POTD Leet Code -1310. XOR Queries of a Subarray

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Efficiently Solving XOR Queries of a Subarray

In the world of programming, efficiently solving problems is crucial, especially when dealing with large datasets. One common challenge is calculating the XOR for specific subarrays based on multiple queries. This article will delve into the “XOR Queries of a Subarray” problem, explaining the approach and providing a practical implementation in JavaScript.

Problem Overview

You are given an array of integers and a set of queries. Each query specifies two indices, and the task is to compute the XOR of the elements in the subarray defined by those indices. The naive approach would involve recalculating the XOR for each query, which can be inefficient for large arrays and multiple queries.

Efficient Approach: Prefix XOR

To optimize our solution, we can use a technique called Prefix XOR. This involves creating a new array that stores the XOR of elements from the start of the array up to each index. Here’s how it works:

1. Build the Prefix XOR Array:

• Create an array, prefixXOR, where each element at index i stores the XOR of all elements from the start of the original array up to i.
• The formula to compute this is:
  [
  prefixXOR[i] = prefixXOR[i-1] \oplus arr[i]
  ]

1. Answering Queries:

• For each query defined by [left, right], the XOR of the subarray can be calculated using:
  [
  XOR(left, right) = prefixXOR[right] \oplus prefixXOR[left – 1]
  ]
• If left is 0, simply return prefixXOR[right].

This method allows us to answer each query in constant time after an initial preprocessing step.

JavaScript Implementation

Here’s a practical implementation of the above approach in JavaScript:

function xorQueries(arr, queries) {
    const n = arr.length;
    const prefixXOR = new Array(n);
    prefixXOR[0] = arr[0];

    // Build the prefix XOR array
    for (let i = 1; i < n; i++) {
        prefixXOR[i] = prefixXOR[i - 1] ^ arr[i];
    }

    const results = [];
    for (const [left, right] of queries) {
        if (left === 0) {
            results.push(prefixXOR[right]);
        } else {
            results.push(prefixXOR[right] ^ prefixXOR[left - 1]);
        }
    }

    return results;
}

// Example usage:
const arr = [1, 3, 4, 8];
const queries = [[0, 1], [1, 2], [0, 3], [3, 3]];
console.log(xorQueries(arr, queries)); // Output: [2, 7, 14, 8]

Conclusion

The prefix XOR technique is a powerful method for efficiently computing the XOR of subarrays in response to multiple queries. By preprocessing the data into a prefix XOR array, we can answer each query in constant time, making this approach highly efficient for large datasets.

Whether you are a beginner or an experienced programmer, understanding and implementing this technique will enhance your problem-solving skills in competitive programming and algorithm design.

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