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[LeetCode] 518. Coin Change 2

2020-06-08 12:54:57 作者：互联网

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

零钱兑换II。题意是给你一些不同面值的硬币coins和一个amount，请你返回有多少种硬币组合可以满足amount。

思路依然是动态规划。dp[i]的定义是当amount = i的时候，到底有几种硬币组合。

以基本情况没有硬币开始组合数量。dp[0] = 1，然后其余等于 0。
遍历所有硬币面值

对于每个硬币，我们将从金额 0 遍历到 amount：
对于每个 x，计算组合数：dp[x] += dp[x - coin]。
返回 dp[amount]

时间O(n^2)

空间O(n)

Java实现

 1 class Solution {
 2     public int change(int amount, int[] coins) {
 3         int[] dp = new int[amount + 1];
 4         dp[0] = 1;
 5         for (int coin : coins) {
 6             for (int x = coin; x < amount + 1; x++) {
 7                 dp[x] += dp[x - coin];
 8             }
 9         }
10         return dp[amount];
11     }
12 }