## 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];
}
}
``````