}
property |punctuation| : {{3, 1, 3, 1, 3, 3}, {1, 3, 1, 1, 3, 1}, missing value, {1, 1, 1, 3, 1, 1, 3}, missing value, ¬
{1, 3, 1, 1, 1}, {1, 3, 3, 3, 3, 1}, {3, 1, 3, 3, 1}, {3, 1, 3, 3, 1, 3}, missing value, ¬
{1, 3, 1, 3, 1}, {3, 3, 1, 1, 3, 3}, {3, 1, 1, 1, 1, 3}, {1, 3, 1, 3, 1, 3}, {3, 1, 1, 3, 1}}
-- Unicode IDs of the message's characters.
property UnicodeIDs : (id of msg) as list
on sendCharacter(ditsAndDahs)
repeat with ditOrDah in ditsAndDahs
tell morseSound to play()
delay (ditOrDah * units)
tell morseSound to stop()
delay (1 * units)
end repeat
delay (2 * units) -- Previous 1 unit + 2 units = 3 units between characters.
end sendCharacter
on sendMessage()
-- Play an extremely short sound to ensure the sound system's awake for the first morse beep.
tell morse to sendCharacter({0})
-- Output the message.
repeat with i from 1 to (count UnicodeIDs)
set thisID to item i of my UnicodeIDs
if ((thisID > 122) or (thisID < 32) or (thisID is in unrecognisedPunctuation)) then
-- Character not catered for. Play alternative sound.
tell unknownCharacterSound to play()
delay (3 * units)
tell unknownCharacterSound to stop()
delay (3 * units)
else if ((thisID > 64) and ((thisID < 91) or (thisID > 96))) then -- English letter.
sendCharacter(item (thisID mod 32) of my letters)
else if (thisID is 95) then -- Underscore.
sendCharacter(underscore)
else if (thisID > 47) then -- Digit, colon, semicolon, equals, or question mark.
sendCharacter(item (thisID - 47) of my digitsAndPunctuation)
else if (thisID > 32) then -- Other recognised punctuation.
sendCharacter(item (thisID - 32) of my |punctuation|)
else -- Space.
delay (4 * units) -- Previous 3 units + 4 units = 7 units between "words".
end if
end repeat
end sendMessage
end script
tell morse to sendMessage()
end morseCode
-- Test code:
morseCode("Coded in AppleScrip†.") |
http://rosettacode.org/wiki/Monty_Hall_problem | Monty Hall problem |
Suppose you're on a game show and you're given the choice of three doors.
Behind one door is a car; behind the others, goats.
The car and the goats were placed randomly behind the doors before the show.
Rules of the game
After you have chosen a door, the door remains closed for the time being.
The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it.
If both remaining doors have goats behind them, he chooses one randomly.
After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door.
Imagine that you chose Door 1 and the host opens Door 3, which has a goat.
He then asks you "Do you want to switch to Door Number 2?"
The question
Is it to your advantage to change your choice?
Note
The player may initially choose any of the three doors (not just Door 1), that the host opens a different door revealing a goat (not necessarily Door 3), and that he gives the player a second choice between the two remaining unopened doors.
Task
Run random simulations of the Monty Hall game. Show the effects of a strategy of the contestant always keeping his first guess so it can be contrasted with the strategy of the contestant always switching his guess.
Simulate at least a thousand games using three doors for each strategy and show the results in such a way as to make it easy to compare the effects of each strategy.
References
Stefan Krauss, X. T. Wang, "The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser.", Journal of Experimental Psychology: General, Vol 132(1), Mar 2003, 3-22 DOI: 10.1037/0096-3445.132.1.3
A YouTube video: Monty Hall Problem - Numberphile.
| #ALGOL_68 | ALGOL 68 | INT trials=100 000;
PROC brand = (INT n)INT: 1 + ENTIER (n * random);
PROC percent = (REAL x)STRING: fixed(100.0*x/trials,0,2)+"%";
main:
(
INT prize, choice, show, not shown, new choice;
INT stay winning:=0, change winning:=0, random winning:=0;
INT doors = 3;
[doors-1]INT other door;
TO trials DO
# put the prize somewhere #
prize := brand(doors);
# let the user choose a door #
choice := brand(doors);
# let us take a list of unchoosen doors #
INT k := LWB other door;
FOR j TO doors DO
IF j/=choice THEN other door[k] := j; k+:=1 FI
OD;
# Monty opens one... #
IF choice = prize THEN
# staying the user will win... Monty opens a random port#
show := other door[ brand(doors - 1) ];
not shown := other door[ (show+1) MOD (doors - 1 ) + 1]
ELSE # no random, Monty can open just one door... #
IF other door[1] = prize THEN
show := other door[2];
not shown := other door[1]
ELSE
show := other door[1];
not shown := other door[2]
FI
FI;
# the user randomly choose one of the two closed doors
(one is his/her previous choice, the second is the
one not shown ) #
other door[1] := choice;
other door[2] := not shown;
new choice := other door[ brand(doors - 1) ];
# now let us count if it takes it or not #
IF choice = prize THEN stay winning+:=1 FI;
IF not shown = prize THEN change winning+:=1 FI;
IF new choice = prize THEN random winning+:=1 FI
OD;
print(("Staying: ", percent(stay winning), new line ));
print(("Changing: ", percent(change winning), new line ));
print(("New random choice: ", percent(random winning), new line ))
) |
http://rosettacode.org/wiki/Modular_inverse | Modular inverse | From Wikipedia:
In modular arithmetic, the modular multiplicative inverse of an integer a modulo m is an integer x such that
a
x
≡
1
(
mod
m
)
.
{\displaystyle a\,x\equiv 1{\pmod {m}}.}
Or in other words, such that:
∃
k
∈
Z
,
a
x
=
1
+
k
m
{\displaystyle \exists k\in \mathbb {Z} ,\qquad a\,x=1+k\,m}
It can be shown that such an inverse exists if and only if a and m are coprime, but we will ignore this for this task.
Task
Either by implementing the algorithm, by using a dedicated library or by using a built-in function in
your language, compute the modular inverse of 42 modulo 2017.
| #BCPL | BCPL | get "libhdr"
let mulinv(a, b) =
b<0 -> mulinv(a, -b),
a<0 -> mulinv(b - (-a rem b), b),
valof
$( let t, nt, r, nr = 0, 1, b, a rem b
until nr = 0
$( let tmp, q = ?, r / nr
tmp := nt ; nt := t - q*nt ; t := tmp
tmp := nr ; nr := r - q*nr ; r := tmp
$)
resultis r>1 -> -1,
t<0 -> t + b,
t
$)
let show(a, b) be
$( let mi = mulinv(a, b)
test mi>=0
do writef("%N, %N -> %N*N", a, b, mi)
or writef("%N, %N -> no inverse*N", a, b)
$)
let start() be
$( show(42, 2017)
show(40, 1)
show(52, -217)
show(-486, 217)
show(40, 2018)
$) |
http://rosettacode.org/wiki/Modular_inverse | Modular inverse | From Wikipedia:
In modular arithmetic, the modular multiplicative inverse of an integer a modulo m is an integer x such that
a
x
≡
1
(
mod
m
)
.
{\displaystyle a\,x\equiv 1{\pmod {m}}.}
Or in other words, such that:
∃
k
∈
Z
,
a
x
=
1
+
k
m
{\displaystyle \exists k\in \mathbb {Z} ,\qquad a\,x=1+k\,m}
It can be shown that such an inverse exists if and only if a and m are coprime, but we will ignore this for this task.
Task
Either by implementing the algorithm, by using a dedicated library or by using a built-in function in
your language, compute the modular inverse of 42 modulo 2017.
| #Bracmat | Bracmat | ( ( mod-inv
= a b b0 x0 x1 q
. !arg:(?a.?b)
& ( !b:1
| (!b.0.1):(?b0.?x0.?x1)
& whl
' ( !a:>1
& div$(!a.!b):?q
& (!b.mod$(!a.!b)):(?a.?b)
& (!x1+-1*!q*!x0.!x0):(?x0.?x1)
)
& (!x:>0|!x1+!b0)
)
)
& out$(mod-inv$(42.2017))
}; |
http://rosettacode.org/wiki/Monads/Writer_monad | Monads/Writer monad | The Writer monad is a programming design pattern which makes it possible to compose functions which return their result values paired with a log string. The final result of a composed function yields both a value, and a concatenation of the logs from each component function application.
Demonstrate in your programming language the following:
Construct a Writer monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that monad (or just use what the language already provides)
Write three simple functions: root, addOne, and half
Derive Writer monad versions of each of these functions
Apply a composition of the Writer versions of root, addOne, and half to the integer 5, deriving both a value for the Golden Ratio φ, and a concatenated log of the function applications (starting with the initial value, and followed by the application of root, etc.) | #PHP | PHP | class WriterMonad {
/** @var mixed */
private $value;
/** @var string[] */
private $logs;
private function __construct($value, array $logs = []) {
$this->value = $value;
$this->logs = $logs;
}
public static function unit($value, string $log): WriterMonad {
return new WriterMonad($value, ["{$log}: {$value}"]);
}
public function bind(callable $mapper): WriterMonad {
$mapped = $mapper($this->value);
assert($mapped instanceof WriterMonad);
return new WriterMonad($mapped->value, [...$this->logs, ...$mapped->logs]);
}
public function value() {
return $this->value;
}
public function logs(): array {
return $this->logs;
}
}
$root = fn(float $i): float => sqrt($i);
$addOne = fn(float $i): float => $i + 1;
$half = fn(float $i): float => $i / 2;
$m = fn (callable $callback, string $log): callable => fn ($value): WriterMonad => WriterMonad::unit($callback($value), $log);
$result = WriterMonad::unit(5, "Initial value")
->bind($m($root, "square root"))
->bind($m($addOne, "add one"))
->bind($m($half, "half"));
print "The Golden Ratio is: {$result->value()}\n";
print join("\n", $result->logs()); |
http://rosettacode.org/wiki/Monads/List_monad | Monads/List monad | A Monad is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as eta and mu, but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of concat and map, which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
Construct a List Monad by writing the 'bind' function and the 'pure' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
Compose the two functions with bind | #Phix | Phix | function bindf(sequence m, integer f)
return f(m)
end function
function unit(sequence m)
return m
end function
function increment(sequence l)
return unit(sq_add(l,1))
end function
function double(sequence l)
return unit(sq_mul(l,2))
end function
sequence m1 = unit({3, 4, 5}),
m2 = bindf(bindf(m1,increment),double)
printf(1,"%v -> %v\n", {m1, m2})
|
http://rosettacode.org/wiki/Monads/List_monad | Monads/List monad | A Monad is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as eta and mu, but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of concat and map, which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
Construct a List Monad by writing the 'bind' function and the 'pure' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
Compose the two functions with bind | #Python | Python | """A List Monad. Requires Python >= 3.7 for type hints."""
from __future__ import annotations
from itertools import chain
from typing import Any
from typing import Callable
from typing import Iterable
from typing import List
from typing import TypeVar
T = TypeVar("T")
class MList(List[T]):
@classmethod
def unit(cls, value: Iterable[T]) -> MList[T]:
return cls(value)
def bind(self, func: Callable[[T], MList[Any]]) -> MList[Any]:
return MList(chain.from_iterable(map(func, self)))
def __rshift__(self, func: Callable[[T], MList[Any]]) -> MList[Any]:
return self.bind(func)
if __name__ == "__main__":
# Chained int and string functions
print(
MList([1, 99, 4])
.bind(lambda val: MList([val + 1]))
.bind(lambda val: MList([f"${val}.00"]))
)
# Same, but using `>>` as the bind operator.
print(
MList([1, 99, 4])
>> (lambda val: MList([val + 1]))
>> (lambda val: MList([f"${val}.00"]))
)
# Cartesian product of [1..5] and [6..10]
print(
MList(range(1, 6)).bind(
lambda x: MList(range(6, 11)).bind(lambda y: MList([(x, y)]))
)
)
# Pythagorean triples with elements between 1 and 25
print(
MList(range(1, 26)).bind(
lambda x: MList(range(x + 1, 26)).bind(
lambda y: MList(range(y + 1, 26)).bind(
lambda z: MList([(x, y, z)])
if x * x + y * y == z * z
else MList([])
)
)
)
)
|
http://rosettacode.org/wiki/Multi-dimensional_array | Multi-dimensional array | For the purposes of this task, the actual memory layout or access method of this data structure is not mandated.
