518.Coin Change 2

#### QUESTION:

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 = 
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.
``````

Example 3:

``````Input: amount = 10, coins = 
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
``````

#### SOLUTION:

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