Leetcode #1354: Construct Target Array With Multiple Sums
In this guide, we solve Leetcode #1354 Construct Target Array With Multiple Sums in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Heap (Priority Queue)
Intuition
We need to repeatedly access the smallest or largest element as the input changes.
A heap provides fast insertions and removals while keeping order.
Approach
Push candidates into the heap as you scan, and pop when you need the best element.
Keep the heap size bounded if the problem requires a top-k structure.
Steps:
- Push candidates into a heap.
- Pop the best candidate when needed.
- Maintain heap size or invariants.
Example
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
Python Solution
class Solution:
def isPossible(self, target: List[int]) -> bool:
s = sum(target)
pq = [-x for x in target]
heapify(pq)
while -pq[0] > 1:
mx = -heappop(pq)
t = s - mx
if t == 0 or mx - t < 1:
return False
x = (mx % t) or t
heappush(pq, -x)
s = s - mx + x
return True
Complexity
The time complexity is and the space complexity is , where is the length of array . The space complexity is , where is the length of array .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.