Forge: Quality-Aware Reinforcement Learning for NP-Hard Optimization in LLMs
Paper โข 2605.08905 โข Published
data_source stringclasses 10
values | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
bootcamp/NpKnapsack | [
{
"content": "'Introduction': 'You are a great expert solving knapsack question. You should propose a solution to this question.', 'Task description': \"The knapsack problem's goal is to choose a subset of items to pack into a limited-capacity bag in a way that maximizes total value without exceeding the weight... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"capacity\": 185, \"items\": {\"0\": {\"weight\": 13, \"value\": 30}, \"1\": {\"weight\": 14, \"value\": 28}, \"2\": {\"weight\": 15, \"value\": 37}, \"7\": {\"weight\": 12, \"value\": 26}, \"9\": {\"weight\": 17, \"value\": 35}, \"12\": {\"weight\": 25, \... | {
"generator_name": "easy",
"index": 149,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpKnapsack | [
{
"content": "'Introduction': 'You are a great expert solving knapsack question. You should propose a solution to this question.', 'Task description': \"The knapsack problem's goal is to choose a subset of items to pack into a limited-capacity bag in a way that maximizes total value without exceeding the weight... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"capacity\": 166, \"items\": {\"4\": {\"weight\": 19, \"value\": 45}, \"5\": {\"weight\": 25, \"value\": 57}, \"7\": {\"weight\": 10, \"value\": 20}, \"8\": {\"weight\": 23, \"value\": 49}, \"9\": {\"weight\": 15, \"value\": 27}, \"10\": {\"weight\": 6, \"... | {
"generator_name": "easy",
"index": 92,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumCliqueProblem | [
{
"content": "'Introduction': 'You are a great expert solving maximum-clique-problem question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Clique Problem aims to find a subset of vertices (a clique) where every two distinct vertices in the clique... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [\"2\", \"4\"], \"1\": [\"2\", \"3\"], \"2\": [\"0\", \"1\"], \"3\": [\"1\", \"4\"], \"4\": [\"0\", \"3\"]}, \"ground_truth\": 2}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 170,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpKnapsack | [
{
"content": "'Introduction': 'You are a great expert solving knapsack question. You should propose a solution to this question.', 'Task description': \"The knapsack problem's goal is to choose a subset of items to pack into a limited-capacity bag in a way that maximizes total value without exceeding the weight... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"capacity\": 164, \"items\": {\"1\": {\"weight\": 12, \"value\": 24}, \"3\": {\"weight\": 10, \"value\": 19}, \"4\": {\"weight\": 15, \"value\": 27}, \"5\": {\"weight\": 14, \"value\": 32}, \"7\": {\"weight\": 17, \"value\": 38}, \"10\": {\"weight\": 16, \... | {
"generator_name": "easy",
"index": 59,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumCliqueProblem | [
{
"content": "'Introduction': 'You are a great expert solving maximum-clique-problem question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Clique Problem aims to find a subset of vertices (a clique) where every two distinct vertices in the clique... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [\"1\", \"3\", \"6\", \"7\"], \"1\": [\"0\", \"3\", \"4\", \"5\", \"6\"], \"2\": [\"3\", \"4\", \"5\", \"6\", \"7\"], \"3\": [\"0\", \"1\", \"2\", \"4\", \"7\"], \"4\": [\"1\", \"2\", \"3\", \"5\", \"6\"], \"5\": [\"1\", \"2\", \"4\", \"6\"], \"6\": ... | {
"generator_name": "easy",
"index": 40,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpHamiltonianCycle | [
{
