# 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.

### 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
1. `0 <= amount <= 5000`

2. `1 <= coin <= 5000`

3. the number of coins is less than `500`

4. the answer is guaranteed to fit into signed `32-bit`

integer

### Solution

```
class Solution {
public int change(int amount, int[] coins) {
int[] combos = new int[amount + 1];
combos[0] = 1;
for (int i = 0; i < coins.length; i++) {
int coin = coins[i];
for (int j = 1; j <= amount; j++) {
if (j >= coin) {
//NEW combo = combo WITH coin + combo WITHOUT coin
combos[j] += combos[j - coin];
// System.out.println(Arrays.toString(combos));
}
}
}
return combos[amount];
}
}
```