1354 Construct Target Array With Multiple Sums

🔀 Pick One

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
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import heapq

class Solution:
    def isPossible(self, target: List[int]) -> bool:
        if len(target) == 1:
            return target == [1]
        
        total = sum(target)

        heap = [-num for num in target]
        heapq.heapify(heap)
        
        while -heap[0] > 1:
            largest = -heap[0]
            rest = total - largest
            if rest == 1:
                # only possible when n=2
                return True
            
            # since the largest was updated every time
            # this is fater than deducting by rest repeatedly
            x = largest % rest
            
            if x == 0 or x == largest:
                return False
            
            # same as pop and push new min, but faster
            heapq.heapreplace(heap, -x)
            total = total - largest + x

        return True