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Solution: Construct Target Array With Multiple Sums

Explore how to solve the problem of constructing a target array from an initial array of ones by working backward with a max heap and modulo operations. Understand the algorithm's steps to efficiently reduce the problem size, avoid excessive computations, and verify whether the target array is achievable, along with analyzing its time and space complexity.

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 ...