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1354. Construct Target Array With Multiple Sums

Difficulty Topics

Description

You are given an array target of n integers. From a starting array arr consisting of n 1's, you may perform the following procedure :

  • let x be the sum of all elements currently in your array.
  • choose index i, such that 0 <= i < n and set the value of arr at index i to x.
  • You may repeat this procedure as many times as needed.

Return true if it is possible to construct the target array from arr, otherwise, return false.

 

Example 1:

Input: target = [9,3,5]
Output: true
Explanation: Start with arr = [1, 1, 1] 
[1, 1, 1], sum = 3 choose index 1
[1, 3, 1], sum = 5 choose index 2
[1, 3, 5], sum = 9 choose index 0
[9, 3, 5] Done

Example 2:

Input: target = [1,1,1,2]
Output: false
Explanation: Impossible to create target array from [1,1,1,1].

Example 3:

Input: target = [8,5]
Output: true

 

Constraints:

  • n == target.length
  • 1 <= n <= 5 * 104
  • 1 <= target[i] <= 109

Solution

construct-target-array-with-multiple-sums.py
class Solution:
    def isPossible(self, target: List[int]) -> bool:
        total = sum(target)
        heap = [-x for x in target]
        heapify(heap)

        while True:
            x = -heappop(heap)
            total -= x

            if x == 1 or total == 1: return True

            if x < total or total == 0 or x % total == 0: return False

            x %= total
            total += x

            heappush(heap, -x)