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25,200 | this timehowevera has no unvisited neighborsso we pop it off the stack but now there' nothing left to popwhich brings up rule remember rule if you can' follow rule or rule you're finished table shows how the stack looks in the various stages of this processas applied to figure table stack contents during depth-first se... |
25,201 | done the contents of the stack is the route you took from the starting vertex to get where you are as you move away from the starting vertexyou push vertices as you go as you move back toward the starting vertexyou pop them the order in which you visit the vertices is abfhcdgie you might say that the depth-first search... |
25,202 | there' no way to delete individual edges or verticesso if you make mistakeyou'll need to start over by clicking the new buttonwhich erases all existing vertices and edges (it warns you before it does this clicking the view button switches you to the adjacency matrix for the graph you've madeas shown in figure clicking ... |
25,203 | depth-first search you can see how this code embodies the three rules listed earlier it loops until the stack is empty within the loopit does four things it examines the vertex at the top of the stackusing peek( it tries to find an unvisited neighbor of this vertex if it doesn' find oneit pops the stack if it finds suc... |
25,204 | thegraph addedge( )thegraph addedge( )thegraph addedge( )/ab /bc /ad /de system out print("visits")thegraph dfs()/depth-first search system out println()figure shows the graph created by this code here' the outputvisitsabcde figure graph used by dfs java and bfs javasearches you can modify this code to create the graph... |
25,205 | /take item off stack return st[top--]public int peek(/peek at top of stack return st[top]public boolean isempty(/true if nothing on stack return (top =- )/end class stackx ///////////////////////////////////////////////////////////////class vertex public char label/label ( ' 'public boolean wasvisited/public vertex(cha... |
25,206 | /public void addedge(int startint endadjmat[start][end adjmat[end][start /public void displayvertex(int vsystem out print(vertexlist[vlabel)/public void dfs(/depth-first search /begin at vertex vertexlist[ wasvisited true/mark it displayvertex( )/display it thestack push( )/push it while!thestack isempty(/until stack e... |
25,207 | /end class graph ///////////////////////////////////////////////////////////////class dfsapp public static void main(string[argsgraph thegraph new graph()thegraph addvertex(' ')/ (start for dfsthegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addedge( )thegraph... |
25,208 | rule visit the next unvisited vertex (if there is onethat' adjacent to the current vertexmark itand insert it into the queue remember rule if you can' carry out rule because there are no more unvisited verticesremove vertex from the queue (if possibleand make it the current vertex remember rule if you can' carry out ru... |
25,209 | fg remove visit gh remove visit hi remove remove done at each momentthe queue contains the vertices that have been visited but whose neighbors have not yet been fully explored (contrast this with the depth-first searchwhere the contents of the stack is the route you took from the starting point to the current vertex th... |
25,210 | /get onevertexlist[ wasvisited true/mark it displayvertex( )/display it thequeue insert( )/insert it /end while(unvisited neighbors/end while(queue not empty/queue is emptyso we're done for(int = <nvertsj++vertexlist[jwasvisited false/reset flags /end bfs(given the same graph as in dfs java (shown earlier in figure )th... |
25,211 | if(front =sizefront return temppublic boolean isempty(/true if queue is empty return rear+ ==front |(front+size- ==rear)/end class queue ///////////////////////////////////////////////////////////////class vertex public char label/label ( ' 'public boolean wasvisited/public vertex(char lab/constructor label labwasvisit... |
25,212 | public void addvertex(char labvertexlist[nverts++new vertex(lab)/public void addedge(int startint endadjmat[start][end adjmat[end][start /public void displayvertex(int vsystem out print(vertexlist[vlabel)/public void bfs(/breadth-first search /begin at vertex vertexlist[ wasvisited true/mark it displayvertex( )/display... |
25,213 | return - /end getadjunvisitedvert(//end class graph ///////////////////////////////////////////////////////////////class bfsapp public static void main(string[argsgraph thegraph new graph()thegraph addvertex(' ')/ (start for dfsthegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addverte... |