"content": "'Introduction': 'You are a great expert solving hamiltonian-cycle question. You should propose a solution to this question.', 'Task description': 'Your objective is to find a subgraph within a given graph G that contains a Hamiltonian circuit, which is a path that visits every vertex exactly once ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [16, 2, 14, 17, 18], \"1\": [10, 14, 8], \"2\": [0, 9, 5, 7, 14, 16], \"3\": [12, 8, 16], \"4\": [11, 18, 6, 9, 14], \"5\": [8, 17, 2, 11, 12, 14], \"6\": [9, 13, 4, 8, 18], \"7\": [13, 11, 2, 8, 10, 12, 18], \"8\": [3, 5, 1, 6, 7], \"9\": [2, 6, 4, ... | {
"generator_name": "easy",
"index": 10,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpGcpD | [
{
"content": "'Introduction': 'You are a great expert solving gcp-d question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph G = ๏ผV, E๏ผ, where V is a set of vertices and E is a set of edges, the Graph Coloring Problem (GCP) asks whether it is possible to assign ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [], \"1\": [7], \"2\": [9], \"3\": [5], \"4\": [], \"5\": [3], \"6\": [7], \"7\": [1, 6, 8, 9], \"8\": [7], \"9\": [2, 7]}, \"ground_truth\": 2}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 83,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpKnapsack | [
{
"content": "'Introduction': 'You are a great expert solving knapsack question. You should propose a solution to this question.', 'Task description': \"The knapsack problem's goal is to choose a subset of items to pack into a limited-capacity bag in a way that maximizes total value without exceeding the weight... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"capacity\": 126, \"items\": {\"0\": {\"weight\": 22, \"value\": 52}, \"4\": {\"weight\": 18, \"value\": 41}, \"5\": {\"weight\": 17, \"value\": 37}, \"13\": {\"weight\": 9, \"value\": 18}, \"15\": {\"weight\": 12, \"value\": 21}, \"16\": {\"weight\": 7, \... | {
"generator_name": "easy",
"index": 30,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"10\": 1, \"8\": 1, \"11\": 1, \"2\": 1, \"13\": 1, \"4\": 1, \"6\": 1}, \"1\": {\"2\": 1, \"3\": 1, \"4\": 1, \"6\": 1, \"7\": 1, \"12\": 1, \"13\": 1}, \"2\": {\"8\": 1, \"1\": 1, \"0\": 1, \"9\": 1, \"3\": 1, \"6\": 1}, \"3\": {\"10\": 1, \"8\":... | {
"generator_name": "easy",
"index": 155,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpHamiltonianCycle | [
{
"content": "'Introduction': 'You are a great expert solving hamiltonian-cycle question. You should propose a solution to this question.', 'Task description': 'Your objective is to find a subgraph within a given graph G that contains a Hamiltonian circuit, which is a path that visits every vertex exactly once ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [8, 7, 2, 4, 13, 15], \"1\": [15, 11, 3, 5, 7, 17], \"2\": [16, 8, 0, 5, 6], \"3\": [18, 14, 1, 6, 7], \"4\": [10, 15, 0, 11], \"5\": [16, 9, 1, 2, 15], \"6\": [14, 13, 2, 3, 12, 15], \"7\": [0, 12, 1, 3, 9, 10], \"8\": [2, 0, 11, 13, 17], \"9\": [17... | {
"generator_name": "easy",
"index": 198,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumCliqueProblem | [
{
"content": "'Introduction': 'You are a great expert solving maximum-clique-problem question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Clique Problem aims to find a subset of vertices (a clique) where every two distinct vertices in the clique... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [\"1\", \"2\", \"4\", \"5\"], \"1\": [\"0\", \"3\", \"4\", \"5\"], \"2\": [\"0\", \"4\", \"5\"], \"3\": [\"1\", \"4\", \"5\"], \"4\": [\"0\", \"1\", \"2\", \"3\", \"5\"], \"5\": [\"0\", \"1\", \"2\", \"3\", \"4\"]}, \"ground_truth\": 4}",
"style": ... | {
"generator_name": "easy",
"index": 84,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMinimumCut | [
{
