1442. Count Triplets That Can Form Two Arrays of Equal XOR
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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 <= 3001 <= arr[i] <= 108
Hints
Hint 1
We are searching for sub-array of length ≥ 2 and we need to split it to 2 non-empty arrays so that the xor of the first array is equal to the xor of the second array. This is equivalent to searching for sub-array with xor = 0.
Hint 2
Keep the prefix xor of arr in another array, check the xor of all sub-arrays in O(n^2), if the xor of sub-array of length x is 0 add x-1 to the answer.