Bitwise Manipulation
In this approach, we directly manipulate bits to compute the XOR of numbers in the given range without using any additional data structures. This approach is based on observing patterns in the XOR operation.
Example: Consider an example where L=4 and R=8. We compute the XOR of all numbers from 4 to 8 by observing patterns in the XOR operation.
function xorRange(L, R) {
let xorLR = 0;
for (let i = L; i <= R; i++) {
xorLR ^= i;
}
return xorLR;
}
const L = 4;
const R = 8;
const result = xorRange(L, R);
console.log(`Bitwise XOR of all numbers from ${L} to ${R} is ${result}`);
Output:
Bitwise XOR of all numbers from 4 to 8 is 8
Time Complexity: O(N), where N is the size of the range.
Space Complexity: O(1)
Compute the Bitwise XOR of all Numbers in a Range using JavaScript
The complexity of bitwise XOR computation for all the numbers in a specific range is the most frequent difficulty that many people face during the problem-solving process.
Problem Description: Given two integers, L and R, find the bitwise XOR of all numbers in the inclusive range from L to R. There are several approaches to computing the bitwise XOR of all numbers in a range using JavaScript which are as follows:
Table of Content
- Bitwise XOR Property
- Segment Trees
- Binary Indexed Trees (Fenwick Trees)
- Bitwise Manipulation