"content": "'Introduction': 'You are a great expert solving minimum-cut question. You should propose a solution to this question.', 'Task description': 'Given a weighted undirected graph, the **Balanced Minimum Bisection Problem** aims to partition the graph into two disjoint subsets of **equal size** (or dif... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"40\": 1, \"4\": 3, \"1\": 8, \"2\": 10, \"3\": 9, \"7\": 10, \"8\": 8, \"9\": 8, \"10\": 9, \"11\": 10, \"12\": 8, \"38\": 1, \"29\": 3, \"16\": 2, \"5\": 4, \"26\": 5}, \"1\": {\"16\": 1, \"0\": 8, \"2\": 9, \"3\": 9, \"6\": 9, \"8\": 10, \"9\": ... | {
"generator_name": "easy",
"index": 115,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"10\": 1, \"8\": 1, \"4\": 1, \"7\": 1, \"14\": 1, \"1\": 1, \"3\": 1, \"5\": 1}, \"1\": {\"0\": 1, \"4\": 1, \"7\": 1, \"12\": 1}, \"2\": {\"8\": 1, \"12\": 1, \"3\": 1, \"9\": 1, \"11\": 1, \"14\": 1}, \"3\": {\"2\": 1, \"10\": 1, \"8\": 1, \"0\"... | {
"generator_name": "easy",
"index": 135,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"2\": 1, \"14\": 1, \"18\": 1, \"9\": 1, \"4\": 1, \"17\": 1, \"13\": 1, \"10\": 1, \"6\": 1, \"3\": 1, \"8\": 1}, \"1\": {\"14\": 1, \"5\": 1, \"4\": 1, \"17\": 1, \"11\": 1, \"6\": 1, \"3\": 1, \"15\": 1, \"8\": 1}, \"2\": {\"5\": 1, \"4\": 1, \"... | {
"generator_name": "easy",
"index": 39,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMeetingSchedule | [
{
"content": "'Introduction': 'You are a great expert solving meeting-schedule question. You should propose a solution to this question.', 'Task description': 'Given a set of meetings, each with a required set of attendees, their availability times, and available meeting rooms with capacities, the Meeting Sched... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"meetings\": {\"0\": {\"attendees\": [1, 2], \"duration\": 90}, \"1\": {\"attendees\": [0, 1, 2], \"duration\": 90}, \"2\": {\"attendees\": [0, 2], \"duration\": 90}, \"3\": {\"attendees\": [0, 2], \"duration\": 30}}, \"attendee_availability\": {\"0\": [[5... | {
"generator_name": "easy",
"index": 4,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpGcpD | [
{
"content": "'Introduction': 'You are a great expert solving gcp-d question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph G = ๏ผV, E๏ผ, where V is a set of vertices and E is a set of edges, the Graph Coloring Problem (GCP) asks whether it is possible to assign ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [10], \"1\": [11], \"2\": [6], \"3\": [], \"4\": [], \"5\": [10], \"6\": [2, 10], \"7\": [], \"8\": [9, 10], \"9\": [8], \"10\": [0, 5, 6, 8], \"11\": [1]}, \"ground_truth\": 2}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 196,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"4\": 1, \"8\": 1, \"11\": 1, \"7\": 1}, \"1\": {\"9\": 1, \"5\": 1, \"3\": 1, \"7\": 1, \"11\": 1}, \"2\": {\"9\": 1, \"18\": 1, \"6\": 1, \"5\": 1, \"10\": 1, \"14\": 1, \"8\": 1, \"12\": 1, \"15\": 1}, \"3\": {\"9\": 1, \"6\": 1, \"17\": 1, \"1\... | {
"generator_name": "easy",
"index": 34,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumCliqueProblem | [
{
"content": "'Introduction': 'You are a great expert solving maximum-clique-problem question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Clique Problem aims to find a subset of vertices (a clique) where every two distinct vertices in the clique... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [\"1\", \"3\"], \"1\": [\"0\", \"2\", \"3\"], \"2\": [\"1\", \"3\"], \"3\": [\"0\", \"1\", \"2\"]}, \"ground_truth\": 3}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 61,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpKnapsack | [
{