It is enough to:
State the number and extent of each index to the array.
Provide specific, ordered, integer indices for all dimensions of the array together with a new value to update the indexed value.
Provide specific, ordered, numeric indices for all dimensions of the array to obtain the arrays value at that indexed position.
Task
State if the language supports multi-dimensional arrays in its syntax and usual implementation.
State whether the language uses row-major or column major order for multi-dimensional array storage, or any other relevant kind of storage.
Show how to create a four dimensional array in your language and set, access, set to another value; and access the new value of an integer-indexed item of the array.
The idiomatic method for the language is preferred.
The array should allow a range of five, four, three and two (or two three four five if convenient), in each of the indices, in order. (For example, if indexing starts at zero for the first index then a range of 0..4 inclusive would suffice).
State if memory allocation is optimised for the array - especially if contiguous memory is likely to be allocated.
If the language has exceptional native multi-dimensional array support such as optional bounds checking, reshaping, or being able to state both the lower and upper bounds of index ranges, then this is the task to mention them.
Show all output here, (but you may judiciously use ellipses to shorten repetitive output text).
| #Raku | Raku | # Raku supports multi dimension arrays natively. There are no arbitrary limits on the number of dimensions or maximum indices. Theoretically, you could have an infinite number of dimensions of infinite length, though in practice more than a few dozen dimensions gets unwieldy. An infinite maximum index is a fairly common idiom though. You can assign an infinite lazy list to an array and it will only produce the values when they are accessed.
my @integers = 1 .. Inf; # an infinite array containing all positive integers
say @integers[100000]; #100001 (arrays are zero indexed.)
# Multi dimension arrays may be predeclared which constrains the indices to the declared size:
my @dim5[3,3,3,3,3];
#Creates a preallocated 5 dimensional array where each branch has 3 storage slots and constrains the size to the declared size.
#It can then be accessed like so:
@dim5[0;1;2;1;0] = 'Raku';
say @dim5[0;1;2;1;0]; # prints 'Raku'
#@dim5[0;1;2;1;4] = 'error'; # runtime error: Index 4 for dimension 5 out of range (must be 0..2)
# Note that the dimensions do not _need_ to be predeclared / allocated. Raku will auto-vivify the necessary storage slots on first access.
my @a2;
@a2[0;1;2;1;0] = 'Raku';
@a2[0;1;2;1;4] = 'not an error';
# It is easy to access array "slices" in Raku.
my @b = map { [$_ X~ 1..5] }, <a b c d>;
.say for @b;
# [a1 a2 a3 a4 a5]
# [b1 b2 b3 b4 b5]
# [c1 c2 c3 c4 c5]
# [d1 d2 d3 d4 d5]
say @b[*;2]; # Get the all of the values in the third "column"
# (a3 b3 c3 d3)
# By default, Raku can store any object in an array, and it is not very compact. You can constrain the type of values that may be stored which can allow the optimizer to store them much more efficiently.
my @c = 1 .. 10; # Stores integers, but not very compactly since there are no constraints on what the values _may_ be
my uint16 @d = 1 .. 10 # Since there are and only can be unsigned 16 bit integers, the optimizer will use a much more compact memory layout.
# Indices must be a positive integer. Negative indices are not permitted, fractional indices will be truncated to an integer. |
http://rosettacode.org/wiki/Multiplication_tables | Multiplication tables | Task
Produce a formatted 12×12 multiplication table of the kind memorized by rote when in primary (or elementary) school.
Only print the top half triangle of products.
| #ARM_Assembly | ARM Assembly |
/* ARM assembly Raspberry PI */
/* program multtable.s */
/************************************/
/* Constantes */
/************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
.equ MAXI, 12
/*********************************/
/* Initialized data */
/*********************************/
.data
sMessValeur: .fill 11, 1, ' ' @ size => 11
szCarriageReturn: .asciz "\n"
sBlanc1: .asciz " "
sBlanc2: .asciz " "
sBlanc3: .asciz " "
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
push {fp,lr} @ saves 2 registers
@ display first line
mov r4,#0
1: @ begin loop
mov r0,r4
ldr r1,iAdrsMessValeur @ display value
bl conversion10 @ call function
mov r2,#0 @ final zéro
strb r2,[r1,r0] @ on display value
ldr r0,iAdrsMessValeur
bl affichageMess @ display message
cmp r4,#10 @ one or two digit in résult
ldrgt r0,iAdrsBlanc2 @ two display two spaces
ldrle r0,iAdrsBlanc3 @ one display 3 spaces
bl affichageMess @ display message
add r4,#1 @ increment counter
cmp r4,#MAXI
ble 1b @ loop
ldr r0,iAdrszCarriageReturn
bl affichageMess @ display carriage return
mov r5,#1 @ line counter
2: @ begin loop lines
mov r0,r5 @ display column 1 with N° line
ldr r1,iAdrsMessValeur @ display value
bl conversion10 @ call function
mov r2,#0 @ final zéro
strb r2,[r1,r0]
ldr r0,iAdrsMessValeur
bl affichageMess @ display message
cmp r5,#10 @ one or two digit in N° line
ldrge r0,iAdrsBlanc2
ldrlt r0,iAdrsBlanc3
bl affichageMess
mov r4,#1 @ counter column
3: @ begin loop columns
mul r0,r4,r5 @ multiplication
mov r3,r0 @ save résult
ldr r1,iAdrsMessValeur @ display value
bl conversion10 @ call function
mov r2,#0
strb r2,[r1,r0]
ldr r0,iAdrsMessValeur
bl affichageMess @ display message
cmp r3,#100 @ 3 digits in résult ?
ldrge r0,iAdrsBlanc1 @ yes, display one space
bge 4f
cmp r3,#10 @ 2 digits in result
ldrge r0,iAdrsBlanc2 @ yes display 2 spaces
ldrlt r0,iAdrsBlanc3 @ no display 3 spaces
4:
bl affichageMess @ display message
add r4,#1 @ increment counter column
cmp r4,r5 @ < counter lines
ble 3b @ loop
ldr r0,iAdrszCarriageReturn
bl affichageMess @ display carriage return
add r5,#1 @ increment line counter
cmp r5,#MAXI @ MAXI ?
ble 2b @ loop
100: @ standard end of the program
mov r0, #0 @ return code
pop {fp,lr} @restaur 2 registers
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsBlanc1: .int sBlanc1
iAdrsBlanc2: .int sBlanc2
iAdrsBlanc3: .int sBlanc3
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr} @ save registres
mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call systeme
pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */
bx lr @ return
/******************************************************************/
/* Converting a register to a decimal unsigned */
/******************************************************************/
/* r0 contains value and r1 address area */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes */
.equ LGZONECAL, 10
conversion10:
push {r1-r4,lr} @ save registers
mov r3,r1
mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @unsigned r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48 @ digit
strb r1,[r3,r2] @ store digit on area
cmp r0,#0 @ stop if quotient = 0 */
subne r2,#1 @ else previous position
bne 1b @ and loop
@ and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
add r2,#1
add r4,#1
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4 @ result length
mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area
add r4,#1 @ next position
cmp r4,#LGZONECAL
ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres
bx lr @return
/***************************************************/
/* division par 10 unsigned */
/***************************************************/
/* r0 dividende */
/* r0 quotient */
/* r1 remainder */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0 @ save value
mov r3,#0xCCCD @ r3 <- magic_number lower
movt r3,#0xCCCC @ r3 <- magic_number upper
umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2 @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr @ leave function
|
http://rosettacode.org/wiki/Multiple_regression | Multiple regression | Task
Given a set of data vectors in the following format:
y
=
{
y
1
,
y
2
,
.
.
.
,
y
n
}
{\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
X
i
=
{
x
i
1
,
x
i
2
,
.
.
.
,
x
i
n
}
,
i
∈
1..
k
{\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
Compute the vector
β
=
{
β
1
,
β
2
,
.
.
.
,
β
k
}
{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}
using ordinary least squares regression using the following equation:
y
j
=
Σ
i
β
i
⋅
x
i
j
,
j
∈
1..
n
{\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
You can assume y is given to you as a vector (a one-dimensional array), and X is given to you as a two-dimensional array (i.e. matrix).
| #Phix | Phix | with javascript_semantics
constant N = 15, M=3
sequence x = {1.47,1.50,1.52,1.55,1.57,
1.60,1.63,1.65,1.68,1.70,
1.73,1.75,1.78,1.80,1.83},
y = {52.21,53.12,54.48,55.84,57.20,
58.57,59.93,61.29,63.11,64.47,
66.28,68.10,69.92,72.19,74.46},
s = repeat(0,N),
t = repeat(0,N),
a = repeat(repeat(0,M+1),M)
for k=1 to 2*M do
for i=1 to N do
s[k] += power(x[i],k-1)
if k<=M then t[k] += y[i]*power(x[i],k-1) end if
end for
end for
-- build linear system
for row=1 to M do
for col=1 to M do
a[row,col] = s[row+col-1]
end for
a[row,M+1] = t[row]
end for
puts(1,"Linear system coefficents:\n")
pp(a,{pp_Nest,1,pp_IntFmt,"%7.1f",pp_FltFmt,"%7.1f"})
for j=1 to M do
integer i = j
while a[i,j]=0 do i += 1 end while
if i=M+1 then
?"SINGULAR MATRIX !"
?9/0
end if
for k=1 to M+1 do
{a[j,k],a[i,k]} = {a[i,k],a[j,k]}
end for
atom Y = 1/a[j,j]
a[j] = sq_mul(a[j],Y)
for k=1 to M do
if k<>j then
Y=-a[k,j]
for m=1 to M+1 do
a[k,m] += Y*a[j,m]
end for
end if
end for
end for
puts(1,"Solutions:\n")
?columnize(a,M+1)[1]
|
http://rosettacode.org/wiki/Multifactorial | Multifactorial | The factorial of a number, written as
n
!
{\displaystyle n!}
, is defined as
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
.
Multifactorials generalize factorials as follows:
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.
{\displaystyle n!!=n(n-2)(n-4)...}
n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.
{\displaystyle n!!!=n(n-3)(n-6)...}
n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.
{\displaystyle n!!!!=n(n-4)(n-8)...}
n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.
{\displaystyle n!!!!!=n(n-5)(n-10)...}
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
| #FreeBASIC | FreeBASIC | ' FB 1.05.0 Win64
Function multiFactorial (n As UInteger, degree As Integer) As UInteger
If n < 2 Then Return 1
Var result = n
For i As Integer = n - degree To 2 Step -degree
result *= i
Next
Return result
End Function
For degree As Integer = 1 To 5
Print "Degree"; degree; " => ";
For n As Integer = 1 To 10
Print multiFactorial(n, degree); " ";
Next n
Print
Next degree
Print
Print "Press any key to quit"
Sleep |
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #M2000_Interpreter | M2000 Interpreter |
Module Checkit {
\\ works when console is the active window
\\ pressing right mouse button exit the loop
While mouse<>2
Print mouse.x, mouse.y
End While
\\ end of part one, now we make a form with title Form1 (same name as the variable name)
Declare Form1 Form
Layer Form1 {
window 16, 10000,8000 ' 16pt font at maximum 10000 twips x 8000 twips
cls #335522, 1 \\ from 2nd line start the split screen (for form's layer)
pen 15 ' white
}
Function Form1.MouseMove {
Read new button, shift, x, y ' we use new because call is local, same scope as Checkit.
