PromptCoT-DS-Dataset

## **Dataset Format**
Each row in the dataset contains:
- **`prompt`**: The input to the **reasoning model**, including a problem statement with the special prompting template.
- **`completion`**: The **expected output** for supervised fine-tuning, containing a **thought process** wrapped in `<think>...</think>`, followed by the final solution.

## **Example**
```json
{
"prompt": "<|begin▁of▁sentence|>Please reason step by step, and put your final answer within \\boxed{{}}.<|User|>\nLet $P$ be a point on a regular $n$-gon. A marker is placed on the vertex $P$ and a random process is used to select a vertex $Q$ uniformly from the remaining $n-1$ vertices. The marker is then moved from $P$ to $Q$ and from $Q$ to a vertex $R$ selected uniformly at random from the remaining $n-1$ vertices. This process is repeated $m$ times, and let $A_m$ be the angle determined by the marker at $P$ after $m$ steps. Let $k$ be a positive integer less than $n/2$ such that $A_k$ is in the angle region $\\Delta n$ determined by $PQ$ and $PR$ and let $\\lfloor x \\rfloor$ denote the greatest integer less than or equal to $x$. Find the smallest positive integer $m$ such that $m \\leq \\lfloor 2n \\lfloor \\theta \\rfloor \\rfloor$, where $\\theta = \\frac{k\\pi}{n}$.<|Assistant|>",
"completion": "<think>...</think>\n\nGiven a regular \( n \)-gon with a marker starting at vertex \( P \), we perform a random process where the marker moves to a uniformly random vertex from the remaining \( n-1 \) vertices at each step. We need to find the smallest positive integer \( m \) such that \( m \leq \lfloor 2n \lfloor \theta \rfloor \rfloor \), where \( \theta = \frac{k\pi}{n} \) and \( k \) is a positive integer less than \( n/2 \) such that \( A_k \) is in the angle region \( \Delta_n \) determined by \( PQ \) and \( PR \).\n\n1. The angle \( \theta \) is defined as \( \theta = \frac{k\pi}{n} \).\n2. The value \( \lfloor \theta \rfloor \) is the greatest integer less than or equal to \( \theta \).\n3. We then compute \( \lfloor 2n \lfloor \theta \rfloor \rfloor \), which is the greatest integer less than or equal to \( 2n \lfloor \theta \rfloor \).\n\nThus, the smallest positive integer \( m \) such that \( m \leq \lfloor 2n \lfloor \theta \rfloor \rfloor \) is given by:\n\n\[\n\boxed{\left\lfloor 2n \left\lfloor \frac{k\pi}{n} \right\rfloor \right\rfloor}\n\]"
}
```

## **Citation**
```
@article{zhao2025promptcot,
author = {Zhao, Xueliang and Wu, Wei and Guan, Jian and Kong, Lingpeng},
title = {PromptCoT: Synthesizing Olympiad-Level Problems for Mathematical Reasoning in Large Language Models},
year = {2025},
journal = {arXiv preprint arXiv:2503.02324},
url = {http://arxiv.org/abs/2503.02324}
}
```

## **数据集格式**
数据集的每一行包含以下内容：
- **`prompt`（提示词）**：输入至**推理模型（reasoning model）**的内容，涵盖搭载特殊提示模板的问题题干。
- **`completion`（补全输出）**：用于监督微调的**预期输出**，包含被`<think>...</think>`标签包裹的**思考过程（thought process）**，其后跟随最终解答。

## **示例**
json
{
"prompt": "<|begin▁of▁sentence|>Please reason step by step, and put your final answer within oxed{{}}.<|User|>
Let $P$ be a point on a regular $n$-gon. A marker is placed on the vertex $P$ and a random process is used to select a vertex $Q$ uniformly from the remaining $n-1$ vertices. The marker is then moved from $P$ to $Q$ and from $Q$ to a vertex $R$ selected uniformly at random from the remaining $n-1$ vertices. This process is repeated $m$ times, and let $A_m$ be the angle determined by the marker at $P$ after $m$ steps. Let $k$ be a positive integer less than $n/2$ such that $A_k$ is in the angle region $Delta n$ determined by $PQ$ and $PR$ and let $lfloor x
floor$ denote the greatest integer less than or equal to $x$. Find the smallest positive integer $m$ such that $m leq lfloor 2n lfloor heta
floor
floor$, where $ heta = frac{kpi}{n}$.<|Assistant|>",
"completion": "<think>...</think>

Given a regular ( n )-gon with a marker starting at vertex ( P ), we perform a random process where the marker moves to a uniformly random vertex from the remaining ( n-1 ) vertices at each step. We need to find the smallest positive integer ( m ) such that ( m leq lfloor 2n lfloor heta
floor
floor ), where ( heta = frac{kpi}{n} ) and ( k ) is a positive integer less than ( n/2 ) such that ( A_k ) is in the angle region ( Delta_n ) determined by ( PQ ) and ( PR ).

1. The angle ( heta ) is defined as ( heta = frac{kpi}{n} ).
2. The value ( lfloor heta
floor ) is the greatest integer less than or equal to ( heta ).
3. We then compute ( lfloor 2n lfloor heta
floor
floor ), which is the greatest integer less than or equal to ( 2n lfloor heta
floor ).

Thus, the smallest positive integer ( m ) such that ( m leq lfloor 2n lfloor heta
floor
floor ) is given by:

[
oxed{leftlfloor 2n leftlfloor frac{kpi}{n}
ight
floor
ight
floor}
]"
}

## **参考文献**

@article{zhao2025promptcot,
author = {Zhao, Xueliang and Wu, Wei and Guan, Jian and Kong, Lingpeng},
title = {PromptCoT: Synthesizing Olympiad-Level Problems for Mathematical Reasoning in 大语言模型（Large Language Model）},
year = {2025},
journal = {arXiv preprint arXiv:2503.02324},
url = {http://arxiv.org/abs/2503.02324}
}