README.md

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 = [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

• 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

Solutions (Rust)

1. Dynamic Programming

impl Solution {
    pub fn change(amount: i32, coins: Vec<i32>) -> i32 {
        let mut dp = vec![0; amount as usize + 1];
        dp[0] = 1;

        for &coin in &coins {
            for i in (coin as usize)..=(amount as usize) {
                dp[i] += dp[i - coin as usize];
            }
        }

        dp[amount as usize]
    }
}