Coin Change2

题目地址：

https://leetcode.com/problems/coin-change-2/description/

题目：

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.

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

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

解题思路：

这道题用dp思想可以解。
Link: https://discuss.leetcode.com/topic/79071/knapsack-problem-java-solution-with-thinking-process-o-nm-time-and-o-m-space

代码：

public int change(int amount, int[] coins) {
    int[][] dp = new int[coins.length+1][amount+1];
    dp[0][0] = 1;

    for (int i = 1; i <= coins.length; i++) {
        dp[i][0] = 1;
        for (int j = 1; j <= amount; j++) {
            dp[i][j] = dp[i-1][j] + (j >= coins[i-1] ? dp[i][j-coins[i-1]] : 0);
        }
    }
    return dp[coins.length][amount];
}