25,214 | - shows edges abbccdand debut edges acceedand db would do just as well the arithmetically inclined will note that the number of edges in minimum spanning tree is always one less than the number of vertices ve= - remember that we're not worried here about the length of the edges we're not trying to find minimum physical... |
25,215 | /reset flags vertexlist[jwasvisited false/end mst(as you can seethis code is very similar to dfs(in the else statementhoweverthe current vertex and its next unvisited neighbor are displayed these two vertices define the edge that the algorithm is currently traveling to get to new vertexand it' these edges that make up ... |
25,216 | ///////////////////////////////////////////////////////////////class stackx private final int size private int[stprivate int toppublic stackx(/constructor st new int[size]/make array top - public void push(int /put item on stack st[++topjpublic int pop(/take item off stack return st[top--]public int peek(/peek at top o... |
25,217 | /constructor vertexlist new vertex[max_verts]/adjacency matrix adjmat new int[max_verts][max_verts]nverts for(int = <max_vertsj++/set adjacency for(int = <max_vertsk++/matrix to adjmat[ ][ thestack new stackx()/end constructor /public void addvertex(char labvertexlist[nverts++new vertex(lab)/public void addedge(int sta... |
25,218 | vertexlist[vwasvisited true/mark it thestack push( )/push it /display edge displayvertex(currentvertex)/from currentv displayvertex( )/to system out print(")/end while(stack not empty/stack is emptyso we're done for(int = <nvertsj++/reset flags vertexlist[jwasvisited false/end tree //returns an unvisited vertex adj to ... |
25,219 | system out print("minimum spanning tree")thegraph mst()/minimum spanning tree system out println()/end main(/end class mstapp ///////////////////////////////////////////////////////////////topological sorting with directed graphs topological sorting is another operation that can be modeled with graphs it' useful in sit... |
25,220 | in programthe difference between non-directed graph and directed graph is that an edge in directed graph has only one entry in the adjacency matrix figure shows small directed graphtable shows its adjacency matrix table adjacency matrix for small directed graph each edge is represented by single the row labels show whe... |
25,221 | the english courses and firstfor examplecfbaedgh this also satisfies all the prerequisites there are many other possible orderings as well when you use an algorithm to generate topological sortthe approach you take and the details of the code determine which of various valid sortings are generated topological sorting c... |
25,222 | steps and are repeated until all the vertices are gone at this pointthe list shows the vertices arranged in topological order you can see the process at work by using the graphd applet construct the graph of figure (or any other graphif you preferby double-clicking to make vertices and dragging to make edges then repea... |
25,223 | /remember how many verts while(nverts /while vertices remain/get vertex with no successorsor - int currentvertex nosuccessors()if(currentvertex =- /must be cycle system out println("errorgraph has cycles")return/insert vertex label in sorted array (start at endsortedarray[nverts- vertexlist[currentvertexlabeldeletevert... |
25,224 | /(or - if no such vertsboolean isedge/edge from row to column in adjmat for(int row= row<nvertsrow++/for each vertexisedge false/check edges for(int col= col<nvertscol++ifadjmat[row][col /if edge to /anotherisedge truebreak/this vertex /has successor /try another if!isedge /if no edgesreturn row/has no successors retur... |
25,225 | thegraph addedge( )/fh /gh thegraph topo()/do the sort /end main(once the graph is createdmain(calls topo(to sort the graph and display the result here' the outputtopologically sorted orderbaedgcfh of courseyou can rewrite main(to generate other graphs the complete topo java program you've seen most of the routines in ... |
25,226 | adjmat[ ][ sortedarray new char[max_verts]/end constructor /matrix to /sorted vert labels /public void addvertex(char labvertexlist[nverts++new vertex(lab)/public void addedge(int startint endadjmat[start][end /public void displayvertex(int vsystem out print(vertexlist[vlabel)/public void topo(/toplogical sort int orig... |
25,227 | successors /(or - if no such vertsboolean isedge/edge from row to column in adjmat for(int row= row<nvertsrow++/for each vertexisedge false/check edges for(int col= col<nvertscol++ifadjmat[row][col /if edge to /anotherisedge truebreak/this vertex /has successor /try another if!isedge /if no edgesreturn row/has no succe... |
25,228 | //end class graph ///////////////////////////////////////////////////////////////class topoapp public static void main(string[argsgraph thegraph new graph()thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addve... |
