518. 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 = 
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

518. Coin Change 2
``````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 = 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!;
let res = 0;
assert_eq!(Solution::change(amount, coins), res);
let amount = 10;
let coins = vec!;
let res = 1;
assert_eq!(Solution::change(amount, coins), res);
}
``````