Bitwise ORs of Subarrays

We have an array A of non-negative integers.

For every (contiguous) subarray B = [A[i], A[i+1], ..., A[j]] (with i <= j), we take the bitwise OR of all the elements in B, obtaining a result A[i] | A[i+1] | ... | A[j].

Return the number of possible results.  (Results that occur more than once are only counted once in the final answer.)

 

Example 1:

Input: [0]
Output: 1
Explanation: 
There is only one possible result: 0.

Example 2:

Input: [1,1,2]
Output: 3
Explanation: 
The possible subarrays are [1], [1], [2], [1, 1], [1, 2], [1, 1, 2].
These yield the results 1, 1, 2, 1, 3, 3.
There are 3 unique values, so the answer is 3.

Example 3:

Input: [1,2,4]
Output: 6
Explanation: 
The possible results are 1, 2, 3, 4, 6, and 7.

 

Note:

  1. 1 <= A.length <= 50000
  2. 0 <= A[i] <= 10^9

Solution:

[1,2,3,4]
The usual way we solve subarrays is (fix i and run j from i to n-1) 
[1][1,2][1,2,3][1,2,3,4]
[2],[2,3][2,3,4]
[3][3,4]
[4]

In this problem it is efficient to arrange subproblems as follows to take full advantage of the partial reulsts to solve other subproblems.

[1]
[1,2][2]
[1,2,3][2,3][3]
[1,2,3,4][2,3,4][3,4][4]

class Solution { public int subarrayBitwiseORs(int[] A) { Set<Integer> res = new HashSet(); Set<Integer> prev = new HashSet(); int n = A.length; for (int i = 0; i < n; i ++) { Set<Integer> curr = new HashSet(); curr.add(A[i]); for (int val : prev) { curr.add(val | A[i]); } res.addAll(curr); prev = curr; } return res.size(); } }