25,229 | algorithm can be based on queue minimum spanning tree (mstconsists of the minimum number of edges necessary to connect all graph' vertices slight modification of the depth-first search algorithm on an unweighted graph yields its minimum spanning tree in directed graphedges have direction (often indicated by an arrowa t... |
25,230 | dollarsof installing cable link between two cities (notice that some links are impractical because of distance or terrainfor examplewe will assume that it' too far from ajo to colina or from danza to florso these links don' need to be considered and don' appear on the graph figure weighted graph how can we pick route t... |
25,231 | now find this graph' minimum spanning tree by stepping through the algorithm with the tree key the result should be the minimum spanning tree shown in figure figure the minimum spanning tree the applet should discover that the minimum spanning tree consists of the edges adabbeecand cffor total edge weight of the order ... |
25,232 | building the ajo-danza link at this point you figure you can send out the construction crew to actually install the cable from ajo to danza how can you be sure the ajo-danza route will eventually be part of the cheapest solution (the minimum spanning tree)so faryou only know the cost of two links in the system don' you... |
25,233 | therethere' no point giving any further consideration to this link the route on which cable has just been installed is always removed from the list at this point it may not be obvious what to do next there are many potential links to choose from what do you imagine is the best strategy nowhere' the ruleremember rulefro... |
25,234 | notedthere' no point in considering links to towns that are already connectedeven by an indirect route from this list we can see that the cheapest route is bordo-erizoat million dollars you send out the crew to install this cable linkand you build an office in erizo (refer to figure building the erizo-colina link from ... |
25,235 | outline of the algorithm let' restate the algorithm in graph terms (as opposed to cable tv terms)start with vertexput it in the tree then repeatedly do the following find all the edges from the newest vertex to other vertices that aren' in the tree put these edges in the priority queue pick the edge with the lowest wei... |
25,236 | bc dc ef ec ef ec bc (ec )dc (ec ef cf cf ef remember that an edge consists of letter for the source (startingvertex of the edgea letter for the destination (ending vertex)and number for the weight the second column in this table corresponds to the lists you kept when constructing the cable tv system it shows all edges... |
25,237 | int distance adjmat[currentvert][ ]ifdistance =infinity/skip if no edge continueputinpq(jdistance)/put it in pq (maybeif(thepq size()== /no vertices in pqsystem out println(graph not connected")return/remove edge with minimum distancefrom pq edge theedge thepq removemin()int sourcevert theedge srcvertcurrentvert theedg... |
25,238 | in step the edge with the minimum weight is removed from the priority queue this edge and its destination vertex are added to the treeand the source vertex (currentvertand destination vertex are displayed at the end of mstw()the vertices are removed from the tree by resetting their isintree variables that isn' strictly... |
25,239 | /mstw java /demonstrates minimum spanning tree with weighted graphs /to run this programc>java mstwapp import java awt *///////////////////////////////////////////////////////////////class edge public int srcvert/index of vertex starting edge public int destvert/index of vertex ending edge public int distance/distance ... |
25,240 | public void removen(int /remove item at for(int =nj<size- ++/move items down quearray[jquearray[ + ]size--public edge peekmin(/peek at minimum item return quearray[size- ]public int size(return size/return number of items public boolean isempty(return (size== )/true if queue is empty public edge peekn(int nreturn quear... |
25,241 | private final int infinity private vertex vertexlist[]/list of vertices private int adjmat[][]/adjacency matrix private int nverts/current number of vertices private int currentvertprivate priorityq thepqprivate int ntree/number of verts in tree /public graph(/constructor vertexlist new vertex[max_verts]/adjacency matr... |
25,242 | /insert edges adjacent to currentvert into pq for(int = <nvertsj++/for each vertexif( ==currentvert/skip if it' us continueif(vertexlist[jisintree/skip if in the tree continueint distance adjmat[currentvert][ ]ifdistance =infinity/skip if no edge continueputinpq(jdistance)/put it in pq (maybeif(thepq size()== /no verti... |