Layer Form1 {
print x, y, button
refresh
}
}
Function Form1.MouseDown {
Read new button, shift, x, y
\\ when we press mouse button we print in console
\\ but only the first time
print x, y, button
refresh
}
\\ open Form1 as modal window above console
Method Form1, "Show", 1
Declare Form1 Nothing
}
CheckIt
|
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | MousePosition["WindowAbsolute"] |
http://rosettacode.org/wiki/N-queens_problem | N-queens problem |
Solve the eight queens puzzle.
You can extend the problem to solve the puzzle with a board of size NxN.
For the number of solutions for small values of N, see OEIS: A000170.
Related tasks
A* search algorithm
Solve a Hidato puzzle
Solve a Holy Knight's tour
Knight's tour
Peaceful chess queen armies
Solve a Hopido puzzle
Solve a Numbrix puzzle
Solve the no connection puzzle
| #Heron | Heron | module NQueens {
inherits {
Heron.Windows.Console;
}
fields {
n : Int = 4;
sols : List = new List();
}
methods {
PosToString(row : Int, col : Int) : String {
return "row " + row.ToString() + ", col " + col.ToString();
}
AddQueen(b : Board, row : Int, col : Int)
{
if (!b.TryAddQueen(row, col))
return;
if (row < n - 1)
foreach (i in 0..n-1)
AddQueen(new Board(b), row + 1, i);
else
sols.Add(b);
}
Main() {
foreach (i in 0..n-1)
AddQueen(new Board(), 0, i);
foreach (b in sols) {
b.Output();
WriteLine("");
}
WriteLine("Found " + sols.Count().ToString() + " solutions");
}
}
}
class Board {
fields {
rows = new List();
}
methods {
Constructor() {
foreach (r in 0..n-1) {
var col = new List();
foreach (c in 0..n-1)
col.Add(false);
rows.Add(col);
}
}
Constructor(b : Board) {
Constructor();
foreach (r in 0..n-1)
foreach (c in 0..n-1)
SetSpaceOccupied(r, c, b.SpaceOccupied(r, c));
}
SpaceOccupied(row : Int, col : Int) : Bool {
return rows[row][col];
}
SetSpaceOccupied(row : Int, col : Int, b : Bool) {
rows[row][col] = b;
}
ValidPos(row : Int, col : Int) : Bool {
return ((row >= 0) && (row < n)) && ((col >= 0) && (col < n));
}
VectorOccupied(row : Int, col : Int, rowDir : Int, colDir : Int) : Bool {
var nextRow = row + rowDir;
var nextCol = col + colDir;
if (!ValidPos(nextRow, nextCol))
return false;
if (SpaceOccupied(nextRow, nextCol))
return true;
return VectorOccupied(nextRow, nextCol, rowDir, colDir);
}
TryAddQueen(row : Int, col : Int) : Bool {
foreach (rowDir in -1..1)
foreach (colDir in -1..1)
if (rowDir != 0 || colDir != 0)
if (VectorOccupied(row, col, rowDir, colDir))
return false;
SetSpaceOccupied(row, col, true);
return true;
}
Output() {
foreach (row in 0..n-1) {
foreach (col in 0..n-1) {
if (SpaceOccupied(row, col)) {
Write("Q");
}
else {
Write(".");
}
}
WriteLine("");
}
}
}
} |
http://rosettacode.org/wiki/Nth_root | Nth root | Task
Implement the algorithm to compute the principal nth root
A
n
{\displaystyle {\sqrt[{n}]{A}}}
of a positive real number A, as explained at the Wikipedia page.
| #XBS | XBS | func nthRoot(x,a){
send x^(1/a);
}{a=2};
log(nthRoot(8,3)); |
http://rosettacode.org/wiki/Nth_root | Nth root | Task
Implement the algorithm to compute the principal nth root
A
n
{\displaystyle {\sqrt[{n}]{A}}}
of a positive real number A, as explained at the Wikipedia page.
| #XPL0 | XPL0 | include c:\cxpl\stdlib;
func real NRoot(A, N); \Return the Nth root of A
real A, N;
real X, X0, Y;
int I;
[X:= 1.0; \initial guess
repeat X0:= X;
Y:= 1.0;
for I:= 1 to fix(N)-1 do Y:= Y*X0;
X:= ((N-1.0)*X0 + A/Y) / N;
until abs(X-X0) < 1.0E-15; \(until X=X0 doesn't always work)
return X;
];
[Format(5, 15);
RlOut(0, NRoot( 2., 2.)); CrLf(0);
RlOut(0, Power( 2., 0.5)); CrLf(0); \for comparison
RlOut(0, NRoot(27., 3.)); CrLf(0);
RlOut(0, NRoot(1024.,10.)); CrLf(0);
] |
http://rosettacode.org/wiki/N%27th | N'th | Write a function/method/subroutine/... that when given an integer greater than or equal to zero returns a string of the number followed by an apostrophe then the ordinal suffix.
Example
Returns would include 1'st 2'nd 3'rd 11'th 111'th 1001'st 1012'th
Task
Use your routine to show here the output for at least the following (inclusive) ranges of integer inputs:
0..25, 250..265, 1000..1025
Note: apostrophes are now optional to allow correct apostrophe-less English.
| #Pascal | Pascal | Program n_th;
function Suffix(N: NativeInt):AnsiString;
var
res: AnsiString;
begin
res:= 'th';
case N mod 10 of
1:IF N mod 100 <> 11 then
res:= 'st';
2:IF N mod 100 <> 12 then
res:= 'nd';
3:IF N mod 100 <> 13 then
res:= 'rd';
else
end;
Suffix := res;
end;
procedure Print_Images(loLim, HiLim: NativeInt);
var
i : NativeUint;
begin
for I := LoLim to HiLim do
write(i,Suffix(i),' ');
writeln;
end;
begin
Print_Images( 0, 25);
Print_Images( 250, 265);
Print_Images(1000, 1025);
end. |
http://rosettacode.org/wiki/Munchausen_numbers | Munchausen numbers | A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.
(Munchausen is also spelled: Münchhausen.)
For instance: 3435 = 33 + 44 + 33 + 55
Task
Find all Munchausen numbers between 1 and 5000.
Also see
The OEIS entry: A046253
The Wikipedia entry: Perfect digit-to-digit invariant, redirected from Munchausen Number
| #PicoLisp | PicoLisp | (for N 5000
(and
(=
N
(sum
'((N) (** N N))
(mapcar format (chop N)) ) )
(println N) ) ) |
http://rosettacode.org/wiki/Mutual_recursion | Mutual recursion | Two functions are said to be mutually recursive if the first calls the second,
and in turn the second calls the first.
Write two mutually recursive functions that compute members of the Hofstadter Female and Male sequences defined as:
F
(
0
)
=
1
;
M
(
0
)
=
0
F
(
n
)
=
n
−
M
(
F
(
n
−
1
)
)
,
n
>
0
M
(
n
)
=
n
−
F
(
M
(
n
−
1
)
)
,
n
>
0.
{\displaystyle {\begin{aligned}F(0)&=1\ ;\ M(0)=0\\F(n)&=n-M(F(n-1)),\quad n>0\\M(n)&=n-F(M(n-1)),\quad n>0.\end{aligned}}}
(If a language does not allow for a solution using mutually recursive functions
then state this rather than give a solution by other means).
| #jq | jq |
def M:
def F: if . == 0 then 1 else . - ((. - 1) | F | M) end;
if . == 0 then 0 else . - ((. - 1) | M | F) end;
def F:
if . == 0 then 1 else . - ((. - 1) | F | M) end; |
http://rosettacode.org/wiki/Monads/Maybe_monad | Monads/Maybe monad | Demonstrate in your programming language the following:
Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
Compose the two functions with bind
A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.
A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.
| #Haskell | Haskell | main = do print $ Just 3 >>= (return . (*2)) >>= (return . (+1)) -- prints "Just 7"
print $ Nothing >>= (return . (*2)) >>= (return . (+1)) -- prints "Nothing" |
http://rosettacode.org/wiki/Monads/Maybe_monad | Monads/Maybe monad | Demonstrate in your programming language the following:
Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
Compose the two functions with bind
A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.
A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.
| #Hoon | Hoon |
:- %say
|= [^ [[txt=(unit ,@tas) ~] ~]]
:- %noun
|^
%+ biff txt
;~ biff
m-parse
m-double
==
++ m-parse
|= a=@tas
^- (unit ,@ud)
(rust (trip a) dem)
::
++ m-double
|= a=@ud
^- (unit ,@ud)
(some (mul a 2))
--
|
http://rosettacode.org/wiki/Monte_Carlo_methods | Monte Carlo methods | A Monte Carlo Simulation is a way of approximating the value of a function
where calculating the actual value is difficult or impossible.
It uses random sampling to define constraints on the value
and then makes a sort of "best guess."
A simple Monte Carlo Simulation can be used to calculate the value for
π
{\displaystyle \pi }
.
If you had a circle and a square where the length of a side of the square
was the same as the diameter of the circle, the ratio of the area of the circle
to the area of the square would be
π
/
4
{\displaystyle \pi /4}
.
So, if you put this circle inside the square and select many random points
inside the square, the number of points inside the circle
divided by the number of points inside the square and the circle
would be approximately
π
/
4
{\displaystyle \pi /4}
.
Task
Write a function to run a simulation like this, with a variable number of random points to select.
Also, show the results of a few different sample sizes.
For software where the number
π
{\displaystyle \pi }
is not built-in,
we give
π
{\displaystyle \pi }
as a number of digits:
3.141592653589793238462643383280
| #BASIC | BASIC | DECLARE FUNCTION getPi! (throws!)
CLS
PRINT getPi(10000)
PRINT getPi(100000)
PRINT getPi(1000000)
PRINT getPi(10000000)
FUNCTION getPi (throws)
inCircle = 0
FOR i = 1 TO throws
'a square with a side of length 2 centered at 0 has
'x and y range of -1 to 1
randX = (RND * 2) - 1'range -1 to 1
randY = (RND * 2) - 1'range -1 to 1
'distance from (0,0) = sqrt((x-0)^2+(y-0)^2)
dist = SQR(randX ^ 2 + randY ^ 2)
IF dist < 1 THEN 'circle with diameter of 2 has radius of 1
inCircle = inCircle + 1
END IF
NEXT i
getPi = 4! * inCircle / throws
END FUNCTION |
http://rosettacode.org/wiki/Move-to-front_algorithm | Move-to-front algorithm | Given a symbol table of a zero-indexed array of all possible input symbols
this algorithm reversibly transforms a sequence
of input symbols into an array of output numbers (indices).
The transform in many cases acts to give frequently repeated input symbols
lower indices which is useful in some compression algorithms.
Encoding algorithm
for each symbol of the input sequence:
output the index of the symbol in the symbol table
move that symbol to the front of the symbol table
Decoding algorithm
# Using the same starting symbol table
for each index of the input sequence:
output the symbol at that index of the symbol table
move that symbol to the front of the symbol table
Example
Encoding the string of character symbols 'broood' using a symbol table of the lowercase characters a-to-z
Input
Output
SymbolTable
broood
1
'abcdefghijklmnopqrstuvwxyz'
broood
1 17
'bacdefghijklmnopqrstuvwxyz'
broood
1 17 15
'rbacdefghijklmnopqstuvwxyz'
broood
1 17 15 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0 5
'orbacdefghijklmnpqstuvwxyz'
Decoding the indices back to the original symbol order:
Input
Output
SymbolTable
1 17 15 0 0 5
b
'abcdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
br
'bacdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
bro
'rbacdefghijklmnopqstuvwxyz'
1 17 15 0 0 5
broo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
brooo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
broood
'orbacdefghijklmnpqstuvwxyz'
Task
Encode and decode the following three strings of characters using the symbol table of the lowercase characters a-to-z as above.
