Coin Change

Coin Change

You are given an integer array coins representing coin 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.

Examples

Example 1:

Input: coins = [1, 5, 10], amount = 12
Output: 3
Explanation: 12 = 10 + 1 + 1. Three coins are needed.

Example 2:

Input: coins = [2], amount = 3
Output: -1
Explanation: The amount 3 cannot be made with coins of denomination 2.

Example 3:

Input: coins = [1], amount = 0
Output: 0
Explanation: No coins are needed for amount 0.

Constraints

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

Expected Complexity

• Time: O(amount * n) where n is the number of coin denominations
• Space: O(amount) for the DP table