"content": "'Introduction': 'You are a great expert solving knapsack question. You should propose a solution to this question.', 'Task description': \"The knapsack problem's goal is to choose a subset of items to pack into a limited-capacity bag in a way that maximizes total value without exceeding the weight... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"capacity\": 166, \"items\": {\"5\": {\"weight\": 15, \"value\": 31}, \"7\": {\"weight\": 8, \"value\": 18}, \"9\": {\"weight\": 22, \"value\": 50}, \"10\": {\"weight\": 22, \"value\": 48}, \"16\": {\"weight\": 9, \"value\": 16}, \"17\": {\"weight\": 18, \... | {
"generator_name": "easy",
"index": 50,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMinimumCut | [
{
"content": "'Introduction': 'You are a great expert solving minimum-cut question. You should propose a solution to this question.', 'Task description': 'Given a weighted undirected graph, the **Balanced Minimum Bisection Problem** aims to partition the graph into two disjoint subsets of **equal size** (or dif... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"9\": 1, \"1\": 8, \"2\": 9, \"3\": 8, \"5\": 10, \"6\": 9, \"7\": 9, \"8\": 10, \"10\": 10, \"11\": 10, \"12\": 10, \"15\": 2, \"14\": 5, \"26\": 5, \"29\": 6, \"40\": 5, \"23\": 4, \"4\": 4}, \"1\": {\"30\": 2, \"0\": 8, \"3\": 10, \"5\": 9, \"7\... | {
"generator_name": "easy",
"index": 141,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpSetCover | [
{
"content": "'Introduction': 'You are a great expert solving set-cover question. You should propose a solution to this question.', 'Task description': 'Given a universal set U and a collection of subsets S, the Set Cover Problem aims to find the smallest possible sub-collection of S whose union equals U. In o... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"U\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], \"S\": {\"0\": [3, 1, 4, 0, 5], \"1\": [9, 2], \"2\": [10], \"3\": [1, 6, 8], \"4\": [6, 9, 7]}}, \"ground_truth\": 5}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 167,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"1\": 1, \"7\": 1, \"5\": 1, \"10\": 1, \"11\": 1, \"8\": 1, \"12\": 1}, \"1\": {\"7\": 1, \"2\": 1, \"5\": 1, \"0\": 1, \"10\": 1, \"11\": 1, \"12\": 1}, \"2\": {\"1\": 1, \"8\": 1, \"6\": 1}, \"3\": {\"7\": 1, \"5\": 1, \"10\": 1, \"8\": 1}, \"4\... | {
"generator_name": "easy",
"index": 33,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpGcpD | [
{
"content": "'Introduction': 'You are a great expert solving gcp-d question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph G = ๏ผV, E๏ผ, where V is a set of vertices and E is a set of edges, the Graph Coloring Problem (GCP) asks whether it is possible to assign ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [3, 7], \"1\": [4], \"2\": [], \"3\": [0, 8, 11], \"4\": [11, 1], \"5\": [10], \"6\": [10], \"7\": [0], \"8\": [3], \"9\": [11], \"10\": [5, 11, 6], \"11\": [9, 10, 4, 3]}, \"ground_truth\": 2}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 220,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpGcpD | [
{
"content": "'Introduction': 'You are a great expert solving gcp-d question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph G = ๏ผV, E๏ผ, where V is a set of vertices and E is a set of edges, the Graph Coloring Problem (GCP) asks whether it is possible to assign ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [1], \"1\": [2, 0, 10], \"2\": [1, 7], \"3\": [5, 6], \"4\": [11, 7], \"5\": [3], \"6\": [11, 3], \"7\": [2, 4], \"8\": [10], \"9\": [10], \"10\": [9, 1, 8], \"11\": [4, 6]}, \"ground_truth\": 2}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 160,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumCliqueProblem | [
{
