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Solution: Coin Change

Explore how to solve the coin change problem by applying dynamic programming techniques. Understand why a greedy approach fails and how breaking the problem into subproblems leads to an optimal solution. Learn to implement a top-down memoized solution that reduces time complexity and efficiently computes the minimum coins needed.

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 ...