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Solution: Coin Change

Understand how to solve the coin change problem using a top-down dynamic programming approach. Explore breaking the problem into subproblems, applying memoization to avoid repeated calculations, and optimizing the solution to find the minimum number of coins needed for a given total.

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 ...