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This approach uses a max-heap (priority queue) to efficiently track and operate on the largest element. The primary idea is to reverse the operation: starting from the target array, every large element in the target can be seen as the result of adding all smaller elements in the array to one of the array's elements during the last operation. By repeatedly transforming the largest element in this manner, we can verify if it is possible to reach the initial array of ones.
The time complexity is O(n log n * log maxValue) due to sorting and heap operations, where n is the number of elements and maxValue is the maximum integer in the target. The space complexity is O(1) since we are sorting and using in-place operations optimistically.
1import java.util.PriorityQueue;
2
3public class Solution {
4 public boolean isPossible(int[] target
This Java solution uses a priority queue for handling the maximum element operations, making it efficient since priority queues provide O(log n) time complexity for insertions and deletions. The core idea is to always replace the largest element with the remainder when divided by the rest of the elements' sum, hence reversing the building operation.
This approach utilizes a sort and modulo method to reverse-track the process involved in constructing the target array from an array containing ones. It revolves around repeatedly reducing the maximum value to the remainder after division with the sum of other elements.
Steps include:
Time complexity is O(n log n * log maxValue); space complexity is O(1) when using in-place operations for sorting and arithmetic.
1def isPossible(target):
2 total = sum(target)
3 target.sort(reverse=True)
4
5 while target[0] != 1:
6 max_val = target[0]
7 rest = total - max_val
8
9 if rest == 0 or max_val <= rest:
10 return False
11
12 new_val = max_val % rest
13 if new_val == 0:
14 return False
15
16 target[0] = new_val
17 total = total - max_val + new_val
18 target.sort(reverse=True)
19 return True
20
21if __name__ == '__main__':
22 target = [8, 5]
23 print(isPossible(target))The Python implementation follows a predictable yet potent approach by reversing and resorting the target array, ensuring orderly checks for the possibility of reaching the target by modulating the largest (lead) element successful tracking of inverting the initial transformation steps.