"content": "'Introduction': 'You are a great expert solving maximum-clique-problem question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Clique Problem aims to find a subset of vertices (a clique) where every two distinct vertices in the clique... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [\"3\", \"6\"], \"1\": [\"2\", \"3\", \"4\", \"5\"], \"2\": [\"1\"], \"3\": [\"0\", \"1\", \"4\", \"5\", \"6\"], \"4\": [\"1\", \"3\", \"6\"], \"5\": [\"1\", \"3\", \"6\"], \"6\": [\"0\", \"3\", \"4\", \"5\"]}, \"ground_truth\": 3}",
"style": "rule... | {
"generator_name": "easy",
"index": 48,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpHamiltonianCycle | [
{
"content": "'Introduction': 'You are a great expert solving hamiltonian-cycle question. You should propose a solution to this question.', 'Task description': 'Your objective is to find a subgraph within a given graph G that contains a Hamiltonian circuit, which is a path that visits every vertex exactly once ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [9, 15, 5, 11], \"1\": [14, 10, 5, 15], \"2\": [5, 7, 14], \"3\": [13, 6, 5, 11, 14], \"4\": [10, 13, 5, 7, 9], \"5\": [15, 2, 0, 1, 3, 4, 6, 9], \"6\": [12, 3, 5, 11], \"7\": [2, 11, 4, 10, 13, 14], \"8\": [11, 14, 12], \"9\": [12, 0, 4, 5, 14], \"1... | {
"generator_name": "easy",
"index": 167,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMeetingSchedule | [
{
"content": "'Introduction': 'You are a great expert solving meeting-schedule question. You should propose a solution to this question.', 'Task description': 'Given a set of meetings, each with a required set of attendees, their availability times, and available meeting rooms with capacities, the Meeting Sched... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"meetings\": {\"0\": {\"attendees\": [0, 1, 2], \"duration\": 60}, \"1\": {\"attendees\": [0, 1, 2], \"duration\": 30}, \"2\": {\"attendees\": [1, 2], \"duration\": 30}, \"3\": {\"attendees\": [0, 1, 2], \"duration\": 60}}, \"attendee_availability\": {\"0\... | {
"generator_name": "easy",
"index": 53,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpTsp | [
{
"content": "'Introduction': 'You are a great expert solving TSP question. You should propose a solution to this question.', 'Task description': 'Given a set of cities and the distances between each pair of cities, the Traveling Salesman Problem (TSP) aims to find the shortest possible route that visits each c... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"0\": 0, \"1\": 81, \"2\": 33, \"3\": 69, \"4\": 54, \"5\": 15, \"6\": 51, \"7\": 44, \"8\": 82, \"9\": 89, \"10\": 42, \"11\": 16}, \"1\": {\"0\": 81, \"1\": 0, \"2\": 91, \"3\": 35, \"4\": 15, \"5\": 16, \"6\": 69, \"7\": 40, \"8\": 50, \"9\": 17... | {
"generator_name": "easy",
"index": 127,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpGcpD | [
{
"content": "'Introduction': 'You are a great expert solving gcp-d question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph G = ๏ผV, E๏ผ, where V is a set of vertices and E is a set of edges, the Graph Coloring Problem (GCP) asks whether it is possible to assign ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [3], \"1\": [], \"2\": [], \"3\": [0], \"4\": [7], \"5\": [], \"6\": [7], \"7\": [4, 6], \"8\": []}, \"ground_truth\": 2}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 15,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"5\": 1, \"9\": 1, \"10\": 1, \"2\": 1, \"8\": 1, \"12\": 1}, \"1\": {\"3\": 1, \"14\": 1, \"9\": 1}, \"2\": {\"0\": 1, \"14\": 1, \"9\": 1, \"10\": 1}, \"3\": {\"5\": 1, \"4\": 1, \"15\": 1, \"1\": 1, \"8\": 1, \"13\": 1}, \"4\": {\"3\": 1, \"14\"... | {
"generator_name": "easy",
"index": 179,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumCliqueProblem | [
{
