Triples with Bitwise AND Equal To Zero

arrayhash tablebit manipulation

Problem Statement

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.

Examples

Example 1

Input: nums = [2,1,3]
Output: 12
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

Constraints

1 <= nums.length <= 1000

0 <= nums[i] < 2 ^16

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table