XOR Operation in an Array

XOR Operation in an Array - Problem

You are given an integer n and an integer start.

Define an array nums where nums[i] = start + 2 * i (0-indexed) and n == nums.length.

Return the bitwise XOR of all elements of nums.

Input & Output

Example 1 — Basic Case

$ Input: n = 5, start = 0

› Output: 8

💡 Note: Array is [0,2,4,6,8]. XOR: 0⊕2⊕4⊕6⊕8 = 8

Example 2 — Different Start

$ Input: n = 4, start = 3

› Output: 8

💡 Note: Array is [3,5,7,9]. XOR: 3⊕5⊕7⊕9 = 8

Example 3 — Single Element

$ Input: n = 1, start = 7

› Output: 7

💡 Note: Array is [7]. XOR of single element is itself: 7

Constraints

1 ≤ n ≤ 1000
0 ≤ start ≤ 1000

Visualization

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Asked in

a Amazon 15 M Microsoft 12 🍎 Apple 8

The key insight is to recognize this as an arithmetic sequence where each element is start + 2*i. The optimal approach computes and XORs elements directly without storing them. Time: O(n), Space: O(1)

Common Approaches

✓ Direct XOR without Array

⏱️ Time: O(n) Space: O(1)

Instead of creating the array first, compute each element on-the-fly and XOR it immediately. This saves space while maintaining the same time complexity.

Generate Array and XOR

⏱️ Time: O(n) Space: O(n)

First create the array where nums[i] = start + 2*i, then iterate through all elements and XOR them together.

Direct XOR without Array — Algorithm Steps

Initialize result = 0
For each i from 0 to n-1, compute start + 2*i
XOR result with the computed value

Visualization

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Step-by-Step Walkthrough

Initialize

result = 0

Compute & XOR

For each i, compute start+2*i and XOR

Final Result

Return accumulated XOR

Code -

solution.c — C

#include <stdio.h>

int solution(int n, int start) {
    int result = 0;
    for (int i = 0; i < n; i++) {
        result ^= (start + 2 * i);
    }
    return result;
}

int main() {
    int n, start;
    scanf("%d", &n);
    scanf("%d", &start);
    
    int result = solution(n, start);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single loop iterating n times to compute and XOR each element

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables, no extra array storage

✓ Linear Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Direct XOR without Array — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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