Show the strings and their encoding here.
Add a check to ensure that the decoded string is the same as the original.
The strings are:
broood
bananaaa
hiphophiphop
(Note the misspellings in the above strings.)
| #Lua | Lua | -- Return table of the alphabet in lower case
function getAlphabet ()
local letters = {}
for ascii = 97, 122 do table.insert(letters, string.char(ascii)) end
return letters
end
-- Move the table value at ind to the front of tab
function moveToFront (tab, ind)
local toMove = tab[ind]
for i = ind - 1, 1, -1 do tab[i + 1] = tab[i] end
tab[1] = toMove
end
-- Perform move-to-front encoding on input
function encode (input)
local symbolTable, output, index = getAlphabet(), {}
for pos = 1, #input do
for k, v in pairs(symbolTable) do
if v == input:sub(pos, pos) then index = k end
end
moveToFront(symbolTable, index)
table.insert(output, index - 1)
end
return table.concat(output, " ")
end
-- Perform move-to-front decoding on input
function decode (input)
local symbolTable, output = getAlphabet(), ""
for num in input:gmatch("%d+") do
output = output .. symbolTable[num + 1]
moveToFront(symbolTable, num + 1)
end
return output
end
-- Main procedure
local testCases, output = {"broood", "bananaaa", "hiphophiphop"}
for _, case in pairs(testCases) do
output = encode(case)
print("Original string: " .. case)
print("Encoded: " .. output)
print("Decoded: " .. decode(output))
print()
end |
http://rosettacode.org/wiki/Morse_code | Morse code | Morse code
It has been in use for more than 175 years — longer than any other electronic encoding system.
Task
Send a string as audible Morse code to an audio device (e.g., the PC speaker).
As the standard Morse code does not contain all possible characters,
you may either ignore unknown characters in the file,
or indicate them somehow (e.g. with a different pitch).
| #Arturo | Arturo | ; set the morse code
code: #[
; letters
a: ".-" b: "-..." c: "-.-." d: "-.." e: "."
f: "..-." g: "--." h: "...." i: ".." j: ".---"
k: "-.-" l: ".-.." m: "--" n: "-." o: "---"
p: ".--." q: "--.-" r: ".-." s: "..." t: "-"
u: "..-" v: "...-" w: ".--" x: "-..-" y: "-.--"
z: "--.."
; digits
"0": "-----"
"1": ".----"
"2": "..---"
"3": "...--"
"4": "....-"
"5": "....."
"6": "-...."
"7": "--..."
"8": "---.."
"9": "----."
]
; print an encoded message
str: "hello world 2019"
out: ""
loop split str 'ch [
if not? whitespace? ch -> 'out ++ code\[ch]
'out ++ " "
]
print out |
http://rosettacode.org/wiki/Monty_Hall_problem | Monty Hall problem |
Suppose you're on a game show and you're given the choice of three doors.
Behind one door is a car; behind the others, goats.
The car and the goats were placed randomly behind the doors before the show.
Rules of the game
After you have chosen a door, the door remains closed for the time being.
The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it.
If both remaining doors have goats behind them, he chooses one randomly.
After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door.
Imagine that you chose Door 1 and the host opens Door 3, which has a goat.
He then asks you "Do you want to switch to Door Number 2?"
The question
Is it to your advantage to change your choice?
Note
The player may initially choose any of the three doors (not just Door 1), that the host opens a different door revealing a goat (not necessarily Door 3), and that he gives the player a second choice between the two remaining unopened doors.
Task
Run random simulations of the Monty Hall game. Show the effects of a strategy of the contestant always keeping his first guess so it can be contrasted with the strategy of the contestant always switching his guess.
Simulate at least a thousand games using three doors for each strategy and show the results in such a way as to make it easy to compare the effects of each strategy.
References
Stefan Krauss, X. T. Wang, "The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser.", Journal of Experimental Psychology: General, Vol 132(1), Mar 2003, 3-22 DOI: 10.1037/0096-3445.132.1.3
A YouTube video: Monty Hall Problem - Numberphile.
| #APL | APL | ∇ Run runs;doors;i;chosen;cars;goats;swap;stay;ix;prices
[1] ⍝0: Monthy Hall problem
[2] ⍝1: http://rosettacode.org/wiki/Monty_Hall_problem
[3]
[4] (⎕IO ⎕ML)←0 1
[5] prices←0 0 1 ⍝ 0=Goat, 1=Car
[6]
[7] ix←⊃,/{3?3}¨⍳runs ⍝ random indexes of doors (placement of car)
[8] doors←(runs 3)⍴prices[ix] ⍝ matrix of doors
[9] stay←+⌿doors[;?3] ⍝ chose randomly one door - is it a car?
[10] swap←runs-stay ⍝ If not, then the other one is!
[11]
[12] ⎕←'Swap: ',(2⍕100×(swap÷runs)),'% it''s a car'
[13] ⎕←'Stay: ',(2⍕100×(stay÷runs)),'% it''s a car'
∇ |
http://rosettacode.org/wiki/Modular_inverse | Modular inverse | From Wikipedia:
In modular arithmetic, the modular multiplicative inverse of an integer a modulo m is an integer x such that
a
x
≡
1
(
mod
m
)
.
{\displaystyle a\,x\equiv 1{\pmod {m}}.}
Or in other words, such that:
∃
k
∈
Z
,
a
x
=
1
+
k
m
{\displaystyle \exists k\in \mathbb {Z} ,\qquad a\,x=1+k\,m}
It can be shown that such an inverse exists if and only if a and m are coprime, but we will ignore this for this task.
Task
Either by implementing the algorithm, by using a dedicated library or by using a built-in function in
your language, compute the modular inverse of 42 modulo 2017.
| #C | C | #include <stdio.h>
int mul_inv(int a, int b)
{
int b0 = b, t, q;
int x0 = 0, x1 = 1;
if (b == 1) return 1;
while (a > 1) {
q = a / b;
t = b, b = a % b, a = t;
t = x0, x0 = x1 - q * x0, x1 = t;
}
if (x1 < 0) x1 += b0;
return x1;
}
int main(void) {
printf("%d\n", mul_inv(42, 2017));
return 0;
} |
http://rosettacode.org/wiki/Monads/Writer_monad | Monads/Writer monad | The Writer monad is a programming design pattern which makes it possible to compose functions which return their result values paired with a log string. The final result of a composed function yields both a value, and a concatenation of the logs from each component function application.
Demonstrate in your programming language the following:
Construct a Writer monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that monad (or just use what the language already provides)
Write three simple functions: root, addOne, and half
Derive Writer monad versions of each of these functions
Apply a composition of the Writer versions of root, addOne, and half to the integer 5, deriving both a value for the Golden Ratio φ, and a concatenated log of the function applications (starting with the initial value, and followed by the application of root, etc.) | #Python | Python | """A Writer Monad. Requires Python >= 3.7 for type hints."""
from __future__ import annotations
import functools
import math
import os
from typing import Any
from typing import Callable
from typing import Generic
from typing import List
from typing import TypeVar
from typing import Union
T = TypeVar("T")
class Writer(Generic[T]):
def __init__(self, value: Union[T, Writer[T]], *msgs: str):
if isinstance(value, Writer):
self.value: T = value.value
self.msgs: List[str] = value.msgs + list(msgs)
else:
self.value = value
self.msgs = list(f"{msg}: {self.value}" for msg in msgs)
def bind(self, func: Callable[[T], Writer[Any]]) -> Writer[Any]:
writer = func(self.value)
return Writer(writer, *self.msgs)
def __rshift__(self, func: Callable[[T], Writer[Any]]) -> Writer[Any]:
return self.bind(func)
def __str__(self):
return f"{self.value}\n{os.linesep.join(reversed(self.msgs))}"
def __repr__(self):
return f"Writer({self.value}, \"{', '.join(reversed(self.msgs))}\")"
def lift(func: Callable, msg: str) -> Callable[[Any], Writer[Any]]:
"""Return a writer monad version of the simple function `func`."""
@functools.wraps(func)
def wrapped(value):
return Writer(func(value), msg)
return wrapped
if __name__ == "__main__":
square_root = lift(math.sqrt, "square root")
add_one = lift(lambda x: x + 1, "add one")
half = lift(lambda x: x / 2, "div two")
print(Writer(5, "initial") >> square_root >> add_one >> half)
|
http://rosettacode.org/wiki/Monads/List_monad | Monads/List monad | A Monad is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as eta and mu, but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of concat and map, which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
Construct a List Monad by writing the 'bind' function and the 'pure' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
Compose the two functions with bind | #Racket | Racket | #lang racket
(define (bind x f) (append-map f x))
(define return list)
(define ((lift f) x) (list (f x)))
(define listy-inc (lift add1))
(define listy-double (lift (λ (x) (* 2 x))))
(bind (bind '(3 4 5) listy-inc) listy-double)
;; => '(8 10 12)
(define (pythagorean-triples n)
(bind (range 1 n)
(λ (x)
(bind (range (add1 x) n)
(λ (y)
(bind (range (add1 y) n)
(λ (z)
(if (= (+ (* x x) (* y y)) (* z z))
(return (list x y z))
'()))))))))
(pythagorean-triples 25)
;; => '((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))
(require syntax/parse/define)
(define-syntax-parser do-macro
[(_ [x {~datum <-} y] . the-rest) #'(bind y (λ (x) (do-macro . the-rest)))]
[(_ e) #'e])
(define (pythagorean-triples* n)
(do-macro
[x <- (range 1 n)]
[y <- (range (add1 x) n)]
[z <- (range (add1 y) n)]
(if (= (+ (* x x) (* y y)) (* z z))
(return (list x y z))
'())))
(pythagorean-triples* 25)
;; => '((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20)) |
http://rosettacode.org/wiki/Monads/List_monad | Monads/List monad | A Monad is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as eta and mu, but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of concat and map, which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
Construct a List Monad by writing the 'bind' function and the 'pure' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
Compose the two functions with bind | #Raku | Raku | multi bind (@list, &code) { @list.map: &code };
multi bind ($item, &code) { $item.&code };
sub divisors (Int $int) { gather for 1 .. $int { .take if $int %% $_ } }
put (^10).&bind(* + 3).&bind(&divisors)».&bind(*.base: 2).join: "\n"; |
http://rosettacode.org/wiki/Multi-dimensional_array | Multi-dimensional array | For the purposes of this task, the actual memory layout or access method of this data structure is not mandated.
It is enough to:
State the number and extent of each index to the array.
Provide specific, ordered, integer indices for all dimensions of the array together with a new value to update the indexed value.
Provide specific, ordered, numeric indices for all dimensions of the array to obtain the arrays value at that indexed position.
Task
State if the language supports multi-dimensional arrays in its syntax and usual implementation.
State whether the language uses row-major or column major order for multi-dimensional array storage, or any other relevant kind of storage.
Show how to create a four dimensional array in your language and set, access, set to another value; and access the new value of an integer-indexed item of the array.
The idiomatic method for the language is preferred.
The array should allow a range of five, four, three and two (or two three four five if convenient), in each of the indices, in order. (For example, if indexing starts at zero for the first index then a range of 0..4 inclusive would suffice).
State if memory allocation is optimised for the array - especially if contiguous memory is likely to be allocated.
If the language has exceptional native multi-dimensional array support such as optional bounds checking, reshaping, or being able to state both the lower and upper bounds of index ranges, then this is the task to mention them.
Show all output here, (but you may judiciously use ellipses to shorten repetitive output text).
| #REXX | REXX | g = antenna.2.0 |
http://rosettacode.org/wiki/Multi-dimensional_array | Multi-dimensional array | For the purposes of this task, the actual memory layout or access method of this data structure is not mandated.
It is enough to:
State the number and extent of each index to the array.
Provide specific, ordered, integer indices for all dimensions of the array together with a new value to update the indexed value.
