Coin Change II
Difficulty: Medium
Category: DSA
Topics: Array, Dynamic Programming
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`