25,243 | /else no actionjust leave the old vertex there /end if else /no edge with same destination vertex /so insert new one edge theedge new edge(currentvertnewvertnewdist)thepq insert(theedge)/end putinpq(//end class graph ///////////////////////////////////////////////////////////////class mstwapp public static void main(st... |
25,244 | that of finding the shortest path between two given vertices the solution to this problem is applicable to wide variety of real-world situationsfrom the layout of printed circuit boards to project scheduling it is more complex problem than we've seen beforeso let' start by looking at (somewhatreal-world scenario in the... |
25,245 | directed graph dijkstra' algorithm the solution we'll show for the shortest-path problem is called dijkstra' algorithmafter edsger dijkstrawho first described it in this algorithm is based on the adjacency matrix representation of graph somewhat surprisinglyit finds not only the shortest path from one specified vertex ... |
25,246 | as that used in the minimum spanning tree problem (the cable tv installationthereyou picked the least expensive single link (edgefrom the connected towns to an unconnected town hereyou pick the least expensive total route from ajo to town with no agent in this particular point in your investigation these two approaches... |
25,247 | from this we decide that from now on we won' need to update the entry for the cheapest fare from ajo to bordo this fare will not changeno matter what we find out about other towns we'll put an next to it to show that there' an agent in the town and that the cheapest fare to it is fixed three kinds of town as in the min... |
25,248 | (via ajoinf (via ajoinf step (via ajo) (via bordo (via ajoinf step (via ajo) (via danza (via ajo) (via danzafigure following step in the shortest-path algorithm the fourth agentin colina now the cheapest path to any town without an agent is the $ trip from ajo to colinagoing via danza accordinglyyou dispatch an agent o... |
25,249 | the last agentin erizo the cheapest path from ajo to any town you know about that doesn' have an agent is now $ to erizovia danza and colina you dispatch an agent to erizobut she reports that there are no routes from erizo to towns without agents (there' route to bordobut bordo has an agent table shows the final line i... |
25,250 | using the workshop applet let' see how this looks using the graphdw (for directed and weightedworkshop applet use the applet to create the graph from figure the result should look something like figure (we'll see how to make the table appear below the graph in moment this is weighteddirected graphso to make an edgeyou ... |
25,251 | enclosed in parentheses the parent is the vertex you reached just before you reached the destination vertex in this case the parents are all because we've only moved one edge away from if fare is unknown (or meaninglessas from to ait' shown as infinityrepresented by "inf,as in the rail-fare notebook entries notice that... |
25,252 | to ea to ( plus edge be (infgreater than or equal to to (infthe newly calculated route from to via ( plus infinityis still greater than or equal to the current one in the array (infinity)so the column is not changed the shortestpath array now looks like table table step the shortest-path array inf( ( ( (ainf(anow we ca... |
25,253 | inf( ( ( ( (dthe shortest path from to non-tree vertex is to vertex cso is added to the tree next time through the shortest-path arrayonly the distance to is considered it can be shortened by going via cso we have the entries shown in table table step the shortest-path array inf( ( ( ( (cnow the last vertexeis added to... |
25,254 | need not be explicitly stored it' only necessary to store the parent of the destination vertex the parent is the vertex reached just before the destination we've seen this in the workshop appletwhereif (dappears in the columnit means that the cheapest path from to is and is the last vertex before on this path there are... |
25,255 | /reset currentvert currentvert indexmin/to closest vert starttocurrent spath[indexmindistance/minimum distance from starttree is /to currentvertand is starttocurrent /put current vertex in tree vertexlist[currentvertisintree truentree++adjust_spath()/update spath[array /end while(ntree<nvertsdisplaypaths()/display spat... |
25,256 | with the column number (the array indexof the entry with the minimum distance public int getmin(/get entry from spath /with minimum distance int mindist infinity/assume large minimum int indexmin for(int = <nvertsj++/for each vertex/if it' in tree and if!vertexlist[jisintree &/smaller than old one spath[jdistance mindi... |
