# Count distinct Bitwise OR of all Subarrays

Given an array A of non-negative integers, where . The task is to count number of distinct possible results obtained by taking the bitwise OR of all the elements in all possible Subarrays.

Examples:

Input: A = [1, 2]
Output: 3
Explanation: The possible subarrays are , , [1, 2].
These Bitwise OR of subarrays are 1, 2, 3.
There are 3 distinct values, so the answer is 3.

Input: A = [1, 2, 4]
Output: 6
Explanation: The possible distinct values are 1, 2, 3, 4, 6, and 7.


Approach:
The Naive approach is to generate all possible subarrays and take bitwise OR of all elements in the subarray. Store each result in set and return length of the set.
Efficient Approach:
We can make the above approach better. The Naive approach is to calculate all possible result where, res(i, j) = A[i] | A[i+1] | … | A[j]. However we can speed this up by taking note of the fact that res(i, j+1) = res(i, j) | A[j+1]. At the kth step, say we have all of the res(i, k) in some set pre. Then we can find the next pre set (for k -> k+1) by using res(i, k+1) = res(i, k) | A[k+1].

However, the number of unique values in this set pre is atmost 32, since the list res(k, k), res(k-1, k), res(k-2, k), … is monotone increasing, and any subsequent values that are different from previous must have more 1’s in it’s binary representation which can have maximum of 32 ones.

Below is the implementation of above approach.

## Python

 # Python implementation of the above approach     # function to return count of distinct bitwise OR  def subarrayBitwiseOR(A):         # res contains distinct values      res = set()         pre = {0}         for x in A:          pre = {x | y for y in pre} | {x}          res |= pre         return len(res)        # Driver program  A = [1, 2, 4]     # print required answer  print(subarrayBitwiseOR(A))     # This code is written by  # Sanjit_Prasad

Output:

6

Time Complexity: O(N*log(K)), where N is the length of A, and K is the maximum size of elements in A.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.