"""
322. Coin Change
Difficulty: Medium
https://leetcode.com/problems/coin-change/

──────────────────────────────────────────────────

You are given an integer array coins representing coins of different
denominations and an integer amount representing a total amount of
money.

Return the fewest number of coins that you need to make up that
amount. If that amount of money cannot be made up by any combination
of the coins, return -1.

You may assume that you have an infinite number of each kind of coin.



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
"""

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]