25,257 | column++continue/calculate distance for one spath entry /get edge from currentvert to column int currenttofringe adjmat[currentvert][column]/add distance from start int starttofringe starttocurrent currenttofringe/get distance of current spath entry int spathdist spath[columndistance/compare distance from start with sp... |
25,258 | the path java program listing is the complete code for the path java program its various components were all discussed earlier listing the path java program /path java /demonstrates shortest path with weighteddirected graphs /to run this programc>java pathapp import java awt *///////////////////////////////////////////... |
25,259 | private int ntreeprivate distpar spath[]private int currentvertprivate int starttocurrent/current number of vertices /number of verts in tree /array for shortest-path data /current vertex /distance to currentvert /public graph(/constructor vertexlist new vertex[max_verts]/adjacency matrix adjmat new int[max_verts][max_... |
25,260 | if(mindist =infinity/if all infinite /or in treesystem out println("there are unreachable vertices")break/spath is complete else /reset currentvert currentvert indexmin/to closest vert starttocurrent spath[indexmindistance/minimum distance from starttree is /to currentvertand is starttocurrent /put current vertex in tr... |
25,261 | /skip starting vertex while(column nverts/go across columns /if this column' vertex already in treeskip it ifvertexlist[columnisintree column++continue/calculate distance for one spath entry /get edge from currentvert to column int currenttofringe adjmat[currentvert][column]/add distance from start int starttofringe st... |
25,262 | graph thegraph new graph()thegraph addvertex(' ')/ (startthegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addvertex(' ')/ thegraph addedge( )thegraph addedge( )thegraph addedge( )thegraph addedge( )thegraph addedge( )thegraph addedge( )thegraph addedge( )thegraph addedge( )/ab /ad /bc... |
25,263 | we've used the adjacency matrix approach throughout this you can consult sedgewick (see appendix "further reading"and other writers for examples of graph algorithms using the adjacency list approach summary in weighted graphedges have an associated number called the weightwhich might represent distancescoststimesor oth... |
25,264 | specialized structures such as stackswhich allow access to only certain data itemswhich of these general-purpose data structures is appropriate for given problemfigure shows first approximation to this question howeverthere are many factors besides those shown in the figure for more detailwe'll explore some general con... |
25,265 | revert to more sophisticated data structures references are faster java has an advantage over some languages in the speed with which objects can be manipulatedbecausein most data structuresjava stores only referencesnot actual objects therefore most algorithms will run faster than in languages where actual objects occu... |
25,266 | faster than in an array)solike arrayslinked lists are best used when the amount of data is comparatively small linked list is somewhat more complicated to program than an arraybut is simple compared with tree or hash table binary search trees binary tree is the first structure to consider when arrays and linked lists p... |
25,267 | table summarizes the speeds of the various general-purpose data storage structures using big notation table general-purpose data storage structures data structure search insertion deletion traversal array (no( ( -ordered array (logno(no(no(nlinked list (no( ( -ordered linked list (no(no(no(nbinary tree (averageo(logno(... |
25,268 | these adts can be seen as conceptual aids their functionality could be obtained using the underlying structure (such as an arraydirectlybut the reduced interface they offer simplifies many problems these adts can' be conveniently searched for an item by key value or traversed stack stack is used when you want access on... |
25,269 | insertion deletion comment stack (array or linked ( listo( deletes most recently inserted item queue (array or linked listo( ( deletes least recently inserted item priority queue (ordered arrayo(no( deletes highestpriority item (logndeletes highestpriority item priority queue (heapo(logncomparison of special-purpose st... |
25,270 | efficient because the most recently inserted item is placed at the end of the arraywhere it' also easy to delete it stack overflow can occurbut is not likely if the array is reasonably sizedbecause stacks seldom contain huge amounts of data if the stack will contain lot of data and the amount can' be predicted accurate... |
25,271 | priority item priority queue (heapo(logno(logndeletes highestpriority item comparison of special-purpose structures table shows the big times for stacksqueuesand priority queues these structures don' support searching or traversal sorting as with the choice of data structuresit' worthwhile initially to try slow but sim... |
