Find N Unique Integers Sum up to Zero

LeetCode 1426 | Difficulty: Easy

Easy

Problem Description

Given an integer n, return any array containing n unique integers such that they add up to 0.

Example 1:

Input: n = 5
Output: [-7,-1,1,3,4]
Explanation: These arrays also are accepted [-5,-1,1,2,3] , [-3,-1,2,-2,4].

Example 2:

Input: n = 3
Output: [-1,0,1]

Example 3:

Input: n = 1
Output: [0]

Constraints:

- `1 <= n <= 1000`

Topics: Array, Math

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Approach

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

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Solutions

Solution 1: C# (Best: 123 ms)

Metric	Value
Runtime	123 ms
Memory	32.7 MB
Date	2021-12-17

Solution

public class Solution {
    public int[] SumZero(int n) {
            int[] result = new int[n];
    int sum = 0;
    
    for(int i=0;i<n-1;i++)
    {
        result[i] = i+1;
        sum += result[i];
    }
    result[n-1] = -sum;
    
    return result;
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• LeetCode provides 2 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: Return an array where the values are symmetric. (+x , -x).

Hint 2: If n is odd, append value 0 in your returned array.