Find N Unique Integers Sum up to Zero

main.md

Question

Approach

To construct an array of n unique integers that sum to zero, I use a simple symmetric pairing method. If n is even, I can generate pairs like (1, -1), (2, -2), …, giving exactly n elements whose sum is zero. If n is odd, I do the same but also include a 0 to balance the count, since adding zero doesn’t affect the sum.

Implementation

class Solution:
    def sumZero(self, n: int) -> List[int]:
        res = []
        for i in range(1, n // 2 + 1):
            res.append(i)
            res.append(-i)
        if n % 2 == 1:
            res.append(0)
        return res

Complexities

• Time: O(n)
• Space: O(1)