Provide specific, ordered, numeric indices for all dimensions of the array to obtain the arrays value at that indexed position.
Task
State if the language supports multi-dimensional arrays in its syntax and usual implementation.
State whether the language uses row-major or column major order for multi-dimensional array storage, or any other relevant kind of storage.
Show how to create a four dimensional array in your language and set, access, set to another value; and access the new value of an integer-indexed item of the array.
The idiomatic method for the language is preferred.
The array should allow a range of five, four, three and two (or two three four five if convenient), in each of the indices, in order. (For example, if indexing starts at zero for the first index then a range of 0..4 inclusive would suffice).
State if memory allocation is optimised for the array - especially if contiguous memory is likely to be allocated.
If the language has exceptional native multi-dimensional array support such as optional bounds checking, reshaping, or being able to state both the lower and upper bounds of index ranges, then this is the task to mention them.
Show all output here, (but you may judiciously use ellipses to shorten repetitive output text).
| #Ring | Ring | # Project : Multi-dimensional array
a4 = newlist4(5,4,3,2)
func main()
m = 1
for i = 1 to 5
for j = 1 to 4
for k = 1 to 3
for l = 1 to 2
a4[i][j][k][l] = m
m = m + 1
next
next
next
next
see "First element = " + a4[1][1][1][1] + nl
a4[1][1][1][1] = 121
see nl
for i = 1 to 5
for j = 1 to 4
for k = 1 to 3
for l = 1 to 2
see "" + a4[i][j][k][l] + " "
next
next
next
next
func newlist(x, y)
if isstring(x) x=0+x ok
if isstring(y) y=0+y ok
alist = list(x)
for t in alist
t = list(y)
next
return alist
func newlist3(x, y, z)
if isstring(x) x=0+x ok
if isstring(y) y=0+y ok
if isstring(z) z=0+z ok
alist = list(x)
for t in alist
t = newlist(y,z)
next
return alist
func newlist4(x, y, z, w)
if isstring(x) x=0+x ok
if isstring(y) y=0+y ok
if isstring(z) z=0+z ok
if isstring(w) w=0+w ok
alist = list(x)
for t in alist
t = newlist3(y,z,w)
next
return alist |
http://rosettacode.org/wiki/Multiplication_tables | Multiplication tables | Task
Produce a formatted 12×12 multiplication table of the kind memorized by rote when in primary (or elementary) school.
Only print the top half triangle of products.
| #Arturo | Arturo | mulTable: function [n][
print [" |"] ++ map 1..n => [pad to :string & 3]
print "----+" ++ join map 1..n => "----"
loop 1..n 'x [
prints (pad to :string x 3) ++ " |"
if x>1 -> loop 1..x-1 'y [prints " "]
loop x..n 'y [prints " " ++ pad to :string x*y 3]
print ""
]
]
mulTable 12 |
http://rosettacode.org/wiki/Multiple_regression | Multiple regression | Task
Given a set of data vectors in the following format:
y
=
{
y
1
,
y
2
,
.
.
.
,
y
n
}
{\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
X
i
=
{
x
i
1
,
x
i
2
,
.
.
.
,
x
i
n
}
,
i
∈
1..
k
{\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
Compute the vector
β
=
{
β
1
,
β
2
,
.
.
.
,
β
k
}
{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}
using ordinary least squares regression using the following equation:
y
j
=
Σ
i
β
i
⋅
x
i
j
,
j
∈
1..
n
{\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
You can assume y is given to you as a vector (a one-dimensional array), and X is given to you as a two-dimensional array (i.e. matrix).
| #PicoLisp | PicoLisp | (scl 20)
# Matrix transposition
(de matTrans (Mat)
(apply mapcar Mat list) )
# Matrix multiplication
(de matMul (Mat1 Mat2)
(mapcar
'((Row)
(apply mapcar Mat2
'(@ (sum */ Row (rest) (1.0 .))) ) )
Mat1 ) )
# Matrix identity
(de matIdent (N)
(let L (need N (1.0) 0)
(mapcar '(() (copy (rot L))) L) ) )
# Reduced row echelon form
(de reducedRowEchelonForm (Mat)
(let (Lead 1 Cols (length (car Mat)))
(for (X Mat X (cdr X))
(NIL
(loop
(T (seek '((R) (n0 (get R 1 Lead))) X)
@ )
(T (> (inc 'Lead) Cols)) ) )
(xchg @ X)
(let D (get X 1 Lead)
(map
'((R) (set R (*/ (car R) 1.0 D)))
(car X) ) )
(for Y Mat
(unless (== Y (car X))
(let N (- (get Y Lead))
(map
'((Dst Src)
(inc Dst (*/ N (car Src) 1.0)) )
Y
(car X) ) ) ) )
(T (> (inc 'Lead) Cols)) ) )
Mat ) |
http://rosettacode.org/wiki/Multiple_regression | Multiple regression | Task
Given a set of data vectors in the following format:
y
=
{
y
1
,
y
2
,
.
.
.
,
y
n
}
{\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
X
i
=
{
x
i
1
,
x
i
2
,
.
.
.
,
x
i
n
}
,
i
∈
1..
k
{\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
Compute the vector
β
=
{
β
1
,
β
2
,
.
.
.
,
β
k
}
{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}
using ordinary least squares regression using the following equation:
y
j
=
Σ
i
β
i
⋅
x
i
j
,
j
∈
1..
n
{\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
You can assume y is given to you as a vector (a one-dimensional array), and X is given to you as a two-dimensional array (i.e. matrix).
| #Python | Python | import numpy as np
height = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63,
1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83]
weight = [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93,
61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46]
X = np.mat(height**np.arange(3)[:, None])
y = np.mat(weight)
print(y * X.T * (X*X.T).I) |
http://rosettacode.org/wiki/Multifactorial | Multifactorial | The factorial of a number, written as
n
!
{\displaystyle n!}
, is defined as
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
.
Multifactorials generalize factorials as follows:
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.
{\displaystyle n!!=n(n-2)(n-4)...}
n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.
{\displaystyle n!!!=n(n-3)(n-6)...}
n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.
{\displaystyle n!!!!=n(n-4)(n-8)...}
n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.
{\displaystyle n!!!!!=n(n-5)(n-10)...}
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
| #FunL | FunL | def multifactorial( n, d ) = product( n..1 by -d )
for d <- 1..5
println( d, [multifactorial(i, d) | i <- 1..10] )) |
http://rosettacode.org/wiki/Multifactorial | Multifactorial | The factorial of a number, written as
n
!
{\displaystyle n!}
, is defined as
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
.
Multifactorials generalize factorials as follows:
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.
{\displaystyle n!!=n(n-2)(n-4)...}
n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.
{\displaystyle n!!!=n(n-3)(n-6)...}
n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.
{\displaystyle n!!!!=n(n-4)(n-8)...}
n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.
{\displaystyle n!!!!!=n(n-5)(n-10)...}
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
| #GAP | GAP | MultiFactorial := function(n, k)
local r;
r := 1;
while n > 1 do
r := r*n;
n := n - k;
od;
return r;
end;
PrintArray(List([1 .. 10], n -> List([1 .. 5], k -> MultiFactorial(n, k))));
[ [ 1, 1, 1, 1, 1 ],
[ 2, 2, 2, 2, 2 ],
[ 6, 3, 3, 3, 3 ],
[ 24, 8, 4, 4, 4 ],
[ 120, 15, 10, 5, 5 ],
[ 720, 48, 18, 12, 6 ],
[ 5040, 105, 28, 21, 14 ],
[ 40320, 384, 80, 32, 24 ],
[ 362880, 945, 162, 45, 36 ],
[ 3628800, 3840, 280, 120, 50 ] ] |
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #MATLAB | MATLAB | get(0,'PointerLocation') |
http://rosettacode.org/wiki/Mouse_position | Mouse position | Task
Get the current location of the mouse cursor relative to the active window.
Please specify if the window may be externally created.
| #MAXScript | MAXScript |
try destroydialog mousePos catch ()
rollout mousePos "Mouse position" width:200
(
label mousePosText "Current mouse position:" pos:[0,0]
label mousePosX "" pos:[130,0]
label mousePosSep "x" pos:[143,0]
label mousePosY "" pos:[160,0]
timer updateTimer interval:50 active:true
on updateTimer tick do
(
mousePosX.text = (mouse.screenpos.x as integer) as string
mousePosY.text = (mouse.screenpos.y as integer) as string
)
)
createdialog mousepos
|
http://rosettacode.org/wiki/N-queens_problem | N-queens problem |
Solve the eight queens puzzle.
You can extend the problem to solve the puzzle with a board of size NxN.
For the number of solutions for small values of N, see OEIS: A000170.
Related tasks
A* search algorithm
Solve a Hidato puzzle
Solve a Holy Knight's tour
Knight's tour
Peaceful chess queen armies
Solve a Hopido puzzle
Solve a Numbrix puzzle
Solve the no connection puzzle
| #Icon_and_Unicon | Icon and Unicon | procedure main()
write(q(1), " ", q(2), " ", q(3), " ", q(4), " ", q(5), " ", q(6), " ", q(7), " ", q(8))
end
procedure q(c)
static udiag, ddiag, row
initial {
udiag := list(15, 0)
ddiag := list(15, 0)
row := list(8, 0)
}
every 0 = row[r := 1 to 8] = ddiag[r + c - 1] = udiag[8 + r - c] do # test if free
suspend row[r] <- ddiag[r + c - 1] <- udiag[8 + r - c] <- r # place and yield
end |
http://rosettacode.org/wiki/Nth_root | Nth root | Task
Implement the algorithm to compute the principal nth root
A
n
{\displaystyle {\sqrt[{n}]{A}}}
of a positive real number A, as explained at the Wikipedia page.
| #Yabasic | Yabasic | data 10, 1024, 3, 27, 2, 2, 125, 5642, 4, 16, 0, 0
do
read e, b
if e = 0 break
print "The ", e, "th root of ", b, " is ", b^(1/e), " (", nthroot(b, e), ")"
loop
sub nthroot(y, n)
local eps, x, d, e
eps = 1e-15 // relative accuracy
x = 1
repeat
d = ( y / ( x^(n-1) ) - x ) / n
x = x + d
e = eps * x // absolute accuracy
until(not(d < -e or d > e ))
return x
end sub |
http://rosettacode.org/wiki/Nth_root | Nth root | Task
Implement the algorithm to compute the principal nth root
A
n
{\displaystyle {\sqrt[{n}]{A}}}
of a positive real number A, as explained at the Wikipedia page.
| #zkl | zkl | fcn nthroot(nth,a,precision=1.0e-5){
x:=prev:=a=a.toFloat(); n1:=nth-1;
do{
prev=x;
x=( prev*n1 + a/prev.pow(n1) ) / nth;
}
while( not prev.closeTo(x,precision) );
x
}
nthroot(5,34) : "%.20f".fmt(_).println() # => 2.02439745849988828041 |
http://rosettacode.org/wiki/N%27th | N'th | Write a function/method/subroutine/... that when given an integer greater than or equal to zero returns a string of the number followed by an apostrophe then the ordinal suffix.
Example
Returns would include 1'st 2'nd 3'rd 11'th 111'th 1001'st 1012'th
Task
Use your routine to show here the output for at least the following (inclusive) ranges of integer inputs:
0..25, 250..265, 1000..1025
Note: apostrophes are now optional to allow correct apostrophe-less English.
| #Perl | Perl | use 5.10.0;
my %irregulars = ( 1 => 'st',
2 => 'nd',
3 => 'rd',
11 => 'th',
12 => 'th',
13 => 'th');
sub nth
{
my $n = shift;
$n . # q(') . # Uncomment this to add apostrophes to output
($irregulars{$n % 100} // $irregulars{$n % 10} // 'th');
}
sub range { join ' ', map { nth($_) } @{$_[0]} }
print range($_), "\n" for ([0..25], [250..265], [1000..1025]); |
http://rosettacode.org/wiki/Munchausen_numbers | Munchausen numbers | A Munchausen number is a natural number n the sum of whose digits (in base 10), each raised to the power of itself, equals n.
