leetcode 322: 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.

题意：所需硬币的最小数目

思路：

例：coins = [1,2,5],amount = 11

则所需硬币数ans[11] = min(ans[11-1], ans[11-2], ans[11-5]);

注意初始状态为-1，即不存在；

class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        if(amount==0)
            return 0;
        int len = coins.size();
        vector<int> v(amount+1,-1);
        v[0] = 0;
        for(int i=1;i<=amount;i++)
        {
            for(int j=0;j<len;j++)
            {
                int tmp = i-coins[j];
                if(tmp<0)
                    continue;
                if(v[tmp]==-1)
                    continue;
                if(v[i]==-1)
                    v[i] = v[tmp]+1;
                else
                    v[i] = min(v[i],v[tmp]+1);
            }
        }
        return v[amount];
    }

};