LeetCode-in-All

322. Coin Change

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 fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

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

Example 1:

Input: coins = [1,2,5], amount = 11

Output: 3

Explanation: 11 = 5 + 5 + 1

Example 2:

Input: coins = [2], amount = 3

Output: -1

Example 3:

Input: coins = [1], amount = 0

Output: 0

Constraints:

• 1 <= coins.length <= 12
• 1 <= coins[i] <= 231 - 1
• 0 <= amount <= 104

Solution

impl Solution {
    pub fn coin_change(coins: Vec<i32>, amount: i32) -> i32 {
        let mut dp = vec![0; (amount + 1) as usize];
        dp[0] = 1;  // Base case: one way to make 0 amount (using no coins)

        for &coin in &coins {
            for i in coin..=amount {
                let prev = dp[(i - coin) as usize];
                if prev > 0 {
                    if dp[i as usize] == 0 {
                        dp[i as usize] = prev + 1;
                    } else {
                        dp[i as usize] = dp[i as usize].min(prev + 1);
                    }
                }
            }
        }
        
        // If the dp[amount] is still 0, it means no solution was found
        if dp[amount as usize] == 0 {
            -1
        } else {
            dp[amount as usize] - 1
        }
    }
}

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