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Solution: Coin Change

Explore how to solve the coin change problem by applying dynamic programming. Understand why a greedy approach fails and learn to implement a top-down method with memoization that optimizes time complexity. This lesson teaches how to break down the problem into subproblems to compute the minimum number of coins needed for any amount.

Statement

Given an integer total that represents the target amount of money and a list of integers coins that represents different coin denominations, find the minimum number of coins required to make up the total amount. If it’s impossible to achieve the target amount using the given coins, return -1. If the target amount is 0, return 0.

Note: You can assume that we have an infinite number of each kind of coin.

Constraints:

  • 11 \leq coins.length 12\leq 12

  • 11 \leq coins[i] 104\leq 10^4

  • 00 \leq ...