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 <= A.length <= 50000
0 <= A[i] <= 10^9
Explaination:
For example, an array is [001, 011, 100, 110, 101] (in binary).
All the subarrays are:
[001]
[001 011] [011]
[001 011 100] [011 100] [100]
[001 011 100 110] [011 100 110] [100 110] [110]
[001 011 100 110 101] [011 100 110 101] [100 110 101] [110 101] [101]
In each line, we add a new number to each array of the previous line.
Calculate the OR operations for each subarray:
001
011 011
111 111 100
111 111 110 110
111 111 111 111 101
There are O(N^2) numbers in total, which is not acceptable.
After removing duplicate numbers in each line, it becomes:
001
011
111 100
111 110
111 101
In each line t
, for any two numbers t[i]
and t[j]
(i < j), t[i]
must have more 1
s than t[j]
. So the length of each line will not exceed 32. So if we remove duplicate numbers, the complexity would not be very large.
The complexity is O(kN), where k is a constant depends on the bitwise length of input numbers. (32 in this problem)
// We can only increase the number of 1s with |
class Solution {
public int subarrayBitwiseORs(int[] arr) {
Set<Integer> ans = new HashSet();
Set<Integer> cur = new HashSet();
for (int x: arr) {
Set<Integer> cur2 = new HashSet();
for (int y: cur)
cur2.add(x | y);
cur2.add(x);
cur = cur2;
ans.addAll(cur);
}
return ans.size();
}
}
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