CodeEasy v0.1

Coin Change

Medium Subject: Dynamic Programming
Time Complexity
O(A * C)
Space Complexity
O(A)

Problem Description

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.

Optimal Solution

Python 
def coinChange(coins, amount):
    # Initialize DP array with amount + 1 (representing infinity)
    dp = [amount + 1] * (amount + 1)
    dp[0] = 0

    for a in range(1, amount + 1):
        for c in coins:
            if a - c >= 0:
                dp[a] = min(dp[a], 1 + dp[a - c])

    return dp[amount] if dp[amount] != amount + 1 else -1