#982
Triples with Bitwise AND Equal To Zero
hard · verified · 60% accepted · 479 likes · top 58%
array · hash table · bit manipulation
Description
Given an integer array nums, return the number of AND triples.
An AND triple is a triple of indices (i, j, k) such that:
- 0 <= i < nums.length
- 0 <= j < nums.length
- 0 <= k < nums.length
- nums[i] & nums[j] & nums[k] == 0, where & represents the bitwise-AND operator.
Example 1:
Input: nums = [2,1,3]
Output: 12
Explanation: We could choose the following i, j, k triples:
(i=0, j=0, k=1) : 2 & 2 & 1
(i=0, j=1, k=0) : 2 & 1 & 2
(i=0, j=1, k=1) : 2 & 1 & 1
(i=0, j=1, k=2) : 2 & 1 & 3
(i=0, j=2, k=1) : 2 & 3 & 1
(i=1, j=0, k=0) : 1 & 2 & 2
(i=1, j=0, k=1) : 1 & 2 & 1
(i=1, j=0, k=2) : 1 & 2 & 3
(i=1, j=1, k=0) : 1 & 1 & 2
(i=1, j=2, k=0) : 1 & 3 & 2
(i=2, j=0, k=1) : 3 & 2 & 1
(i=2, j=1, k=0) : 3 & 1 & 2
Example 2:
Input: nums = [0,0,0]
Output: 27
Solution