(Munchausen is also spelled: Münchhausen.)
For instance: 3435 = 33 + 44 + 33 + 55
Task
Find all Munchausen numbers between 1 and 5000.
Also see
The OEIS entry: A046253
The Wikipedia entry: Perfect digit-to-digit invariant, redirected from Munchausen Number
| #PL.2FI | PL/I | munchausen: procedure options(main);
/* precalculate powers */
declare (pows(0:5), i) fixed;
pows(0) = 0; /* 0^0=0 for Munchausen numbers */
do i=1 to 5; pows(i) = i**i; end;
declare (d1, d2, d3, d4, num, dpow) fixed;
do d1=0 to 5;
do d2=0 to 5;
do d3=0 to 5;
do d4=1 to 5;
num = d1*1000 + d2*100 + d3*10 + d4;
dpow = pows(d1) + pows(d2) + pows(d3) + pows(d4);
if num=dpow then put skip list(num);
end;
end;
end;
end;
end munchausen; |
http://rosettacode.org/wiki/Mutual_recursion | Mutual recursion | Two functions are said to be mutually recursive if the first calls the second,
and in turn the second calls the first.
Write two mutually recursive functions that compute members of the Hofstadter Female and Male sequences defined as:
F
(
0
)
=
1
;
M
(
0
)
=
0
F
(
n
)
=
n
−
M
(
F
(
n
−
1
)
)
,
n
>
0
M
(
n
)
=
n
−
F
(
M
(
n
−
1
)
)
,
n
>
0.
{\displaystyle {\begin{aligned}F(0)&=1\ ;\ M(0)=0\\F(n)&=n-M(F(n-1)),\quad n>0\\M(n)&=n-F(M(n-1)),\quad n>0.\end{aligned}}}
(If a language does not allow for a solution using mutually recursive functions
then state this rather than give a solution by other means).
| #Jsish | Jsish | /* Mutual recursion, is jsish */
function f(num):number { return (num === 0) ? 1 : num - m(f(num - 1)); }
function m(num):number { return (num === 0) ? 0 : num - f(m(num - 1)); }
function range(n=10, start=0, step=1):array {
var a = Array(n).fill(0);
for (var i in a) a[i] = start+i*step;
return a;
}
var a = range(21);
puts(a.map(function (n) { return f(n); }).join(', '));
puts(a.map(function (n) { return m(n); }).join(', '));
/*
=!EXPECTSTART!=
1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13
0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12
=!EXPECTEND!=
*/ |
http://rosettacode.org/wiki/Monads/Maybe_monad | Monads/Maybe monad | Demonstrate in your programming language the following:
Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
Compose the two functions with bind
A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.
A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.
| #J | J |
NB. monad implementation:
unit=: <
bind=: (@>)( :: ])
NB. monad utility
safeVersion=: (<@) ( ::((<_.)"_))
safeCompose=:dyad define
dyad def 'x`:6 bind y'/x,unit y
)
NB. unsafe functions (fail with infinite arguments)
subtractFromSelf=: -~
divideBySelf=: %~
NB. wrapped functions:
safeSubtractFromSelf=: subtractFromSelf safeVersion
safeDivideBySelf=: divideBySelf safeVersion
NB. task example:
safeSubtractFromSelf bind safeDivideBySelf 1
┌─┐
│0│
└─┘
safeSubtractFromSelf bind safeDivideBySelf _
┌──┐
│_.│
└──┘ |
http://rosettacode.org/wiki/Monads/Maybe_monad | Monads/Maybe monad | Demonstrate in your programming language the following:
Construct a Maybe Monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> Maybe Int and Int -> Maybe String
Compose the two functions with bind
A Monad is a single type which encapsulates several other types, eliminating boilerplate code. In practice it acts like a dynamically typed computational sequence, though in many cases the type issues can be resolved at compile time.
A Maybe Monad is a monad which specifically encapsulates the type of an undefined value.
| #JavaScript | JavaScript | (function () {
'use strict';
// START WITH SOME SIMPLE (UNSAFE) PARTIAL FUNCTIONS:
// Returns Infinity if n === 0
function reciprocal(n) {
return 1 / n;
}
// Returns NaN if n < 0
function root(n) {
return Math.sqrt(n);
}
// Returns -Infinity if n === 0
// Returns NaN if n < 0
function log(n) {
return Math.log(n);
}
// NOW DERIVE SAFE VERSIONS OF THESE SIMPLE FUNCTIONS:
// These versions use a validity test, and return a wrapped value
// with a boolean .isValid property as well as a .value property
function safeVersion(f, fnSafetyCheck) {
return function (v) {
return maybe(fnSafetyCheck(v) ? f(v) : undefined);
}
}
var safe_reciprocal = safeVersion(reciprocal, function (n) {
return n !== 0;
});
var safe_root = safeVersion(root, function (n) {
return n >= 0;
});
var safe_log = safeVersion(log, function (n) {
return n > 0;
});
// THE DERIVATION OF THE SAFE VERSIONS USED THE 'UNIT' OR 'RETURN'
// FUNCTION OF THE MAYBE MONAD
// Named maybe() here, the unit function of the Maybe monad wraps a raw value
// in a datatype with two elements: .isValid (Bool) and .value (Number)
// a -> Ma
function maybe(n) {
return {
isValid: (typeof n !== 'undefined'),
value: n
};
}
// THE PROBLEM FOR FUNCTION NESTING (COMPOSITION) OF THE SAFE FUNCTIONS
// IS THAT THEIR INPUT AND OUTPUT TYPES ARE DIFFERENT
// Our safe versions of the functions take simple numeric arguments, but return
// wrapped results. If we feed a wrapped result as an input to another safe function,
// it will choke on the unexpected type. The solution is to write a higher order
// function (sometimes called 'bind' or 'chain') which handles composition, taking a
// a safe function and a wrapped value as arguments,
// The 'bind' function of the Maybe monad:
// 1. Applies a 'safe' function directly to the raw unwrapped value, and
// 2. returns the wrapped result.
// Ma -> (a -> Mb) -> Mb
function bind(maybeN, mf) {
return (maybeN.isValid ? mf(maybeN.value) : maybeN);
}
// Using the bind function, we can nest applications of safe_ functions,
// without their choking on unexpectedly wrapped values returned from
// other functions of the same kind.
var rootOneOverFour = bind(
bind(maybe(4), safe_reciprocal), safe_root
).value;
// -> 0.5
// We can compose a chain of safe functions (of any length) with a simple foldr/reduceRight
// which starts by 'lifting' the numeric argument into a Maybe wrapping,
// and then nests function applications (working from right to left)
function safeCompose(lstFunctions, value) {
return lstFunctions
.reduceRight(function (a, f) {
return bind(a, f);
}, maybe(value));
}
// TEST INPUT VALUES WITH A SAFELY COMPOSED VERSION OF LOG(SQRT(1/X))
var safe_log_root_reciprocal = function (n) {
return safeCompose([safe_log, safe_root, safe_reciprocal], n).value;
}
return [-2, -1, -0.5, 0, 1 / Math.E, 1, 2, Math.E, 3, 4, 5].map(
safe_log_root_reciprocal
);
})(); |
http://rosettacode.org/wiki/Monte_Carlo_methods | Monte Carlo methods | A Monte Carlo Simulation is a way of approximating the value of a function
where calculating the actual value is difficult or impossible.
It uses random sampling to define constraints on the value
and then makes a sort of "best guess."
A simple Monte Carlo Simulation can be used to calculate the value for
π
{\displaystyle \pi }
.
If you had a circle and a square where the length of a side of the square
was the same as the diameter of the circle, the ratio of the area of the circle
to the area of the square would be
π
/
4
{\displaystyle \pi /4}
.
So, if you put this circle inside the square and select many random points
inside the square, the number of points inside the circle
divided by the number of points inside the square and the circle
would be approximately
π
/
4
{\displaystyle \pi /4}
.
Task
Write a function to run a simulation like this, with a variable number of random points to select.
Also, show the results of a few different sample sizes.
For software where the number
π
{\displaystyle \pi }
is not built-in,
we give
π
{\displaystyle \pi }
as a number of digits:
3.141592653589793238462643383280
| #BASIC256 | BASIC256 |
# Monte Carlo Simulator
# Determine value of pi
# 21010513
tosses = 1000
in_c = 0
i = 0
for i = 1 to tosses
x = rand
y = rand
x2 = x * x
y2 = y * y
xy = x2 + y2
d_xy = sqr(xy)
if d_xy <= 1 then
in_c += 1
endif
next i
print float(4*in_c/tosses) |
http://rosettacode.org/wiki/Monte_Carlo_methods | Monte Carlo methods | A Monte Carlo Simulation is a way of approximating the value of a function
where calculating the actual value is difficult or impossible.
It uses random sampling to define constraints on the value
and then makes a sort of "best guess."
A simple Monte Carlo Simulation can be used to calculate the value for
π
{\displaystyle \pi }
.
If you had a circle and a square where the length of a side of the square
was the same as the diameter of the circle, the ratio of the area of the circle
to the area of the square would be
π
/
4
{\displaystyle \pi /4}
.
So, if you put this circle inside the square and select many random points
inside the square, the number of points inside the circle
divided by the number of points inside the square and the circle
would be approximately
π
/
4
{\displaystyle \pi /4}
.
Task
Write a function to run a simulation like this, with a variable number of random points to select.
Also, show the results of a few different sample sizes.
For software where the number
π
{\displaystyle \pi }
is not built-in,
we give
π
{\displaystyle \pi }
as a number of digits:
3.141592653589793238462643383280
| #BBC_BASIC | BBC BASIC | PRINT FNmontecarlo(1000)
PRINT FNmontecarlo(10000)
PRINT FNmontecarlo(100000)
PRINT FNmontecarlo(1000000)
PRINT FNmontecarlo(10000000)
END
DEF FNmontecarlo(t%)
LOCAL i%, n%
FOR i% = 1 TO t%
IF RND(1)^2 + RND(1)^2 < 1 n% += 1
NEXT
= 4 * n% / t% |
http://rosettacode.org/wiki/Move-to-front_algorithm | Move-to-front algorithm | Given a symbol table of a zero-indexed array of all possible input symbols
this algorithm reversibly transforms a sequence
of input symbols into an array of output numbers (indices).
The transform in many cases acts to give frequently repeated input symbols
lower indices which is useful in some compression algorithms.
Encoding algorithm
for each symbol of the input sequence:
output the index of the symbol in the symbol table
move that symbol to the front of the symbol table
Decoding algorithm
# Using the same starting symbol table
for each index of the input sequence:
output the symbol at that index of the symbol table
move that symbol to the front of the symbol table
Example
Encoding the string of character symbols 'broood' using a symbol table of the lowercase characters a-to-z
Input
Output
SymbolTable
broood
1
'abcdefghijklmnopqrstuvwxyz'
broood
1 17
'bacdefghijklmnopqrstuvwxyz'
broood
1 17 15
'rbacdefghijklmnopqstuvwxyz'
broood
1 17 15 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0 5
'orbacdefghijklmnpqstuvwxyz'
Decoding the indices back to the original symbol order:
Input
Output
SymbolTable
1 17 15 0 0 5
b
'abcdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
br
'bacdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
bro
'rbacdefghijklmnopqstuvwxyz'
1 17 15 0 0 5
broo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
brooo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
broood
'orbacdefghijklmnpqstuvwxyz'
Task
Encode and decode the following three strings of characters using the symbol table of the lowercase characters a-to-z as above.
Show the strings and their encoding here.
Add a check to ensure that the decoded string is the same as the original.
