3514. Number of Unique XOR Triplets II

Problem Link

Description

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You are given an integer array nums.

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 = [1,3]

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

The unique XOR values are {1, 3}. Thus, the output is 2.

Example 2:

Input: nums = [6,7,8,9]

Output: 4

Explanation:

The possible XOR triplet values are {6, 7, 8, 9}. Thus, the output is 4.

 

Constraints:

• 1 <= nums.length <= 1500
• 1 <= nums[i] <= 1500

Solution

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Python3

class Solution:
    def uniqueXorTriplets(self, nums: List[int]) -> int:
        N = len(nums)
 
        if N == 1: return 1
        
        res = set()
        nums.sort()
        pairs = set()
        
        for i in range(N):
            for j in range(i):
                pairs.add(nums[i] ^ nums[j])
 
        for x in nums:
            for pair in pairs:
                res.add(x ^ pair)
        
        return len(res)