ALL TRANSACTIONS
gtfFepQOaWsQAYlJ
CONSUMP_PREPOST_GRANT
completed · 8/30/2026, 9:26:37 PM
Statuscompleted
Date8/30/2026, 9:26:37 PM
User85242227@qq.com
User AmountCNY 0.0009225
User BalancegrvvOoGQ6TYr3Stt
Vendortokease
Vendor CostCNY -0.00084884
Vendor BalancegrUOO3gPM2QLOqUW
Aliasdeepseek-v4-flash-g1 / grUORIPWk0XTl4W7
Mode / Protoreq-v1-chatcmpl / openai-chatcmpl
Log MIDgtfFepM4RXiSR3YS
SETTLEMENT TELEMETRY
Inference Log
Log MIDgtfFepM4RXiSR3YS
Typechat_completion
Aliasdeepseek-v4-flash-g1 / grUORIPWk0XTl4W7
Hostinforaxi-server:3300:v1.1.3736-1-gf63106d5c
Mode / Protoreq-v1-chatcmplopenai-chatcmpl
Vendor/LLMtokease/deepseek-v4-flash/yd
Statussuccess
User Pricing
30 × 0.75 = 0.000023
0 × 0.015 = 0.000000
600 × 1.5 = 0.000900
CNY 0.000922
Vendor Cost
30 × 0.69034 = 0.000021
0 × 0.013802 = 0.000000
600 × 1.380211 = 0.000828
CNY 0.000849
Latency13.02580183s
Summary
{
"system_prefix": null,
"history_count": 1,
"user_summary": {
"text": "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。",
"has_image": false,
"has_tool_result": false
},
"assistant_summary": {
"text": "### 递归(Recursion)的详细解释\n\n递归是一种在编程和数学中广泛使用的解决问题的方法。它的核心思想是:**一个函数(或过程)直接或间接地调用自身**,从而将一个大问题分解为若干个与原问题**结构相同**但**规模更小**的子问题,直到子问题小到可以直接求解(称为**基准情形**,即 ba",
"tool_calls": [],
"stop_reason": "length"
}
}Stop Reasonlength
Vendor Request
Method: POST
URL: https://tokease.cn/v1/chat/completions
Headers:
{
"authorization": "Bearer sk-oRd5RE9JhT1bDLQ3lOZgdkESeCuowucrcNX16gZEgHecnxmu",
"content-type": "application/json"
}
Body:
{
"max_tokens": 600,
"messages": [
{
"content": "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。",
"role": "user"
}
],
"model": "deepseek-v4-flash/yd"
}Vendor Response
Headers:
{
"content-length": "3033",
"content-type": "application/json",
"date": "Sun, 30 Aug 2026 13:26:50 GMT",
"req-arrive-time": "1788096397272",
"req-cost-time": "12930",
"resp-start-time": "1788096410202",
"server": "nginx",
"set-cookie": "route=75f379117db1ce19429dcd576b3552d8; Path=/",
"vary": "Accept-Encoding",
"via": "1.1 Caddy",
"x-envoy-upstream-service-time": "12925",
"x-new-api-version": "v0.0.0",
"x-oneapi-request-id": "202608301326372390959418268d9d6PcLxb82K",
"x-request-id": "172b3f87-1929-4995-8890-ec372b502ee8"
}
Body:
{
"id": "chatcmpl-172b3f87-1929-4995-8890-ec372b502ee8",
"object": "chat.completion",
"created": 1788096397,
"model": "deepseek-v4-flash",
"service_tier": null,
"system_fingerprint": null,
"choices": [
{
"index": 0,
"message": {
"role": "assistant",
"content": "### 递归(Recursion)的详细解释\n\n递归是一种在编程和数学中广泛使用的解决问题的方法。它的核心思想是:**一个函数(或过程)直接或间接地调用自身**,从而将一个大问题分解为若干个与原问题**结构相同**但**规模更小**的子问题,直到子问题小到可以直接求解(称为**基准情形**,即 base case),然后逐层返回结果,组合成原问题的解。\n\n递归包含两个关键要素:\n1. **基准情形(Base Case)**:最小的、无需再分解就能直接返回结果的结束条件。缺少它会导致无限递归(栈溢出)。\n2. **递归步骤(Recursive Step)**:将当前问题转化为更小规模的同类问题,并调用自身。\n\n---\n\n### 递归的详细展开论述\n\n为了全面理解递归,我从以下五个方面进行分点论述:\n\n#### 1. 递归的数学基础 —— 递推关系\n递归最早源于数学中的**递推公式**。例如斐波那契数列的定义:\n- `F(0) = 0, F(1) = 1` (基准情形)\n- `F(n) = F(n-1) + F(n-2)` (递归步骤,当 n ≥ 2)\n\n这种定义方式天然适合编程中的递归实现。递归的本质是“用自身定义自身”,但必须有一个“起点”来终止。\n\n#### 2. 递归的执行过程 —— 调用栈(Call Stack)\n递归在计算机中依赖**系统调用栈**:\n- 每次函数调用自身时,系统会将当前函数的局部变量、参数和返回地址压入栈中。\n- 当遇到基准情形时,不再压栈,开始**回溯**(返回),依次弹出栈帧,计算并返回结果。\n- 因此,递归深度不能太大,否则栈空间耗尽(栈溢出)。\n\n**示例执行过程**(以计算阶乘 `factorial(4)` 为例):\n```\nfactorial(4) = 4 * factorial(3)\n = 4 * (3 * factorial(2))\n = 4 * (3 * (2 * factorial(1)))\n = 4 * (3 * (2 * 1)) // factorial(1)=1 是基准情形\n = 4 * (3 * 2)\n = 4 * 6\n = 24\n```\n可见,递归是“层层递进,层层回归”。\n\n#### 3. 递归与迭代(循环)的对比\n| 比较项 | 递归 | 迭代(循环) |\n|-------|------|-------------|\n| 实现方式 | 函数自调用 | 使用 `for`、`while` 等循环 |\n| 代码可读性 | 对分治、树、图等结构更直观 | 对累加、遍历等更",