"content": "'Introduction': 'You are a great expert solving maximum-clique-problem question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Clique Problem aims to find a subset of vertices (a clique) where every two distinct vertices in the clique... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [\"2\", \"4\", \"5\", \"6\"], \"1\": [\"2\", \"4\", \"6\"], \"2\": [\"0\", \"1\", \"5\"], \"3\": [\"5\", \"6\"], \"4\": [\"0\", \"1\", \"6\"], \"5\": [\"0\", \"2\", \"3\"], \"6\": [\"0\", \"1\", \"3\", \"4\"]}, \"ground_truth\": 3}",
"style": "rule... | {
"generator_name": "easy",
"index": 196,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpTsp | [
{
"content": "'Introduction': 'You are a great expert solving TSP question. You should propose a solution to this question.', 'Task description': 'Given a set of cities and the distances between each pair of cities, the Traveling Salesman Problem (TSP) aims to find the shortest possible route that visits each c... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"0\": 0, \"1\": 75, \"2\": 53, \"3\": 12, \"4\": 14, \"5\": 71, \"6\": 23, \"7\": 43, \"8\": 32, \"9\": 84, \"10\": 70, \"11\": 56, \"12\": 75, \"13\": 10, \"14\": 26, \"15\": 91, \"16\": 83, \"17\": 61, \"18\": 69, \"19\": 62}, \"1\": {\"0\": 75, ... | {
"generator_name": "easy",
"index": 155,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpGcpD | [
{
"content": "'Introduction': 'You are a great expert solving gcp-d question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph G = ๏ผV, E๏ผ, where V is a set of vertices and E is a set of edges, the Graph Coloring Problem (GCP) asks whether it is possible to assign ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [5], \"1\": [3, 7], \"2\": [], \"3\": [1], \"4\": [5], \"5\": [0, 4, 6], \"6\": [5], \"7\": [1], \"8\": []}, \"ground_truth\": 2}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 38,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"7\": 1, \"1\": 1, \"11\": 1, \"4\": 1, \"5\": 1, \"12\": 1, \"8\": 1, \"13\": 1, \"2\": 1, \"3\": 1, \"16\": 1}, \"1\": {\"15\": 1, \"0\": 1, \"4\": 1, \"12\": 1, \"8\": 1, \"3\": 1, \"2\": 1, \"9\": 1, \"10\": 1, \"16\": 1}, \"2\": {\"15\": 1, \"... | {
"generator_name": "easy",
"index": 56,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMeetingSchedule | [
{
"content": "'Introduction': 'You are a great expert solving meeting-schedule question. You should propose a solution to this question.', 'Task description': 'Given a set of meetings, each with a required set of attendees, their availability times, and available meeting rooms with capacities, the Meeting Sched... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"meetings\": {\"0\": {\"attendees\": [0, 1], \"duration\": 30}, \"1\": {\"attendees\": [1, 2], \"duration\": 60}, \"2\": {\"attendees\": [0, 1, 2], \"duration\": 30}, \"3\": {\"attendees\": [0, 1, 2], \"duration\": 60}}, \"attendee_availability\": {\"0\": ... | {
"generator_name": "easy",
"index": 97,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpKnapsack | [
{
"content": "'Introduction': 'You are a great expert solving knapsack question. You should propose a solution to this question.', 'Task description': \"The knapsack problem's goal is to choose a subset of items to pack into a limited-capacity bag in a way that maximizes total value without exceeding the weight... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"capacity\": 155, \"items\": {\"0\": {\"weight\": 14, \"value\": 34}, \"1\": {\"weight\": 6, \"value\": 12}, \"3\": {\"weight\": 9, \"value\": 20}, \"4\": {\"weight\": 12, \"value\": 25}, \"7\": {\"weight\": 16, \"value\": 36}, \"8\": {\"weight\": 14, \"va... | {
"generator_name": "easy",
"index": 39,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMinimumCut | [
{
