Coin Change

You are given coins of different denominations and a total amount of money amount. Write a function to compute 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.

Example 1:
coins = [1, 2, 5], amount = 11
return 3 (11 = 5 + 5 + 1)

Example 2:
coins = [2], amount = 3
return -1.

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

Analysis

DP problem:

• State: dp[sum]: the minimum counts needed to get total amount of sum
• Transfer:
  • 循环coin
    • dp[sum] = dp[sum-coin]+1 (if dp[sum-coin]!=-1) or -1
• Initialize: dp[0]=0
• Return: dp[amount]

Code

public class Solution {
    public int coinChange(int[] coins, int amount) {
        if (amount<1) return 0;
        int[] dp = new int[amount+1];

        for(int sum=1; sum<=amount; sum++){
            int min = -1;
            for (int coin:coins){
                if (coin<=sum && dp[sum-coin]!=-1){
                    int temp = dp[sum-coin]+1;
                    min = min < 0 ? temp : Math.min(min, temp);
                }
            }
            dp[sum]=min;
        }


        return dp[amount];
    }
}

Reference

Leetcode