518. Coin Change 2

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

class Solution {
    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];
    }
}