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 1s 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)
42.68 %
class Solution {
public int subarrayBitwiseORs(int[] A) {
if (A == null || A.length == 0) {
return 0;
}
Set<Integer> result = new HashSet<>();
Set<Integer> prev = new HashSet<>();
Set<Integer> curr;
for(int a : A) {
curr = new HashSet<>();
curr.add(a);
for (int b : prev) {
curr.add(a | b);
}
result.addAll(curr);
prev = curr;
}
return result.size();
}
}
Version #1 Naive DP [TLE]
class Solution {
public int subarrayBitwiseORs(int[] A) {
if (A == null || A.length == 0) {
return 0;
}
int len = A.length;
// bitwise OR of subarray [i,j]
int[] dp = new int[len];
Set<Integer> visited = new HashSet<>();
for (int i = 0; i < len; i++) {
for (int j = i; j >= 0; j--) {
if (i == j) {
dp[j] = A[i];
} else {
dp[j] = A[j] | dp[j + 1];
}
visited.add(dp[j]);
}
}
return visited.size();
}
}
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