ALL TRANSACTIONS
gsTs4lpjlKB1gV0g
CONSUMP_PREPOST_GRANT
completed · 8/21/2026, 4:24:52 PM
Statuscompleted
Date8/21/2026, 4:24:52 PM
User85242227@qq.com
User AmountCNY 0.0004725
User BalancegrvvOoGQ6TYr3Stt
Vendortokease
Vendor CostCNY -0.00043477
Vendor BalancegrUOO3gPM2QLOqUW
Aliasdeepseek-v4-flash-g1 / grUORIPWk0XTl4W7
Mode / Protoreq-v1-chatcmpl / openai-chatcmpl
Log MIDgsTs4lkkMeDpzX9g
SETTLEMENT TELEMETRY
Inference Log
Log MIDgsTs4lkkMeDpzX9g
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
Latency19.45923397s
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
Method: POST
URL: https://tokease.cn/v1/chat/completions
Headers:
{
"Authorization": "Bearer sk-oRd5RE9JhT1bDLQ3lOZgdkESeCuowucrcNX16gZEgHecnxmu",
"Content-Type": "application/json"
}
Body:
{
"max_tokens": 300,
"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。"
}
],
"model": "deepseek-v4-flash/yd"
}Vendor Response
Headers:
{
"Content-Length": "2054",
"Content-Type": "application/json",
"Date": "Fri, 21 Aug 2026 08:24:56 GMT",
"Req-Arrive-Time": "1787300692851",
"Req-Cost-Time": "3202",
"Resp-Start-Time": "1787300696053",
"Server": "nginx",
"Set-Cookie": "route=b6817f60ab83a9ecf16ead57be0f0f66; Path=/",
"Vary": "Accept-Encoding",
"Via": "1.1 Caddy",
"X-Envoy-Upstream-Service-Time": "3195",
"X-New-Api-Version": "v0.0.0",
"X-Oneapi-Request-Id": "202608210824528210524188268d9d6BFZ5DVDI",
"X-Request-Id": "2ab4e2e6-9082-4c8f-afa4-e73be7270743"
}
Body:
{
"id": "chatcmpl-c29f7c50-fd51-4a8b-8bc1-46df9e02d6e3",
"object": "chat.completion",
"created": 1787300696,
"model": "deepseek-v4-flash",
"choices": [
{
"index": 0,
"message": {
"role": "assistant",
"content": "递归(Recursion)是一种在计算机科学和数学中非常核心的解决问题的方法。它的本质是**“函数直接或间接地调用自身”**。但递归绝不仅仅是“自己调用自己”这么简单,它更是一种**“将大问题分解为结构相同的小问题,直到小问题简单到可以直接解决”**的思维模式。\n\n下面我将从**定义、核心要素、执行原理、经典举例、优缺点**及**与迭代的对比**几个方面,分点详细论述。\n\n---\n\n### 一、什么是递归?—— 定义与核心思想\n\n**1. 形式化定义** \n递归是指:一个函数(或过程)在其定义或实现中,直接或间接地调用自身的一种方法。\n\n**2. 核心思想(分治思想)** \n递归基于**“分而治之”**的策略:\n- **把原问题**转化为一个**规模更小**、但**结构完全相同**的子问题。\n- 持续分解,直到子问题小到可以直接得出答案(称为**基准情形 / 基线条件**)。\n- 然后将子问题的答案**逐层回溯**,组合成原问题的答案。\n\n**3. 两个关键要素(缺一不可)** \n- **基线条件(Base Case)**:递归的“出口”。当满足该条件时,函数不再调用自身,直接返回结果。没有基线条件会导致无限递归(栈溢出)。\n- **递归步骤",
"refusal": null,
"annotations": null,
"audio": null,
"function_call": null,
"reasoning": null
},
"logprobs": null,
"finish_reason": "length",
"stop_reason": null,
"token_ids": null,
"routed_experts": null
}
],
"service_tier": null,
"system_fingerprint": "vllm-0.25.1-dp8-ep-1d021cfb",
"usage": {
"prompt_tokens": 30,
"total_tokens": 330,
"completion_tokens": 300,
"prompt_tokens_details": {
"cached_tokens": 0,
"multimodal_tokens": null
}
},
"prompt_logprobs": null,
"prompt_token_ids": null,
"prompt_text": null,
"kv_transfer_params": null,
"metrics": null
}Token Usage
{
"prompt_tokens": 30,
"total_tokens": 330,
"completion_tokens": 300,
"prompt_tokens_details": {
"cached_tokens": 0,
"multimodal_tokens": null
}
}User Request
Method: POST
URL: /v1/chat/completions
Headers:
{
"Accept": "*/*",
"Accept-Encoding": "gzip",
"Authorization": "Bearer sk_r4gAXloJQt74Cp4prb19OItKzoG77lLhjmWT4ei20Ua",
"Content-Length": "211",
"Content-Type": "application/json",
"User-Agent": "Go-http-client/2.0",
"Via": "2.0 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": 300
}User Response
Body:
{
"choices": [
{
"finish_reason": "length",
"index": 0,
"logprobs": null,
"message": {
"annotations": null,
"audio": null,
"content": "递归(Recursion)是一种在计算机科学和数学中非常核心的解决问题的方法。它的本质是**“函数直接或间接地调用自身”**。但递归绝不仅仅是“自己调用自己”这么简单,它更是一种**“将大问题分解为结构相同的小问题,直到小问题简单到可以直接解决”**的思维模式。\n\n下面我将从**定义、核心要素、执行原理、经典举例、优缺点**及**与迭代的对比**几个方面,分点详细论述。\n\n---\n\n### 一、什么是递归?—— 定义与核心思想\n\n**1. 形式化定义** \n递归是指:一个函数(或过程)在其定义或实现中,直接或间接地调用自身的一种方法。\n\n**2. 核心思想(分治思想)** \n递归基于**“分而治之”**的策略:\n- **把原问题**转化为一个**规模更小**、但**结构完全相同**的子问题。\n- 持续分解,直到子问题小到可以直接得出答案(称为**基准情形 / 基线条件**)。\n- 然后将子问题的答案**逐层回溯**,组合成原问题的答案。\n\n**3. 两个关键要素(缺一不可)** \n- **基线条件(Base Case)**:递归的“出口”。当满足该条件时,函数不再调用自身,直接返回结果。没有基线条件会导致无限递归(栈溢出)。\n- **递归步骤",
"function_call": null,
"reasoning": null,
"refusal": null,
"role": "assistant"
},
"routed_experts": null,
"stop_reason": null,
"token_ids": null
}
],
"created": 1787300696,
"id": "chatcmpl-gsTs4lpjlKB1gV0g",
"kv_transfer_params": null,
"metrics": null,
"model": "deepseek-v4-flash-g1",
"object": "chat.completion",
"prompt_logprobs": null,
"prompt_text": null,
"prompt_token_ids": null,
"service_tier": null,
"system_fingerprint": "vllm-0.25.1-dp8-ep-1d021cfb",
"usage": {
"completion_tokens": 300,
"prompt_tokens": 30,
"prompt_tokens_details": {
"cached_tokens": 0,
"multimodal_tokens": null
},
"total_tokens": 330
}
}Created At8/21/2026, 4:24:52 PM
TRANSACTION DETAILS