# 518. Coin Change 2

#### Medium

***

You are given an integer array `coins` representing coins of different denominations and an integer `amount` representing a total amount of money.

Return *the number of combinations that make up that amount*. If that amount of money cannot be made up by any combination of the coins, return `0`.

You may assume that you have an infinite number of each kind of coin.

The answer is **guaranteed** to fit into a 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
```

 

**Constraints:**

* `1 <= coins.length <= 300`
* `1 <= coins[i] <= 5000`
* All the values of `coins` are **unique**.
* `0 <= amount <= 5000`

```python
class Solution:
    def change(self, amount: int, coins: List[int]) -> int:
        dp = [0]*(amount+1)
        dp[0] = 1
    
        for coin in coins:
            for a in range(coin, amount+1):
                if a - coin >= 0:
                    dp[a] += dp[a-coin] 

        return dp[amount]
        
```