Claude Opus via x402 Gateway

{
  "messages": [
    {
      "role": "user",
      "content": "Explain the concept of recursion in programming with a simple example."
    }
  ]
}

{
  "model": "anthropic/claude-4.6-opus-20260205",
  "usage": {
    "cost": 0.015755,
    "is_byok": false,
    "cost_details": {
      "upstream_inference_cost": 0.015755,
      "upstream_inference_prompt_cost": 0.000105,
      "upstream_inference_completions_cost": 0.01565
    },
    "total_tokens": 647,
    "prompt_tokens": 21,
    "completion_tokens": 626,
    "prompt_tokens_details": {
      "audio_tokens": 0,
      "video_tokens": 0,
      "cached_tokens": 0,
      "cache_write_tokens": 0
    },
    "completion_tokens_details": {
      "audio_tokens": 0,
      "image_tokens": 0,
      "reasoning_tokens": 0
    }
  },
  "content": "# Recursion in Programming\n\n## What is Recursion?\n\n**Recursion** is a technique where a function **calls itself** to solve a problem by breaking it down into smaller, simpler sub-problems. It continues until it reaches a **base case** — a condition that stops the recursion.\n\n## Two Essential Components\n\n1. **Base Case** — The stopping condition (prevents infinite loops)\n2. **Recursive Case** — The function calling itself with a *simpler* version of the problem\n\n---\n\n## Simple Example: Factorial\n\nThe factorial of a number (e.g., `5! = 5 × 4 × 3 × 2 × 1 = 120`)\n\n```python\ndef factorial(n):\n    # Base case: stop when n is 0 or 1\n    if n <= 1:\n        return 1\n\n    # Recursive case: n * factorial of (n-1)\n    return n * factorial(n - 1)\n\nprint(factorial(5))  # Output: 120\n```\n\n## How It Works (Step by Step)\n\n```\nfactorial(5)\n│\n├── 5 * factorial(4)\n│       ├── 4 * factorial(3)\n│       │       ├── 3 * factorial(2)\n│       │       │       ├── 2 * factorial(1)\n│       │       │       │       └── returns 1  ← BASE CASE\n│       │       │       └── returns 2 * 1 = 2\n│       │       └── returns 3 * 2 = 6\n│       └── returns 4 * 6 = 24\n└── returns 5 * 24 = 120\n```\n\n## Analogy\n\nThink of **Russian nesting dolls** 🪆 — you keep opening a smaller doll inside until you reach the tiniest one (the base case), then you put them all back together.\n\n---\n\n## Key Warnings\n\n| Issue | Description |\n|-------|-------------|\n| **Missing base case** | Causes infinite recursion → **stack overflow** |\n| **Deep recursion** | Too many calls can exceed memory (call stack limit) |\n| **Performance** | Can be slower than loops without optimization (e.g., memoization) |\n\n## When to Use Recursion\n\n- **Tree/graph traversal** (file systems, DOM)\n- **Divide and conquer** algorithms (merge sort, quicksort)\n- Problems with **naturally recursive structure** (Fibonacci, fractals)\n\n> **Rule of thumb:** If a problem can be defined in terms of a *smaller version of itself*, recursion is a natural fit."
}