25,272 | ( *logno( *lognfair yes heapsort ( *logno( *lognfair no table summarizes the running time for various sorting algorithms the column labeled comparison attempts to estimate the minor speed differences between algorithms with the same average big times (there' no entry for shellsort because there are no other algorithms ... |
25,273 | correspond to blocks on the disk as in other treesthe algorithms find their way down the treereading one block at each level -trees provide searchinginsertionand deletion of records in (logntime this is quite fast and works even for very large files howeverthe programming is not trivial hashing if it' acceptable to use... |
25,274 | appendix list appendix how to run the workshop applets and example aprograms appendix further reading bappendix ahow to run the workshop applets and example programs overview in this appendix we discuss the details of running the workshop applets and the example programs the workshop applets are graphics-based demonstr... |
25,275 | "advancedstructureshoweverare characterized by their change of value and structure during the execution of program more sophisticated techniques are therefore needed for their implementation the sequence appears as hybrid in this classification it certainly varies its lengthbut that change in structure is of trivial na... |
25,276 | reader is led through gradual development of the programhe is given various snapshots in the evolution of programwhereby this development becomes manifest as stepwise refinement of the details consider it essential that programs are shown in final form with sufficient attention to detailsfor in programmingthe devil hid... |
25,277 | preface to the edition this new edition incorporates many revisions of details and several changes of more significant nature they were all motivated by experiences made in the ten years since the first edition appeared most of the contents and the style of the texthoweverhave been retained we briefly summarize the maj... |
25,278 | notation the following notationsadopted from publications of dijkstraare used in this book in logical expressionsthe character denotes conjunction and is pronounced as and the character oboznachaet otritsanie chitaetsia kak denotes negation and is pronounced as not boldface and are used to denote the universal and exis... |
25,279 | fundamental data structures introduction the modern digital computer was invented and intended as device that should facilitate and speed up complicated and time-consuming computations in the majority of applications its capability to store and access large amounts of information plays the dominant part and is consider... |
25,280 | knowledge that the data are to be stored in computermay lead to binarypositional representation of integersand the final decision could be to represent binary digits by the electric charge in semiconductor storage device evidentlythe first decision in this chain is mainly influenced by the problem situationand the late... |
25,281 | so on this notion of classification is equally if not more important in data processing we will adhere to the principle that every constantvariableexpressionor function is of certain type this type essentially characterizes the set of values to which constant belongsor which can be assumed by variable or expressionor w... |
25,282 | have to be some standardpredefined types they usually include numbers and logical values if an ordering exists among the individual valuesthen the type is said to be ordered or scalar in oberonall unstructured types are orderedin the case of explicit enumerationthe values are assumed to be ordered by their enumeration ... |
25,283 | division (/divwhereas the slash denotes ordinary division resulting in value of type realthe operator div denotes integer division resulting in value of type integer if we define the quotient div and the remainder mod nthe following relations holdassuming * and < < examples div mod - div - - mod we know that dividing b... |
25,284 | the type boolean the two values of the standard type boolean are denoted by the identifiers true and false the boolean operators are the logical conjunctiondisjunctionand negation whose values are defined in table the logical conjunction is denoted by the symbol &the logical disjunction by orand negation by "~note that... |
25,285 | (" < ( <" "implies that is capital letter (" < ( <" "implies that is lower-case letter (" < ( <" "implies that is decimal digit the type char contains non-printingblank character and line-end character that may be used as separators this is text fig representations of text the availability of two standard type transfer... |
