SETTLEMENT TELEMETRY

Inference Log

MID: gsTs4lv3mqWpMCBt

Log MIDgsTs4lv3mqWpMCBt
Typechat_completion
Aliasdeepseek-v4-flash-g1 / grUORIPWk0XTl4W7
Hostinfogaxi-server:3300:v1.1.3395-0-ga307a73fe
Mode / Protoreq-v1-chatcmplopenai-chatcmpl
Vendor/LLMtokease/deepseek-v4-flash/yd
Statussuccess
User Pricing
30 × 0.75 = 0.000023
0 × 0.015 = 0.000000
300 × 1.5 = 0.000450
CNY 0.000472
Vendor Cost
30 × 0.69034 = 0.000021
0 × 0.013802 = 0.000000
300 × 1.380211 = 0.000414
CNY 0.000435
Latency18.42317514s
Summary
请详细回答以下问题:解释什么是递归,并举例说明。请展开论述,分点说明,条理清晰。
Stop Reasonlength
Vendor Request
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URL: https://tokease.cn/v1/chat/completions

Headers:
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Body:
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    }
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  "model": "deepseek-v4-flash/yd"
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Vendor Response
Headers:
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  "Content-Type": "application/json",
  "Date": "Fri, 21 Aug 2026 08:24:53 GMT",
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Body:
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  "created": 1787300693,
  "model": "deepseek-v4-flash",
  "choices": [
    {
      "index": 0,
      "message": {
        "role": "assistant",
        "content": "## 什么是递归\n\n递归(Recursion)是一种在数学和计算机科学中广泛使用的编程技术,其核心思想是**函数直接或间接地调用自身**,通过将一个大问题分解为若干个规模更小、结构相似的子问题,逐步求解,最终汇总结果。\n\n递归包含两个核心要素:\n\n1. **基线条件(Base Case)**:递归停止的条件,当问题规模小到可以直接求解时,不再继续调用自身。缺少基线条件会导致无限递归(栈溢出)。\n2. **递归条件(Recursive Case)**:将当前问题转化为一个或多个同类型但规模更小的子问题,并调用自身来解决。\n\n---\n\n## 递归的工作原理\n\n递归的执行过程可以分为两个阶段:\n\n- **递推(递去)**:每次调用自身时,问题规模逐渐缩小,直到触底(达到基线条件)。\n- **回归(归来)**:当基线条件满足后,函数开始逐层返回结果,并将各层结果合并,最终得到原问题的解。\n\n---\n\n## 经典举例\n\n### 例子1:阶乘(Factorial)\n\n阶乘的定义:\n- `n! = n × (n-1) × ... × 1`  \n- 特别地,`0! = 1`\n\n递归实现(Python):\n```python\ndef factorial(n):\n    # 基线条件\n    if n == 0 or n == 1:\n        return 1\n    #",
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Token Usage
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User Request
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Headers:
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Body:
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    }
  ],
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}
User Response
Body:
{
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    {
      "finish_reason": "length",
      "index": 0,
      "logprobs": null,
      "message": {
        "annotations": null,
        "audio": null,
        "content": "## 什么是递归\n\n递归(Recursion)是一种在数学和计算机科学中广泛使用的编程技术,其核心思想是**函数直接或间接地调用自身**,通过将一个大问题分解为若干个规模更小、结构相似的子问题,逐步求解,最终汇总结果。\n\n递归包含两个核心要素:\n\n1. **基线条件(Base Case)**:递归停止的条件,当问题规模小到可以直接求解时,不再继续调用自身。缺少基线条件会导致无限递归(栈溢出)。\n2. **递归条件(Recursive Case)**:将当前问题转化为一个或多个同类型但规模更小的子问题,并调用自身来解决。\n\n---\n\n## 递归的工作原理\n\n递归的执行过程可以分为两个阶段:\n\n- **递推(递去)**:每次调用自身时,问题规模逐渐缩小,直到触底(达到基线条件)。\n- **回归(归来)**:当基线条件满足后,函数开始逐层返回结果,并将各层结果合并,最终得到原问题的解。\n\n---\n\n## 经典举例\n\n### 例子1:阶乘(Factorial)\n\n阶乘的定义:\n- `n! = n × (n-1) × ... × 1`  \n- 特别地,`0! = 1`\n\n递归实现(Python):\n```python\ndef factorial(n):\n    # 基线条件\n    if n == 0 or n == 1:\n        return 1\n    #",
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Created At8/21/2026, 4:24:52 PM