count-triplets-that-can-form-two-arrays-of-equal-xor

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1442. Count Triplets That Can Form Two Arrays of Equal XOR (Medium)

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

Related Topics

[Array] [Hash Table] [Math] [Bit Manipulation] [Prefix Sum]

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.