LeetCode : 518. Coin Change 2凑硬币-蒲公英云

LeetCode : 518. Coin Change 2凑硬币

试题

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
Note:
You can assume that
0 <= amount <= 5000
1 <= coin <= 5000
the number of coins is less than 500
the answer is guaranteed to fit into signed 32-bit integer

代码
这一题明显动归，但是循环嵌套很有技巧。如果我们把amount放在外循环，就会出现重复统计的情况，而把coins放在外部循环就能很好避免这种情况。

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