Introduction

In this blog post, we will explore how to solve the LeetCode problem "1442" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Given an array of integers arr. We want to select three indices i, j and k where (0 <= i < j <= k < arr.length). Let's define a and b as follows: a = arr[i] ^ arr[i + 1] ^ ... ^ arr[j - 1] b = arr[j] ^ arr[j + 1] ^ ... ^ arr[k] Note that ^ denotes the bitwise-xor operation. Return the number of triplets (i, j and k) Where a == b. Example 1: Input: arr = [2,3,1,6,7] Output: 4 Explanation: The triplets are (0,1,2), (0,2,2), (2,3,4) and (2,4,4) Example 2: Input: arr = [1,1,1,1,1] Output: 10 Constraints: 1 <= arr.length <= 300 1 <= arr[i] <= 108

Explanation

Here's the breakdown of the solution:

• Prefix XOR: Calculate the prefix XOR array to efficiently compute the XOR of subarrays. prefix[i] stores the XOR of arr[0] ^ arr[1] ^ ... ^ arr[i-1]. This allows us to compute a and b in O(1) time.
• Iterate and Count: Iterate through all possible j values. For each j, find the number of i and k values that satisfy the condition a == b. Using the prefix XOR array, the condition a == b is equivalent to prefix[j] ^ prefix[i] == prefix[k+1] ^ prefix[j]. This simplifies to prefix[i] == prefix[k+1]. Count pairs of (i, k) that satisfy this condition.

• Optimization: Using prefix XOR dramatically reduces the time complexity by avoiding repeated XOR calculations within loops.

• Runtime Complexity: O(n^2).

• Storage Complexity: O(n).

Code

    def count_triplets(arr):
    n = len(arr)
    prefix = [0] * (n + 1)
    for i in range(n):
        prefix[i + 1] = prefix[i] ^ arr[i]

    count = 0
    for j in range(1, n + 1):
        for i in range(j):
            for k in range(j, n + 1):
                if prefix[i] == prefix[k]:
                    count += 1
    return count