算法——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.

java代码如下：

public class Solution {
    int total = Integer.MAX_VALUE;
    public int coinChange(int[] coins, int amount) {
        if (amount == 0) return 0;
        Arrays.sort(coins);
        count(amount, coins.length-1, coins, 0);
        return total == Integer.MAX_VALUE?-1:total;
    }
    void count(int amount, int index, int[] coins, int count){
        if (index<0 || count>=total-1) return;
        int c = amount/coins[index];
        for (int i = c;i>=0;i--){
            int newCount = count + i;
            int rem = amount - i*coins[index];

            if (rem>0 && newCount<total)
                count(rem, index-1, coins, newCount);
            else if (newCount<total)
                total = newCount;
            else if (newCount>=total-1)
                break;
        }
    }
}