"content": "'Introduction': 'You are a great expert solving minimum-cut question. You should propose a solution to this question.', 'Task description': 'Given a weighted undirected graph, the **Balanced Minimum Bisection Problem** aims to partition the graph into two disjoint subsets of **equal size** (or dif... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"17\": 1, \"16\": 2, \"13\": 3, \"2\": 9, \"3\": 9, \"5\": 10, \"6\": 10, \"7\": 8, \"8\": 8, \"9\": 10, \"10\": 9, \"11\": 10, \"12\": 8, \"38\": 4, \"29\": 1, \"24\": 4}, \"1\": {\"26\": 1, \"5\": 1, \"6\": 1, \"14\": 10, \"22\": 9, \"28\": 10, \... | {
"generator_name": "easy",
"index": 16,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpSubsetSum | [
{
"content": "'Introduction': 'You are a great expert solving subset-sum question. You should propose a solution to this question.', 'Task description': 'The subset sum problem asks whether a subset of numbers adds up to a given target. In this variation, the goal is not just to find any solution, but one that ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"target\": 21, \"numbers\": {\"0\": 2, \"1\": 2, \"2\": 5, \"3\": 2, \"4\": 1, \"5\": 4, \"6\": 5}}, \"ground_truth\": 7}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 11,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpTsp | [
{
"content": "'Introduction': 'You are a great expert solving TSP question. You should propose a solution to this question.', 'Task description': 'Given a set of cities and the distances between each pair of cities, the Traveling Salesman Problem (TSP) aims to find the shortest possible route that visits each c... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"0\": 0, \"1\": 60, \"2\": 83, \"3\": 39, \"4\": 38, \"5\": 38, \"6\": 88, \"7\": 94, \"8\": 76, \"9\": 73, \"10\": 19, \"11\": 34, \"12\": 78, \"13\": 25}, \"1\": {\"0\": 60, \"1\": 0, \"2\": 94, \"3\": 51, \"4\": 86, \"5\": 94, \"6\": 19, \"7\": ... | {
"generator_name": "easy",
"index": 83,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMaximumSet | [
{
"content": "'Introduction': 'You are a great expert solving maximum-set question. You should propose a solution to this question.', 'Task description': 'Given an undirected graph, the Maximum Independent Set Problem aims to find the largest set of vertices where no two vertices are adjacent (i.e., no two vert... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"13\": 1, \"9\": 1, \"14\": 1, \"17\": 1, \"19\": 1, \"4\": 1, \"2\": 1, \"15\": 1}, \"1\": {\"9\": 1, \"14\": 1, \"17\": 1, \"18\": 1, \"4\": 1, \"5\": 1, \"2\": 1, \"16\": 1, \"8\": 1, \"15\": 1}, \"2\": {\"1\": 1, \"9\": 1, \"19\": 1, \"4\": 1, ... | {
"generator_name": "easy",
"index": 118,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpMinimumCut | [
{
"content": "'Introduction': 'You are a great expert solving minimum-cut question. You should propose a solution to this question.', 'Task description': 'Given a weighted undirected graph, the **Balanced Minimum Bisection Problem** aims to partition the graph into two disjoint subsets of **equal size** (or dif... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": {\"16\": 2, \"1\": 2, \"2\": 8, \"3\": 8, \"4\": 9, \"5\": 10, \"8\": 9, \"9\": 9, \"10\": 10, \"12\": 9, \"13\": 9, \"11\": 3, \"26\": 1, \"21\": 3}, \"1\": {\"40\": 2, \"0\": 2, \"17\": 9, \"26\": 9, \"16\": 10, \"33\": 10, \"39\": 9, \"27\": 5}, \... | {
"generator_name": "easy",
"index": 167,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpHamiltonianCycle | [
{
"content": "'Introduction': 'You are a great expert solving hamiltonian-cycle question. You should propose a solution to this question.', 'Task description': 'Your objective is to find a subgraph within a given graph G that contains a Hamiltonian circuit, which is a path that visits every vertex exactly once ... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"0\": [3, 13, 10, 17, 18], \"1\": [5, 11, 7], \"2\": [14, 9, 15], \"3\": [7, 0, 5, 14], \"4\": [11, 6, 7, 9, 14, 18], \"5\": [12, 1, 3, 7, 8, 9, 11], \"6\": [4, 17, 9, 13, 15, 16], \"7\": [15, 3, 1, 4, 5, 9], \"8\": [10, 12, 5], \"9\": [2, 10, 4, 5, 6, 7, ... | {
