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:4Explanation: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:0Explanation: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

- 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

```
struct Solution;
impl Solution {
fn change(amount: i32, coins: Vec<i32>) -> i32 {
let amount = amount as usize;
let n = amount + 1;
let mut dp: Vec<i32> = vec![0; n];
dp[0] = 1;
for coin in coins {
let mut sum = coin as usize;
while sum <= amount {
dp[sum] += dp[sum - coin as usize];
sum += 1;
}
}
dp[amount]
}
}
#[test]
fn test() {
let amount = 5;
let coins = vec![1, 2, 5];
let res = 4;
assert_eq!(Solution::change(amount, coins), res);
let amount = 3;
let coins = vec![2];
let res = 0;
assert_eq!(Solution::change(amount, coins), res);
let amount = 10;
let coins = vec![10];
let res = 1;
assert_eq!(Solution::change(amount, coins), res);
}
```