LeetCode - Coin Change

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

 

ChatGPT's Solution:

class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        # Initialize the DP array with amount+1, which is an impossible high value
        dp = [amount + 1] * (amount + 1)
        dp[0] = 0  # base case: 0 coins needed to make amount 0

        for coin in coins:
            for x in range(coin, amount + 1):
                dp[x] = min(dp[x], dp[x - coin] + 1)
        
        return dp[amount] if dp[amount] != amount + 1 else -1

 

 

Explanation:

• We use a dynamic programming array dp where dp[i] stores the minimum number of coins needed for amount i.

• For each coin, we update the dp array from that coin value up to the target amount.

• If after processing all coins, dp[amount] is still amount + 1, it means it's not possible to make up that amount.