June Leetcoding Challenge(6.7)

Coin Change 2 (LeetCode518)

Solution
You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

Example 1:

Input: amount = 5, coins = [1, 2, 5]
Output: 4
Explanation: there are four ways to make up the amount:
5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1
Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.
Example 3:

Input: amount = 10, coins = [10] 
Output: 1

分析与思路

使用动态规划即可完成。以Example1为例，当只有一个1分钱硬币时，每个amount都有一种方式，当amount=2，有1分和2分钱两种硬币时，有两种情况，第一种只用1分钱硬币，那么就有1种情况，即d[0,2],，第二种情况就是，要用一个2分钱硬币，那么剩下部分2-2=0，0对应的有1种组合，那么当amount=2时，就会有1+1=2种组合。

代码

class Solution {
    public int change(int amount, int[] coins) {
        int[] dp = new int[amount+1];
        dp[0]=1;
        for(int j=1;j<amount+1;j++)
            dp[j]=0;
        for(int c: coins)
            for(int i=c;i<amount+1;i++)
                dp[i] +=dp[i-c];
        return dp[amount];
    }
}