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Solution: Count Triplets That Can Form Two Arrays of Equal XOR

Explore how to count triplets in an integer array that form two subarrays with equal XOR using advanced bitwise manipulation techniques. Understand the prefix XOR optimization and hash map approach to reduce complexity from cubic to linear, enabling efficient handling of large datasets in coding interviews.

Statement

Given an array of integers, arr, we need to find three indices, i, j, and k, such that 00\leq i << j \leq k << arr.length.

We define two values, a and b, as follows:

  • a = arr[i] ^ arr[i + 1] ^ ... ^ arr[j - 1]

  • b = arr[j] ^ arr[j + 1] ^ ... ^ arr[k]

Note: ^ denotes the bitwise XOR operation.

Return the count of triplets (i, j, k) for which a is equal to b.

Constraints:

  • 11 \leq ...