25,286 | operatorwhich is classified as relational operator following are examples of set expressions and their fully parenthesized equivalentsr + ( *st rst ( *tr + ( -st + ( /tx in in ( + the array structure the array is probably the most widely used data structurein some languages it is even the only one available an array co... |
25,287 | generality not only provides most significant and powerful programming facilitybut at the same time it also gives rise to one of the most frequently encountered programming mistakesthe resulting value may be outside the interval specified as the range of indices of the array we will assume that decent computing systems... |
25,288 | procedure power (var wtexts writerninteger) (adens *(*compute decimal representation of negative powers of *var ikrintegerdarray of integerbegin for : to - do texts write( ") : for : to - do : * [ ] [ : div : mod texts write(wchr( [iord(" "))endd[ : texts write( " ")texts writeln(wend end power the resulting output tex... |
25,289 | examples type complex record reimreal end type date record daymonthyearinteger end type person record namefirstnamenamebirthdatedatemaleboolean end we may visualize particularrecord-structured values offor examplethe variables zcomplex ddate pperson as shown in fig complex date person smith - john true fig records of t... |
25,290 | entirely correctlybut it is close enough for practical purposesand it is the responsibility of the programmer to ensure that meaningless values never occur during the execution of program the following short excerpt from program shows the use of record variables its purpose is to count the number of persons represented... |
25,291 | case)then is usually rounded up to the next larger integer each array component then occupies wordswhereby - words are left unused (see figs and rounding up of the number of words needed to the next whole number is called padding the storage utilization factor is the quotient of the minimal amounts of storage needed to... |
25,292 | data structures howeverit should be possible to indicate the desirability of packing at least in those cases in which more than one component would fit into single wordi when gain of storage economy by factor of and more could be achieved we propose the convention to indicate the desirability of packing by prefixing th... |
25,293 | these logical operations are available on all digital computersand moreover they operate concurrently on all corresponding elements (bitsof word it therefore appears that in order to be able to implement the basic set operations in an efficient mannersets must be represented in smallfixed number of words upon which not... |
25,294 | filled this results in very significantly more effective use of secondary storage given sequential access onlythe buffering mechanism is reasonably straightforward for all sequences and all media it can therefore safely be built into system for general useand the programmer need not be burdened by incorporating it in t... |
25,295 | sequence is generated by appending elements at its end after having placed rider on the file assuming the declaration var rrider we position the rider on the file by the statement set(rfposwhere pos designates the beginning of the file (sequencea typical pattern for generating the sequence iswhile more do compute next ... |
25,296 | definition files (adens _files *type file(*sequence of characters*rider record eofboolean endprocedure new(var namearray of char)fileprocedure old(var namearray of char)fileprocedure close(var ffile)procedure set(var rridervar ffileposinteger)procedure write(var rriderchchar)procedure read(var rridervar chchar)procedur... |
25,297 | end closeprocedure set (var rriderffileposinteger)begin (*assume nil* :fr eof :falseif pos > then if pos < len then pos :pos else pos : len end else pos : end end setprocedure write (var rriderchchar)begin if ( pos < len( pos maxlengththen [ pos:chinc( pos)if pos len then inc( lenend else eof :true end end writeprocedu... |
25,298 | relatively large blocks once the tape is moving similar conditions hold for magnetic diskswhere the data are allocated on tracks with fixed number of blocks of fixed sizethe so-called block size in facta disk should be regarded as an array of blockseach block being read or written as wholecontaining typically bytes wit... |
25,299 | module buffer(*implements circular buffers*const (*buffer size*var ninoutintegerbufarray of charprocedure deposit (xchar)begin if then halt endinc( )buf[in:xin :(in mod end depositprocedure fetch (var xchar)begin if then halt enddec( ) :buf[out]out :(out mod end fetchbegin : in : out : end buffer this simple implementa... |
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