Find N Unique Integers Sum up to Zero - Practice Coding Problems

Find N Unique Integers Sum up to Zero - Problem

Array Math Easy

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

The array should contain exactly n distinct integers, and their sum must equal zero. You can return any valid combination that satisfies these constraints.

Note: There are multiple valid answers for each input, so any correct solution will be accepted.

Input & Output

Example 1 — Even Number

$ Input: n = 4

› Output: [1,-1,2,-2]

💡 Note: Create 2 pairs of opposite numbers: (1,-1) and (2,-2). Sum: 1 + (-1) + 2 + (-2) = 0

Example 2 — Odd Number

$ Input: n = 5

› Output: [0,1,-1,2,-2]

💡 Note: Since n is odd, add 0 first, then create 2 pairs: (1,-1) and (2,-2). Sum: 0 + 1 + (-1) + 2 + (-2) = 0

Example 3 — Minimum Case

$ Input: n = 1

› Output: [0]

💡 Note: Only one unique integer that sums to zero is 0 itself

Constraints

1 ≤ n ≤ 1000

Visualization

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Understanding the Visualization

Input

Given integer n (number of unique integers needed)

Process

Create symmetric pairs that cancel out, add 0 if n is odd

Output

Array of n unique integers with sum = 0

Key Takeaway

🎯 Key Insight: Symmetric pairs of numbers always cancel out, making zero sum guaranteed

Asked in

G Google 15 M Microsoft 12 a Amazon 8

The key insight is to use symmetric pairs of numbers that cancel each other out. Best approach uses mathematical pairing: for even n, create n/2 pairs like (1,-1), (2,-2). For odd n, add 0 first then create pairs. Time: O(n), Space: O(n).

Common Approaches

Approach	Time	Space	Notes
✓ Mathematical Symmetric Pairs	O(n)	O(n)	Use symmetric pairs (-1,1), (-2,2), etc., with 0 if n is odd
Random Generation with Validation	O(n)	O(n)	Generate random unique integers and adjust until sum equals zero

Mathematical Symmetric Pairs — Algorithm Steps

Step 1: Check if n is odd or even
Step 2: If odd, add 0 to result and decrease n by 1
Step 3: Create n/2 pairs of opposite numbers: (-1,1), (-2,2), etc.
Step 4: Add all pairs to result array

Visualization

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Step-by-Step Walkthrough

Check Parity

If n is odd, add 0 to handle the extra element

Create Pairs

Generate symmetric pairs: 1,-1 then 2,-2, etc.

Combine

All pairs cancel out for a sum of zero

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int* solution(int n) {
    int* result = (int*)malloc(n * sizeof(int));
    int idx = 0;
    
    // If n is odd, add 0
    if (n % 2 == 1) {
        result[idx++] = 0;
        n--;
    }
    
    // Add symmetric pairs
    for (int i = 1; i <= n / 2; i++) {
        result[idx++] = i;
        result[idx++] = -i;
    }
    
    printf("[");
    for (int i = 0; i < idx; i++) {
        printf("%d", result[i]);
        if (i < idx - 1) printf(",");
    }
    printf("]\n");
    return result;
}

int main() {
    int n;
    scanf("%d", &n);
    solution(n);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single loop to generate n numbers

✓ Linear Growth

Space Complexity

O(n)

Result array stores n integers

⚡ Linearithmic Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Symmetric Pairs — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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