322. Coin Change

MediumLeetCode

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

How to solve the problem

• Optimized Dynamic Programming

class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        # f[c]: min coins to make amount c; f[0]=0, others are inf
        f = [0] + [inf] * amount

        for x in coins:
            for c in range(x, amount + 1):
                # Try using coin x for amount c
                f[c] = min(f[c], f[c - x] + 1)

        # Return result, or -1 if impossible
        return f[amount] if f[amount] < inf else -1

Complexity

Time complexity: O(n * amount)

Space complexity: O(n * amount)