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Solution: Coin Change

Explore how to solve the coin change problem by using dynamic programming to minimize the number of coins needed for a target amount. Learn to break the problem into subproblems, use memoization for efficiency, and understand why a greedy approach does not work.

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 ...