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Solution: Construct Target Array With Multiple Sums

Explore how to verify if it is possible to construct a target array from an array of ones by applying a reverse engineering strategy using heaps. Understand how using a max heap to process the largest elements combined with modulo operations optimizes this problem. This lesson guides you through the algorithm, its time and space complexity, and demonstrates how working backward simplifies otherwise exponential growth in computations.

Statement

You are given an array target of n integers.

Starting from an array arr of size n where every element is 1, you may perform the following operation any number of times:

  • Let x be the sum of all current elements in arr.

  • Pick an index i and set arr[i] = x.

Your task is to return True if it’s possible to construct target from arr, otherwise return False.

Constraints:

  • n == target.length

  • 11 \leq n 1000\leq 1000 ...