3513. Number of Unique XOR Triplets I

Description

You are given an integer array nums of length n, where nums is a of the numbers in the range [1, n].

A XOR triplet is defined as the XOR of three elements nums[i] XOR nums[j] XOR nums[k] where i <= j <= k.

Return the number of unique XOR triplet values from all possible triplets (i, j, k).

 

Example 1:

Input: nums = [1,2]

Output: 2

Explanation:

The possible XOR triplet values are:

• (0, 0, 0) → 1 XOR 1 XOR 1 = 1
• (0, 0, 1) → 1 XOR 1 XOR 2 = 2
• (0, 1, 1) → 1 XOR 2 XOR 2 = 1
• (1, 1, 1) → 2 XOR 2 XOR 2 = 2

The unique XOR values are {1, 2}, so the output is 2.

Example 2:

Input: nums = [3,1,2]

Output: 4

Explanation:

The possible XOR triplet values include:

• (0, 0, 0) → 3 XOR 3 XOR 3 = 3
• (0, 0, 1) → 3 XOR 3 XOR 1 = 1
• (0, 0, 2) → 3 XOR 3 XOR 2 = 2
• (0, 1, 2) → 3 XOR 1 XOR 2 = 0

The unique XOR values are {0, 1, 2, 3}, so the output is 4.

 

Constraints:

• 1 <= n == nums.length <= 105
• 1 <= nums[i] <= n
• nums is a permutation of integers from 1 to n.

 

Solutions

Solution: Math

• Time complexity: O(1)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
const uniqueXorTriplets = function (nums) {
  const n = nums.length;

  if (n <= 2) return n;

  const maxK = 32 - Math.clz32(n);

  return 2 ** maxK;
};