"generator_name": "easy",
"index": 24,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpKnapsack | [
{
"content": "'Introduction': 'You are a great expert solving knapsack question. You should propose a solution to this question.', 'Task description': \"The knapsack problem's goal is to choose a subset of items to pack into a limited-capacity bag in a way that maximizes total value without exceeding the weight... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"capacity\": 228, \"items\": {\"0\": {\"weight\": 12, \"value\": 29}, \"2\": {\"weight\": 8, \"value\": 15}, \"6\": {\"weight\": 22, \"value\": 52}, \"7\": {\"weight\": 24, \"value\": 47}, \"10\": {\"weight\": 22, \"value\": 47}, \"12\": {\"weight\": 13, \... | {
"generator_name": "easy",
"index": 142,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpSetCover | [
{
"content": "'Introduction': 'You are a great expert solving set-cover question. You should propose a solution to this question.', 'Task description': 'Given a universal set U and a collection of subsets S, the Set Cover Problem aims to find the smallest possible sub-collection of S whose union equals U. In o... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"U\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], \"S\": {\"0\": [4, 6, 5, 1], \"1\": [0], \"2\": [2, 7, 11, 3], \"3\": [4], \"4\": [6, 5, 8], \"5\": [4, 10], \"6\": [0, 5, 9], \"7\": [2], \"8\": [7]}}, \"ground_truth\": 5}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 154,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpSetCover | [
{
"content": "'Introduction': 'You are a great expert solving set-cover question. You should propose a solution to this question.', 'Task description': 'Given a universal set U and a collection of subsets S, the Set Cover Problem aims to find the smallest possible sub-collection of S whose union equals U. In o... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"U\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], \"S\": {\"0\": [7, 8], \"1\": [5, 6], \"2\": [4, 9, 3, 10], \"3\": [7], \"4\": [3], \"5\": [0, 7], \"6\": [0, 1, 2, 3], \"7\": [2, 3], \"8\": [8, 9, 7, 0]}}, \"ground_truth\": 4}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 10,
"need_tools_kwargs": false,
"split": "train"
} |
bootcamp/NpSetCover | [
{
"content": "'Introduction': 'You are a great expert solving set-cover question. You should propose a solution to this question.', 'Task description': 'Given a universal set U and a collection of subsets S, the Set Cover Problem aims to find the smallest possible sub-collection of S whose union equals U. In o... | {
"ground_truth": "{\"difficulty\": \"easy\", \"question\": {\"U\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], \"S\": {\"0\": [0, 10, 6], \"1\": [9, 7, 6, 8, 2], \"2\": [11, 3, 7], \"3\": [10], \"4\": [8, 3, 11, 4], \"5\": [3, 1, 11, 12, 5], \"6\": [8, 9]}}, \"ground_truth\": 4}",
"style": "rule"
} | {
"generator_name": "easy",
"index": 147,
"need_tools_kwargs": false,
"split": "train"
} |
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๐๏ธ Citation
If you find this work helpful, please consider to star๐ and cite this repo. Thanks for your support!
@misc{npengine,
title={NP-Engine: Empowering Optimization Reasoning in Large Language Models with Verifiable Synthetic NP Problems},
author={Xiaozhe Li and Xinyu Fang and Shengyuan Ding and Linyang Li and Haodong Duan and Qingwen Liu and Kai Chen},
year={2025},
eprint={2510.16476},
archivePrefix={arXiv},
primaryClass={cs.AI},
url={https://arxiv.org/abs/2510.16476},
}
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