LeetCode 1304 - Find N Unique Integers Sum up to Zero

Difficulty: Easy
Topic: Array, Math
Daily Question: 7th September 2025

Video Explanation

Watch the complete solution walkthrough on my YouTube channel!

Intuition

When we want n unique integers that sum to zero, the first idea is symmetry.
Pairs like (x, -x) cancel each other out perfectly. So the solution is to build the array from opposite pairs, and if needed, include 0 as a neutral element.

Approach

  • If n is even: take n // 2 pairs of opposite numbers, e.g. (1, -1), (2, -2), ....
  • If n is odd: do the same for n // 2 pairs and add a single 0 at the end.
  • The order does not matter, since the problem does not require sorting.

This guarantees:

  • ✅ Uniqueness: Each number appears exactly once
  • ✅ Correct count: Exactly n elements
  • ✅ Sum equals zero: Opposite pairs cancel out

Complexity Analysis

  • Time complexity: O(n) - We construct the result with one loop up to n // 2.
  • Space complexity: O(n) - For storing the resulting array of size n.

Solution

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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

Example Walkthrough

Example 1: n = 5

  • Pairs: (1, -1), (2, -2) → [1, -1, 2, -2]
  • n is odd, add 0 → [1, -1, 2, -2, 0]
  • Sum: 1 + (-1) + 2 + (-2) + 0 = 0 ✅

Example 2: n = 4

  • Pairs: (1, -1), (2, -2) → [1, -1, 2, -2]
  • Sum: 1 + (-1) + 2 + (-2) = 0 ✅

Key Takeaways

  1. Symmetry approach is perfect for sum-to-zero problems
  2. Handle odd/even cases separately for completeness
  3. Simple mathematics often leads to elegant solutions
  4. Order independence simplifies the implementation

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