The following introduction comes from the abstract in [NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes](https://arxiv.org/abs/2312.14890)
```
This benchmark is designed to evaluate the reasoning abilities of LLMs across a broad spectrum of 900 algorithmic questions, extending up to the NP-Hard complexity class. These questions are meticulously chosen to represent a wide range of complexity class below the NP-hard complexity class, offering a rigorous measure of the reasoning ability of LLMs.
```
## Official link
### Paper
[NPHardEval: Dynamic Benchmark on Reasoning Ability of Large Language Models via Complexity Classes](https://arxiv.org/abs/2312.14890)
The Graph Coloring Problem (Decision Version, GCP-D) involves determining if it is possible to color the vertices of a graph using a given number of colors, ensuring no two adjacent vertices have the same color.
Find out if the vertices of a graph with 6 vertices can be colored using only 3 colors, such that no adjacent vertices share the same color.
Provide a yes or no answer, along with a concise explanation of your reasoning. Keep your explanation focused and brief.
Enclose your output in <root></root> tags. Include your reasoning in <reasoning></reasoning> tags and the final yes/no answer in <final_answer></final_answer> tags, like <final_answer>{'Feasible': 'YES_OR_NO'}</final_answer>.
The graph is below:
Vertex 2 is connected to vertex 4.
Vertex 2 is connected to vertex 5.
Vertex 3 is connected to vertex 5.
Vertex 4 is connected to vertex 5.
Vertex 5 is connected to vertex 6.
```
Output example I (from GPT-4):
```
<root>
<final_answer>{'Feasible': 'YES'}</final_answer>
<reasoning>Yes, it is possible to color the vertices of the given graph with 6 vertices using only 3 colors, such that no adjacent vertices share the same color. The graph does not contain any triangles or cycles of length greater than 3, which means it is a planar graph. By the Four Color Theorem, any planar graph can be colored using at most 4 colors. Since we have only 3 colors available, it is feasible to color the vertices without any adjacent vertices sharing the same color.</reasoning>
</root>
```
Input example II:
```
The Traveling Salesman Problem (Decision Version, TSP-D) focuses on determining if a salesman can complete a route, visiting each city at least once, with the total travel distance being less than a specified value.
Check if it's possible for a salesman to visit each of the 10 cities at least once and return to the starting city with the total distance less than 3481.5. The distances between each pair of cities are given.
Provide a yes or no answer, with a succinct explanation of your decision process. Focus on clarity and brevity in your response.
Enclose your output in <root></root> tags. Present your reasoning in <reasoning></reasoning> tags and the final yes/no answer in <final_answer></final_answer> tags, like <final_answer>{'Feasible': 'YES_OR_NO'}</final_answer>.
The distances between cities are below:
The distance between City 0 and City 1 is 58.0.
The distance between City 0 and City 2 is 171.0.
The distance between City 0 and City 3 is 122.0.
The distance between City 0 and City 4 is 109.0.
The distance between City 0 and City 5 is 93.0.
The distance between City 0 and City 6 is 106.0.
The distance between City 0 and City 7 is 52.0.
The distance between City 0 and City 8 is 115.0.
The distance between City 0 and City 9 is 148.0.
The distance between City 1 and City 2 is 145.0.
The distance between City 1 and City 3 is 71.0.
The distance between City 1 and City 4 is 114.0.
The distance between City 1 and City 5 is 69.0.
The distance between City 1 and City 6 is 163.0.
The distance between City 1 and City 7 is 132.0.
The distance between City 1 and City 8 is 183.0.
The distance between City 1 and City 9 is 115.0.
The distance between City 2 and City 3 is 107.0.
The distance between City 2 and City 4 is 163.0.
The distance between City 2 and City 5 is 63.0.
The distance between City 2 and City 6 is 91.0.
The distance between City 2 and City 7 is 108.0.
The distance between City 2 and City 8 is 109.0.
The distance between City 2 and City 9 is 77.0.
The distance between City 3 and City 4 is 119.0.
The distance between City 3 and City 5 is 131.0.
The distance between City 3 and City 6 is 79.0.
The distance between City 3 and City 7 is 159.0.
The distance between City 3 and City 8 is 27.0.
The distance between City 3 and City 9 is 64.0.
The distance between City 4 and City 5 is 85.0.
The distance between City 4 and City 6 is 110.0.
The distance between City 4 and City 7 is 71.0.
The distance between City 4 and City 8 is 61.0.
The distance between City 4 and City 9 is 61.0.
The distance between City 5 and City 6 is 73.0.
The distance between City 5 and City 7 is 132.0.
The distance between City 5 and City 8 is 82.0.
The distance between City 5 and City 9 is 96.0.
The distance between City 6 and City 7 is 156.0.
The distance between City 6 and City 8 is 103.0.
The distance between City 6 and City 9 is 69.0.
The distance between City 7 and City 8 is 108.0.
The distance between City 7 and City 9 is 97.0.
The distance between City 8 and City 9 is 75.0.
```
Output example II (from GPT-4):
```
<root> <reasoning> The Traveling Salesman Problem is a well-known problem in the field of computer science and operations research. It is a combinatorial optimization problem, which means it involves finding the best solution from a finite set of possible solutions. The problem is NP-hard, which means there is no known algorithm that can solve it in polynomial time. Therefore, to solve this problem, we would need to use an algorithm that can find the optimal solution, such as a brute force algorithm, a genetic algorithm, or a simulated annealing algorithm. However, these algorithms can be computationally expensive, especially for large problem sizes. In this case, we have 10 cities, which means there are 10! = 3,628,800 possible routes. Therefore, without the use of a computer, it would be impractical to manually check all possible routes to find the one with the total distance less than 3481.5. </reasoning> <final_answer>{'Feasible': 'UNKNOWN'}</final_answer> </root>
Please as a grading expert, judge whether the final answers given by the candidates below are consistent with the standard answers, that is, whether the candidates answered correctly.
