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Intuition

To solve this problem, we need to find the number of triplets (i, j, k) such that the XOR of the subarray from i to j-1 is equal to the XOR of the subarray from j to k. This can be achieved using the properties of the XOR operation.

Approach

  1. Prefix XOR: Compute the prefix XOR for each position in the array. The prefix XOR up to index i is the XOR of all elements from the start of the array to index i.
  2. Utilize Prefix XOR to Find Triplets: For a triplet (i, j, k) to satisfy the condition a==b: if prefix[j−1]==prefix[k], it implies the condition is satisfied.

Complexity

  • Time complexity: $O(n^2)$, where $n$ is the length of the array. The nested loops run in quadratic time.

  • Space complexity: $O(n)$ for the prefix XOR array.

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