{ "data": { "question": { "questionId": "3820", "questionFrontendId": "3514", "categoryTitle": "Algorithms", "boundTopicId": 3648752, "title": "Number of Unique XOR Triplets II", "titleSlug": "number-of-unique-xor-triplets-ii", "content": "
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).
\n
Example 1:
\n\nInput: nums = [1,3]
\n\nOutput: 2
\n\nExplanation:
\n\nThe possible XOR triplet values are:
\n\n(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 = 3The unique XOR values are {1, 3}. Thus, the output is 2.
Example 2:
\n\nInput: nums = [6,7,8,9]
\n\nOutput: 4
\n\nExplanation:
\n\nThe possible XOR triplet values are {6, 7, 8, 9}. Thus, the output is 4.
\n
Constraints:
\n\n1 <= nums.length <= 15001 <= nums[i] <= 1500给你一个整数数组 nums 。
XOR 三元组 定义为三个元素的异或值 nums[i] XOR nums[j] XOR nums[k],其中 i <= j <= k。
返回所有可能三元组 (i, j, k) 中 不同 的 XOR 值的数量。
\n\n
示例 1:
\n\n输入: nums = [1,3]
\n\n输出: 2
\n\n解释:
\n\n所有可能的 XOR 三元组值为:
\n\n(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不同的 XOR 值为 {1, 3} 。因此输出为 2 。
示例 2:
\n\n输入: nums = [6,7,8,9]
\n\n输出: 4
\n\n解释:
\n\n不同的 XOR 值为 {6, 7, 8, 9} 。因此输出为 4 。
\n\n
提示:
\n\n1 <= nums.length <= 15001 <= nums[i] <= 1500max_xor.",
"For each index i, consider all pairs of indices (j, k) such that i <= j <= k. For each such pair, compute the triplet XOR as nums[i] XOR nums[j] XOR nums[k].",
"You can optimize the calculation by precomputing or reusing intermediate XOR results. For example, after fixing an index i, compute XORs of pairs (j, k) in O(n2) time instead of checking all three indices independently.",
"Finally, count the number of unique XOR values obtained from all triplets."
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