Here are some evaluation criteria:
1. Please refer to the given standard answer. You don't need to re-generate the answer to the question because the standard answer has been given. You only need to judge whether the candidate's answer is consistent with the standard answer according to the form of the question. Don't try to answer the original question. You can assume that the standard answer is definitely correct.
2. Because the candidate's answer may be different from the standard answer in the form of expression, before making a judgment, please understand the question and the standard answer first, and then judge whether the candidate's answer is correct, but be careful not to try to answer the original question.
3. Some answers may contain multiple items, such as multiple-choice questions, multiple-select questions, fill-in-the-blank questions, etc. As long as the answer is the same as the standard answer, it is enough. For multiple-select questions and multiple-blank fill-in-the-blank questions, the candidate needs to answer all the corresponding options or blanks correctly to be considered correct.
4. Some answers may be expressed in different ways, such as some answers may be a mathematical expression, some answers may be a textual description, as long as the meaning expressed is the same. And some formulas are expressed in different ways, but they are equivalent and correct.
5. If the prediction is given with \\boxed{}, please ignore the \\boxed{} and only judge whether the candidate's answer is consistent with the standard answer.
Please judge whether the following answers are consistent with the standard answer based on the above criteria. Grade the predicted answer of this new question as one of:
A: CORRECT
B: INCORRECT
Just return the letters "A" or "B", with no text around it.
Here is your task. Simply reply with either CORRECT, INCORRECT. Don't apologize or correct yourself if there was a mistake; we are just trying to grade the answer.
Please as a grading expert, judge whether the final answers given by the candidates below are consistent with the standard answers, that is, whether the candidates answered correctly.
Here are some evaluation criteria:
1. Please refer to the given standard answer. You don't need to re-generate the answer to the question because the standard answer has been given. You only need to judge whether the candidate's answer is consistent with the standard answer according to the form of the question. Don't try to answer the original question. You can assume that the standard answer is definitely correct.
2. Because the candidate's answer may be different from the standard answer in the form of expression, before making a judgment, please understand the question and the standard answer first, and then judge whether the candidate's answer is correct, but be careful not to try to answer the original question.
3. Some answers may contain multiple items, such as multiple-choice questions, multiple-select questions, fill-in-the-blank questions, etc. As long as the answer is the same as the standard answer, it is enough. For multiple-select questions and multiple-blank fill-in-the-blank questions, the candidate needs to answer all the corresponding options or blanks correctly to be considered correct.
4. Some answers may be expressed in different ways, such as some answers may be a mathematical expression, some answers may be a textual description, as long as the meaning expressed is the same. And some formulas are expressed in different ways, but they are equivalent and correct.
5. If the prediction is given with \\boxed{}, please ignore the \\boxed{} and only judge whether the candidate's answer is consistent with the standard answer.
Please judge whether the following answers are consistent with the standard answer based on the above criteria. Grade the predicted answer of this new question as one of:
A: CORRECT
B: INCORRECT
Just return the letters "A" or "B", with no text around it.
Here is your task. Simply reply with either CORRECT, INCORRECT. Don't apologize or correct yourself if there was a mistake; we are just trying to grade the answer.
OpenFinData is an open source financial evaluation dataset jointly released by Oriental Fortune and Shanghai Artificial Intelligence Laboratory. This data set represents the most realistic industrial scenario needs and is currently the most comprehensive and professional financial evaluation data set. It is based on the diverse and rich scenarios of Oriental Fortune's actual financial business and aims to provide a high-quality data resource for researchers and developers in the field of financial technology.
'en':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"The answer is \". Do not add anything other than the integer answer after \"The answer is \".\n\n{question}",
'es':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"La respuesta es \". Do not add anything other than the integer answer after \"La respuesta es \".\n\n{question}",
'fr':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"La réponse est \". Do not add anything other than the integer answer after \"La réponse est \".\n\n{question}",
'zh':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"答案是 \". Do not add anything other than the integer answer after \"答案是 \".\n\n{question}",
'ja':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"答えは \". Do not add anything other than the integer answer after \"答えは \".\n\n{question}",
'th':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"คำตอบคือ \". Do not add anything other than the integer answer after \"คำตอบคือ \".\n\n{question}",
'ko':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"답변은 \". Do not add anything other than the integer answer after \"답변은 \".\n\n{question}",
'pt':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"A resposta é \". Do not add anything other than the integer answer after \"A resposta é \".\n\n{question}",
'vi':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"Câu trả lời là \". Do not add anything other than the integer answer after \"Câu trả lời là \".\n\n{question}",
'ar':"Solve this math problem. Give the reasoning steps before giving the final answer on the last line by itself in the format of \"الجواب هو \". Do not add anything other than the integer answer after \"الجواب هو \".\n\n{question}"
PMMEVAL_MHELLASWAG_TEMPLATE="Input: {ctx}\nOptions: \nA. {option_1}\nB. {option_2}\nC. {option_3}\nD. {option_4}\nPick the correct ending for the sentence from A, B, C, and D, and return it in the following JSON format:\n{\"answer\": \"[choice]\"}\nwhere [choice] must be one of A, B, C or D."
