**Coin Change Problem Description** ===================================== ### Problem Statement Given an array of distinct positive integers `coins` representing various coin denominations and a non-negative integer `amount`, determine the number of ways to make change for the amount using the available coin denominations. The goal is to find the minimum number of coins required to sum up to the given amount. ### Rules and Constraints - The input array `coins` contains distinct positive integers, each representing a coin denomination. - The `amount` is a non-negative integer, and it is guaranteed that there is a way to make change for it with the available coin denominations. - You can assume the input arrays will not be empty, and the `amount` will not be zero. - The function should return the minimum number of coins required to reach the given `amount`, or throw an error if it's impossible to make change. - The time complexity for solving this problem should be O(amount \* coins.length), where `coins.length` is the number of distinct coin denominations. - The space complexity should be O(amount), as we need to use dynamic programming to solve this problem iteratively. Note: The order in which the coins are selected does not matter, and you can use each coin denomination any number of times to make change. ### Example **Input:** {"input_data":[1,2,3]} **Output:** [1,2,3]