"refusal": null,
"annotations": null,
"audio": null,
"function_call": null
},
"logprobs": null,
"finish_reason": "length",
"stop_reason": null,
"token_ids": null,
"routed_experts": null
}
],
"usage": {
"prompt_tokens": 30,
"total_tokens": 630,
"completion_tokens": 600,
"prompt_tokens_details": {
"cached_tokens": 0
},
"completion_tokens_details": null
},
"prompt_logprobs": null,
"prompt_token_ids": null,
"prompt_text": null,
"kv_transfer_params": null
}Token Usage
{
"completion_tokens": 600,
"completion_tokens_details": null,
"prompt_tokens": 30,
"prompt_tokens_details": {
"cached_tokens": 0
},
"total_tokens": 630
}Fixes
User Request
Method: POST
URL: /v1/chat/completions
Headers:
{
"accept-encoding": "gzip",
"authorization": "Bearer sk_r4gAXloJQt74Cp4prb19OItKzoG77lLhjmWT4ei20Ua",
"content-length": "339",
"content-type": "application/json",
"host": "api.tokendiet.cn",
"via": "1.1 Caddy",
"x-forwarded-for": "13.212.110.206",
"x-forwarded-host": "api.tokendiet.cn",
"x-forwarded-proto": "https"
}
Body:
{
"model": "deepseek-v4-flash-g1",
"messages": [
{
"role": "user",
"content": "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。"
}
],
"max_tokens": 600
}User Response
Body:
{
"choices": [
{
"finish_reason": "length",
"index": 0,
"logprobs": null,
"message": {
"annotations": null,
"audio": null,
"content": "### 递归(Recursion)的详细解释\n\n递归是一种在编程和数学中广泛使用的解决问题的方法。它的核心思想是:**一个函数(或过程)直接或间接地调用自身**,从而将一个大问题分解为若干个与原问题**结构相同**但**规模更小**的子问题,直到子问题小到可以直接求解(称为**基准情形**,即 base case),然后逐层返回结果,组合成原问题的解。\n\n递归包含两个关键要素:\n1. **基准情形(Base Case)**:最小的、无需再分解就能直接返回结果的结束条件。缺少它会导致无限递归(栈溢出)。\n2. **递归步骤(Recursive Step)**:将当前问题转化为更小规模的同类问题,并调用自身。\n\n---\n\n### 递归的详细展开论述\n\n为了全面理解递归,我从以下五个方面进行分点论述:\n\n#### 1. 递归的数学基础 —— 递推关系\n递归最早源于数学中的**递推公式**。例如斐波那契数列的定义:\n- `F(0) = 0, F(1) = 1` (基准情形)\n- `F(n) = F(n-1) + F(n-2)` (递归步骤,当 n ≥ 2)\n\n这种定义方式天然适合编程中的递归实现。递归的本质是“用自身定义自身”,但必须有一个“起点”来终止。\n\n#### 2. 递归的执行过程 —— 调用栈(Call Stack)\n递归在计算机中依赖**系统调用栈**:\n- 每次函数调用自身时,系统会将当前函数的局部变量、参数和返回地址压入栈中。\n- 当遇到基准情形时,不再压栈,开始**回溯**(返回),依次弹出栈帧,计算并返回结果。\n- 因此,递归深度不能太大,否则栈空间耗尽(栈溢出)。\n\n**示例执行过程**(以计算阶乘 `factorial(4)` 为例):\n```\nfactorial(4) = 4 * factorial(3)\n = 4 * (3 * factorial(2))\n = 4 * (3 * (2 * factorial(1)))\n = 4 * (3 * (2 * 1)) // factorial(1)=1 是基准情形\n = 4 * (3 * 2)\n = 4 * 6\n = 24\n```\n可见,递归是“层层递进,层层回归”。\n\n#### 3. 递归与迭代(循环)的对比\n| 比较项 | 递归 | 迭代(循环) |\n|-------|------|-------------|\n| 实现方式 | 函数自调用 | 使用 `for`、`while` 等循环 |\n| 代码可读性 | 对分治、树、图等结构更直观 | 对累加、遍历等更",
"function_call": null,
"refusal": null,
"role": "assistant"
},
"routed_experts": null,
"stop_reason": null,
"token_ids": null
}
],
"created": 1788096397,
"id": "chatcmpl-172b3f87-1929-4995-8890-ec372b502ee8",
"kv_transfer_params": null,
"model": "deepseek-v4-flash-g1",
"object": "chat.completion",
"prompt_logprobs": null,
"prompt_text": null,
"prompt_token_ids": null,
"service_tier": null,
"system_fingerprint": null,
"usage": {
"completion_tokens": 600,
"completion_tokens_details": null,
"prompt_tokens": 30,
"prompt_tokens_details": {
"cached_tokens": 0
},
"total_tokens": 630
}
}Created At8/30/2026, 9:26:37 PM
TRANSACTION DETAILS