The strings are:
broood
bananaaa
hiphophiphop
(Note the misspellings in the above strings.)
| #M2000_Interpreter | M2000 Interpreter |
Module CheckIt {
Global All$, nl$
\\ upgrade to document
Document All$
Nl$<={
}
Function Encode$(Inp$) {
Def SymbolTable$="abcdefghijklmnopqrstuvwxyz", Out$=""
For i=1 to Len(Inp$)
c$=Mid$(Inp$, i, 1)
k=Instr(SymbolTable$, c$)
Insert k, 1 SymbolTable$=""
Out$=If$(Out$="" -> Quote$(k-1),Quote$(Param(Out$), k-1))
Insert 1 SymbolTable$=c$
\\ we use <= for globals
All$<=Format$(" {0} {1:30} {2}", c$, Out$, SymbolTable$)+nl$
Next i
=Out$
}
Function Decode$(Inp$) {
Def SymbolTable$="abcdefghijklmnopqrstuvwxyz", Out$=""
flush
Data Param(Inp$)
While not empty {
k=Number+1
c$=Mid$(SymbolTable$, k, 1)
Out$+=c$
Insert k, 1 SymbolTable$="" ' erase at position k
Insert 1 SymbolTable$=c$
All$<=Format$("{0::-2} {1} {2:30} {3}", k-1, c$, Out$, SymbolTable$)+nl$
}
=Out$
}
TryThis("broood")
TryThis("bananaaa")
TryThis("hiphophiphop")
ClipBoard All$
Sub TryThis(a$)
Local Out$=Encode$(a$)
Local final$=Decode$(Out$)
Print final$, final$=a$
End Sub
}
CheckIt
|
http://rosettacode.org/wiki/Move-to-front_algorithm | Move-to-front algorithm | Given a symbol table of a zero-indexed array of all possible input symbols
this algorithm reversibly transforms a sequence
of input symbols into an array of output numbers (indices).
The transform in many cases acts to give frequently repeated input symbols
lower indices which is useful in some compression algorithms.
Encoding algorithm
for each symbol of the input sequence:
output the index of the symbol in the symbol table
move that symbol to the front of the symbol table
Decoding algorithm
# Using the same starting symbol table
for each index of the input sequence:
output the symbol at that index of the symbol table
move that symbol to the front of the symbol table
Example
Encoding the string of character symbols 'broood' using a symbol table of the lowercase characters a-to-z
Input
Output
SymbolTable
broood
1
'abcdefghijklmnopqrstuvwxyz'
broood
1 17
'bacdefghijklmnopqrstuvwxyz'
broood
1 17 15
'rbacdefghijklmnopqstuvwxyz'
broood
1 17 15 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0
'orbacdefghijklmnpqstuvwxyz'
broood
1 17 15 0 0 5
'orbacdefghijklmnpqstuvwxyz'
Decoding the indices back to the original symbol order:
Input
Output
SymbolTable
1 17 15 0 0 5
b
'abcdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
br
'bacdefghijklmnopqrstuvwxyz'
1 17 15 0 0 5
bro
'rbacdefghijklmnopqstuvwxyz'
1 17 15 0 0 5
broo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
brooo
'orbacdefghijklmnpqstuvwxyz'
1 17 15 0 0 5
broood
'orbacdefghijklmnpqstuvwxyz'
Task
Encode and decode the following three strings of characters using the symbol table of the lowercase characters a-to-z as above.
Show the strings and their encoding here.
Add a check to ensure that the decoded string is the same as the original.
The strings are:
broood
bananaaa
hiphophiphop
(Note the misspellings in the above strings.)
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | mtf[word_]:=Module[{f,f2,p,q},
f[{output_,symList_},next_]:=Module[{index},index=Position[symList,next][[1,1]]-1;
{output~Append~index,Prepend[Delete[symList,index+1],next]}];
p=Fold[f,{{},CharacterRange["a","z"]},Characters[ToString[word]]][[1]];
f2[{output_,symList_},next_]:=Module[{index},index=symList[[next+1]];
{output~Append~index,Prepend[DeleteCases[symList,ToString[index]],index]}];
q=Fold[f2,{{},CharacterRange["a","z"]},p][[1]];
Print["'", word,"' encodes to: ",p, " - " ,p," decodes to: '",StringJoin@q,"' - Input equals Output: " ,word===StringJoin@q];] |
http://rosettacode.org/wiki/Morse_code | Morse code | Morse code
It has been in use for more than 175 years — longer than any other electronic encoding system.
Task
Send a string as audible Morse code to an audio device (e.g., the PC speaker).
As the standard Morse code does not contain all possible characters,
you may either ignore unknown characters in the file,
or indicate them somehow (e.g. with a different pitch).
| #AutoHotkey | AutoHotkey | TestString := "Hello World! abcdefg @\;" ;Create a string to be sent with multiple caps and some punctuation
MorseBeep(teststring) ;Beeps our string after conversion
return ;End Auto-Execute Section
MorseBeep(passedString)
{
StringLower, passedString, passedString ;Convert to lowercase for simpler checking
Loop, Parse, passedString ;This loop stores each character in A_loopField one by one using the more compact form of "if else", by var := x>y ? val1 : val2 which stores val1 in var if x > y, otherwise it stores val2, this can be used together to make a single line of if else
morse .= A_LoopField = " " ? " " : A_LoopField = "a" ? ".- " : A_LoopField = "b" ? "-... " : A_LoopField = "c" ? "-.-. " : A_LoopField = "d" ? "-.. " : A_LoopField = "e" ? ". " : A_LoopField = "f" ? "..-. " : A_LoopField = "g" ? "--. " : A_LoopField = "h" ? ".... " : A_LoopField = "i" ? ".. " : A_LoopField = "j" ? ".--- " : A_LoopField = "k" ? "-.- " : A_LoopField = "l" ? ".-.. " : A_LoopField = "m" ? "-- " : A_LoopField = "n" ? "-. " : A_LoopField = "o" ? "--- " : A_LoopField = "p" ? ".--. " : A_LoopField = "q" ? "--.- " : A_LoopField = "r" ? ".-. " : A_LoopField = "s" ? "... " : A_LoopField = "t" ? "- " : A_LoopField = "u" ? "..- " : A_LoopField = "v" ? "...- " : A_LoopField = "w" ? ".-- " : A_LoopField = "x" ? "-..- " : A_LoopField = "y" ? "-.-- " : A_LoopField = "z" ? "--.. " : A_LoopField = "!" ? "---. " : A_LoopField = "\" ? ".-..-. " : A_LoopField = "$" ? "...-..- " : A_LoopField = "'" ? ".----. " : A_LoopField = "(" ? "-.--. " : A_LoopField = ")" ? "-.--.- " : A_LoopField = "+" ? ".-.-. " : A_LoopField = "," ? "--..-- " : A_LoopField = "-" ? "-....- " : A_LoopField = "." ? ".-.-.- " : A_LoopField = "/" ? "-..-. " : A_LoopField = "0" ? "----- " : A_LoopField = "1" ? ".---- " : A_LoopField = "2" ? "..--- " : A_LoopField = "3" ? "...-- " : A_LoopField = "4" ? "....- " : A_LoopField = "5" ? "..... " : A_LoopField = "6" ? "-.... " : A_LoopField = "7" ? "--... " : A_LoopField = "8" ? "---.. " : A_LoopField = "9" ? "----. " : A_LoopField = ":" ? "---... " : A_LoopField = ";" ? "-.-.-. " : A_LoopField = "=" ? "-...- " : A_LoopField = "?" ? "..--.. " : A_LoopField = "@" ? ".--.-. " : A_LoopField = "[" ? "-.--. " : A_LoopField = "]" ? "-.--.- " : A_LoopField = "_" ? "..--.- " : "ERROR" ; ---End conversion loop---
Loop, Parse, morse
{
morsebeep := 120
if (A_LoopField = ".")
SoundBeep, 10*morsebeep, morsebeep ;Format: SoundBeep, frequency, duration
If (A_LoopField = "-")
SoundBeep, 10*morsebeep, 3*morsebeep ;Duration can be an expression
If (A_LoopField = " ")
Sleep, morsebeep ;Above, each character is followed by a space, and literal
} ;Spaces are extended. Sleep pauses the script
return morse ;Returns the text in morse code
} ; ---End Function Morse--- |
http://rosettacode.org/wiki/Monty_Hall_problem | Monty Hall problem |
Suppose you're on a game show and you're given the choice of three doors.
Behind one door is a car; behind the others, goats.
The car and the goats were placed randomly behind the doors before the show.
Rules of the game
After you have chosen a door, the door remains closed for the time being.
The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it.
If both remaining doors have goats behind them, he chooses one randomly.
After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door.
Imagine that you chose Door 1 and the host opens Door 3, which has a goat.
He then asks you "Do you want to switch to Door Number 2?"
The question
Is it to your advantage to change your choice?
Note
The player may initially choose any of the three doors (not just Door 1), that the host opens a different door revealing a goat (not necessarily Door 3), and that he gives the player a second choice between the two remaining unopened doors.
Task
Run random simulations of the Monty Hall game. Show the effects of a strategy of the contestant always keeping his first guess so it can be contrasted with the strategy of the contestant always switching his guess.
Simulate at least a thousand games using three doors for each strategy and show the results in such a way as to make it easy to compare the effects of each strategy.
References
Stefan Krauss, X. T. Wang, "The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser.", Journal of Experimental Psychology: General, Vol 132(1), Mar 2003, 3-22 DOI: 10.1037/0096-3445.132.1.3
A YouTube video: Monty Hall Problem - Numberphile.
| #Arturo | Arturo | stay: 0
swit: 0
loop 1..1000 'i [
lst: shuffle new [1 0 0]
rand: random 0 2
user: lst\[rand]
remove 'lst rand
huh: 0
loop lst 'i [
if zero? i [
remove 'lst huh
break
]
huh: huh + 1
]
if user=1 -> stay: stay+1
if and? [0 < size lst] [1 = first lst] -> swit: swit+1
]
print ["Stay:" stay]
print ["Switch:" swit] |
http://rosettacode.org/wiki/Modular_inverse | Modular inverse | From Wikipedia:
In modular arithmetic, the modular multiplicative inverse of an integer a modulo m is an integer x such that
a
x
≡
1
(
mod
m
)
.
{\displaystyle a\,x\equiv 1{\pmod {m}}.}
Or in other words, such that:
∃
k
∈
Z
,
a
x
=
1
+
k
m
{\displaystyle \exists k\in \mathbb {Z} ,\qquad a\,x=1+k\,m}
It can be shown that such an inverse exists if and only if a and m are coprime, but we will ignore this for this task.
Task
Either by implementing the algorithm, by using a dedicated library or by using a built-in function in
your language, compute the modular inverse of 42 modulo 2017.
| #C.23 | C# | public class Program
{
static void Main()
{
System.Console.WriteLine(42.ModInverse(2017));
}
}
public static class IntExtensions
{
public static int ModInverse(this int a, int m)
{
if (m == 1) return 0;
int m0 = m;
(int x, int y) = (1, 0);
while (a > 1) {
int q = a / m;
(a, m) = (m, a % m);
(x, y) = (y, x - q * y);
}
return x < 0 ? x + m0 : x;
}
} |
http://rosettacode.org/wiki/Monads/Writer_monad | Monads/Writer monad | The Writer monad is a programming design pattern which makes it possible to compose functions which return their result values paired with a log string. The final result of a composed function yields both a value, and a concatenation of the logs from each component function application.
