1354-construct-target-array-with-multiple-sums

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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(Python)

class Solution:
    def isPossible(self, target: List[int]) -> bool:
        total = sum(target)
        target = [-a for a in target]
        heapq.heapify(target)
        while True:
            a = -heapq.heappop(target)
            total -= a
            if a == 1 or total == 1: return True
            if a < total or total == 0 or a % total == 0:
                return False
            a %= total
            total += a
            heapq.heappush(target, -a)