Description
You are given an integer array nums of length n, where nums is a permutation 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 <= 1051 <= nums[i] <= nnumsis a permutation of integers from1ton.
Solutions
The mathematician way.
Language: javascript(2026-07-23 07:24)DONE
CPU Performance100.00%
Memory Performance77.74%
/**
* @param {number[]} nums
* @return {number}
*/
var uniqueXorTriplets = function (nums) {
const n = nums.length;
if (n <= 2) {
return n;
}
let ans = 1;
while (ans <= n) {
ans <<= 1;
}
return ans;
};