Demonstrate in your programming language the following:
Construct a Writer monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that monad (or just use what the language already provides)
Write three simple functions: root, addOne, and half
Derive Writer monad versions of each of these functions
Apply a composition of the Writer versions of root, addOne, and half to the integer 5, deriving both a value for the Golden Ratio φ, and a concatenated log of the function applications (starting with the initial value, and followed by the application of root, etc.) | #Raku | Raku | # 20200508 Raku programming solution
class Writer { has Numeric $.value ; has Str $.log }
sub Bind (Writer \v, &code) {
my \n = v.value.&code;
Writer.new: value => n.value, log => v.log ~ n.log
};
sub Unit(\v, \s) { Writer.new: value=>v, log=>sprintf "%-17s: %.12f\n",s,v}
sub root(\v) { Unit v.sqrt, "Took square root" }
sub addOne(\v) { Unit v+1, "Added one" }
sub half(\v) { Unit v/2, "Divided by two" }
say Unit(5, "Initial value").&Bind(&root).&Bind(&addOne).&Bind(&half).log; |
http://rosettacode.org/wiki/Monads/Writer_monad | Monads/Writer monad | The Writer monad is a programming design pattern which makes it possible to compose functions which return their result values paired with a log string. The final result of a composed function yields both a value, and a concatenation of the logs from each component function application.
Demonstrate in your programming language the following:
Construct a Writer monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that monad (or just use what the language already provides)
Write three simple functions: root, addOne, and half
Derive Writer monad versions of each of these functions
Apply a composition of the Writer versions of root, addOne, and half to the integer 5, deriving both a value for the Golden Ratio φ, and a concatenated log of the function applications (starting with the initial value, and followed by the application of root, etc.) | #Wren | Wren | import "/fmt" for Fmt
class Mwriter {
construct new(value, log) {
_value = value
_log = log
}
value { _value }
log {_log}
log=(value) { _log = value }
bind(f) {
var n = f.call(_value)
n.log = _log + n.log
return n
}
static unit(v, s) { Mwriter.new(v, " %(Fmt.s(-17, s)): %(v)\n") }
}
var root = Fn.new { |v| Mwriter.unit(v.sqrt, "Took square root") }
var addOne = Fn.new { |v| Mwriter.unit(v + 1, "Added one") }
var half = Fn.new { |v| Mwriter.unit( v / 2, "Divided by two") }
var mw1 = Mwriter.unit(5, "Initial value")
var mw2 = mw1.bind(root).bind(addOne).bind(half)
System.print("The Golden Ratio is %(mw2.value)")
System.print("\nThis was derived as follows:-")
System.print(mw2.log) |
http://rosettacode.org/wiki/Monads/List_monad | Monads/List monad | A Monad is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as eta and mu, but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of concat and map, which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
Construct a List Monad by writing the 'bind' function and the 'pure' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
Compose the two functions with bind | #Ring | Ring |
# Project : Monads/List monad
func main()
str = "["
for x in [3,4,5]
y = x+1
z = y*2
str = str + z + ", "
next
str = left(str, len(str) -2)
str = str + "]"
see str + nl
|
http://rosettacode.org/wiki/Monads/List_monad | Monads/List monad | A Monad is a combination of a data-type with two helper functions written for that type.
The data-type can be of any kind which can contain values of some other type – common examples are lists, records, sum-types, even functions or IO streams. The two special functions, mathematically known as eta and mu, but usually given more expressive names like 'pure', 'return', or 'yield' and 'bind', abstract away some boilerplate needed for pipe-lining or enchaining sequences of computations on values held in the containing data-type.
The bind operator in the List monad enchains computations which return their values wrapped in lists. One application of this is the representation of indeterminacy, with returned lists representing a set of possible values. An empty list can be returned to express incomputability, or computational failure.
A sequence of two list monad computations (enchained with the use of bind) can be understood as the computation of a cartesian product.
The natural implementation of bind for the List monad is a composition of concat and map, which, used with a function which returns its value as a (possibly empty) list, provides for filtering in addition to transformation or mapping.
Demonstrate in your programming language the following:
Construct a List Monad by writing the 'bind' function and the 'pure' (sometimes known as 'return') function for that Monad (or just use what the language already has implemented)
Make two functions, each which take a number and return a monadic number, e.g. Int -> List Int and Int -> List String
Compose the two functions with bind | #Ruby | Ruby |
class Array
def bind(f)
flat_map(&f)
end
def self.unit(*args)
args
end
# implementing lift is optional, but is a great helper method for turning
# ordinary funcitons into monadic versions of them.
def self.lift(f)
-> e { self.unit(f[e]) }
end
end
inc = -> n { n + 1 }
str = -> n { n.to_s }
listy_inc = Array.lift(inc)
listy_str = Array.lift(str)
Array.unit(3,4,5).bind(listy_inc).bind(listy_str) #=> ["4", "5", "6"]
# Note that listy_inc and listy_str cannot be composed directly,
# as they don't have compatible type signature.
# Due to duck typing (Ruby will happily turn arrays into strings),
# in order to show this, a new function will have to be used:
doub = -> n { 2*n }
listy_doub = Array.lift(doub)
[3,4,5].bind(listy_inc).bind(listy_doub) #=> [8, 10, 12]
# Direct composition will cause a TypeError, as Ruby cannot evaluate 2*[4, 5, 6]
# Using bind with the composition is *supposed* to fail, no matter the programming language.
comp = -> f, g {-> x {f[g[x]]}}
[3,4,5].bind(comp[listy_doub, listy_inc]) #=> TypeError: Array can't be coerced into Fixnum
# Composition needs to be defined in terms of bind
class Array
def bind_comp(f, g)
bind(g).bind(f)
end
end
[3,4,5].bind_comp(listy_doub, listy_inc) #=> [8, 10, 12]
|
http://rosettacode.org/wiki/Multi-dimensional_array | Multi-dimensional array | For the purposes of this task, the actual memory layout or access method of this data structure is not mandated.
It is enough to:
State the number and extent of each index to the array.
Provide specific, ordered, integer indices for all dimensions of the array together with a new value to update the indexed value.
Provide specific, ordered, numeric indices for all dimensions of the array to obtain the arrays value at that indexed position.
Task
State if the language supports multi-dimensional arrays in its syntax and usual implementation.
State whether the language uses row-major or column major order for multi-dimensional array storage, or any other relevant kind of storage.
Show how to create a four dimensional array in your language and set, access, set to another value; and access the new value of an integer-indexed item of the array.
The idiomatic method for the language is preferred.
The array should allow a range of five, four, three and two (or two three four five if convenient), in each of the indices, in order. (For example, if indexing starts at zero for the first index then a range of 0..4 inclusive would suffice).
State if memory allocation is optimised for the array - especially if contiguous memory is likely to be allocated.
If the language has exceptional native multi-dimensional array support such as optional bounds checking, reshaping, or being able to state both the lower and upper bounds of index ranges, then this is the task to mention them.
Show all output here, (but you may judiciously use ellipses to shorten repetitive output text).
| #Scala | Scala | object MultiDimensionalArray extends App {
// Create a regular 4 dimensional array and initialize successive elements to the values 1 to 120
val a4 = Array.fill[Int](5, 4, 3, 2) { m += 1; m }
var m = 0
println("First element = " + a4(0)(0)(0)(0)) // access and print value of first element
println("Last element = " + a4.last.last.last.last)
a4(0)(0)(0)(0) = 121 // change value of first element
println(a4.flatten.flatten.flatten.mkString(", "))
} |
http://rosettacode.org/wiki/Multiplication_tables | Multiplication tables | Task
Produce a formatted 12×12 multiplication table of the kind memorized by rote when in primary (or elementary) school.
Only print the top half triangle of products.
| #ASIC | ASIC |
REM Multiplication tables
N = 12
PREDN = N - 1
WDTH = 3
CLS
FOR J = 1 TO PREDN
INTVAL = J
GOSUB PRINTINT:
PRINT " ";
NEXT J
INTVAL = N
GOSUB PRINTINT:
PRINT
FOR J = 0 TO PREDN
PRINT "----";
NEXT J
PRINT "+"
FOR I = 1 TO N
WDTH = 3
FOR J = 1 TO N
IF J < I THEN
PRINT " ";
ELSE
INTVAL = I * J
GOSUB PRINTINT:
PRINT " ";
ENDIF
NEXT J
PRINT "| ";
INTVAL = I
WDTH = 2
GOSUB PRINTINT:
PRINT
NEXT I
END
PRINTINT:
REM Writes the value of INTVAL in a field of the given WDTH
S2$ = STR$(INTVAL)
S2$ = LTRIM$(S2$)
SPNUM = LEN(S2$)
SPNUM = WDTH - SPNUM
S1$ = SPACE$(SPNUM)
PRINT S1$;
PRINT S2$;
RETURN
|
http://rosettacode.org/wiki/Multiple_regression | Multiple regression | Task
Given a set of data vectors in the following format:
y
=
{
y
1
,
y
2
,
.
.
.
,
y
n
}
{\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
X
i
=
{
x
i
1
,
x
i
2
,
.
.
.
,
x
i
n
}
,
i
∈
1..
k
{\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
Compute the vector
β
=
{
β
1
,
β
2
,
.
.
.
,
β
k
}
{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}
using ordinary least squares regression using the following equation:
y
j
=
Σ
i
β
i
⋅
x
i
j
,
j
∈
1..
n
{\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
You can assume y is given to you as a vector (a one-dimensional array), and X is given to you as a two-dimensional array (i.e. matrix).
| #R | R | x <- c(1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83)
y <- c(52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46)
lm( y ~ x + I(x^2)) |
http://rosettacode.org/wiki/Multiple_regression | Multiple regression | Task
Given a set of data vectors in the following format:
y
=
{
y
1
,
y
2
,
.
.
.
,
y
n
}
{\displaystyle y=\{y_{1},y_{2},...,y_{n}\}\,}
X
i
=
{
x
i
1
,
x
i
2
,
.
.
.
,
x
i
n
}
,
i
∈
1..
k
{\displaystyle X_{i}=\{x_{i1},x_{i2},...,x_{in}\},i\in 1..k\,}
Compute the vector
β
=
{
β
1
,
β
2
,
.
.
.
,
β
k
}
{\displaystyle \beta =\{\beta _{1},\beta _{2},...,\beta _{k}\}}
using ordinary least squares regression using the following equation:
y
j
=
Σ
i
β
i
⋅
x
i
j
,
j
∈
1..
n
{\displaystyle y_{j}=\Sigma _{i}\beta _{i}\cdot x_{ij},j\in 1..n}
You can assume y is given to you as a vector (a one-dimensional array), and X is given to you as a two-dimensional array (i.e. matrix).
| #Racket | Racket |
#lang racket
(require math)
(define T matrix-transpose)
(define (fit X y)
(matrix-solve (matrix* (T X) X) (matrix* (T X) y)))
|
http://rosettacode.org/wiki/Multifactorial | Multifactorial | The factorial of a number, written as
n
!
{\displaystyle n!}
, is defined as
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
.
Multifactorials generalize factorials as follows:
n
!
=
n
(
n
−
1
)
(
n
−
2
)
.
.
.
(
2
)
(
1
)
{\displaystyle n!=n(n-1)(n-2)...(2)(1)}
n
!
!
=
n
(
n
−
2
)
(
n
−
4
)
.
.
.
{\displaystyle n!!=n(n-2)(n-4)...}
n
!
!
!
=
n
(
n
−
3
)
(
n
−
6
)
.
.
.
{\displaystyle n!!!=n(n-3)(n-6)...}
n
!
!
!
!
=
n
(
n
−
4
)
(
n
−
8
)
.
.
.
{\displaystyle n!!!!=n(n-4)(n-8)...}
n
!
!
!
!
!
=
n
(
n
−
5
)
(
n
−
10
)
.
.
.
{\displaystyle n!!!!!=n(n-5)(n-10)...}
In all cases, the terms in the products are positive integers.
If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:
Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.
Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.
| #Go | Go | package main
import "fmt"
func multiFactorial(n, k int) int {
r := 1
for ; n > 1; n -= k {
r *= n
}
return r
}
func main() {
for k := 1; k <= 5; k++ {
fmt.Print("degree ", k, ":")
for n := 1; n <= 10; n++ {
fmt.Print(" ", multiFactorial(n, k))
}
fmt.Println()
}
} |
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