---
title: '322. Coin Change'
description: You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money
icon: dot
topics:
  - { name: "Array", slug: "array" }
  - { name: "Dynamic Programming", slug: "dynamic-programming" }
  - { name: "Breadth-First Search", slug: "breadth-first-search" }
  - { name: "Knapsack Problem", slug: "knapsack-problem" }
  - { name: "Complete Knapsack", slug: "complete-knapsack" }
sidebar:
  label: 'Coin Change'
  badge: 'Medium'
---

### Example 1:
- Input: `coins = [1,2,5], amount = 11`
- Output: `3`
- Explanation: `11 = 5 + 5 + 1`

### Example 2:
- Input: `coins = [2], amount = 3`
- Output: `-1`

### Example 3:
- Input: `coins = [1], amount = 0`
- Output: `0`

### Constraints:

- `1 <= coins.length <= 12`
- `1 <= coins[i] <= 2^31 - 1`
- `0 <= amount <= 10^4`

## Solution

```py
from math import inf


class Solution:
    def coinChange(self, coins: list[int], amount: int) -> int:
        n = len(coins)
        memo = [[-1] * (amount + 1) for _ in range(n + 1)]

        def min_coins(coins, i, amount, memo):
            if amount == 0:
                return 0
            if i == 0 or amount < 0:
                return inf
            if memo[i][amount] != -1:
                return memo[i][amount]

            skip = min_coins(coins, i - 1, amount, memo)
            use = min_coins(coins, i, amount - coins[i - 1], memo)
            if use != inf:
                use += 1

            memo[i][amount] = min(skip, use)
            return memo[i][amount]

        result = min_coins(coins, n, amount, memo)
        return result if result != inf else -1  # pyright: ignore[reportReturnType]
```