Find bitwise OR of all possible sub-arrays

Given an array A of size N where, $1\leq N \leq 10^{5}$ . The task is to find the OR of all possible sub-arrays of A and then the OR of all these results.

Examples:

Input : 1 4 6
Output : 7
All possible subarrays are 
{1}, {1, 4}, {4, 6} and {1, 4, 6}
ORs of these subarrays are 1, 5, 6
and 7. OR of these ORs is 7.

Input : 10 100 1000
Output : 1006

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: In SET 1 we have seen how to find bitwise AND of all possible subarrays. Simillar approach is also aplicable here.
The Naive solution is to find the OR of all the sub-arrays and then output the OR of their results. This will lead to O(N²) solution.

Efficient Solution: Using the property that $X\|X\|...\|X=X$ i:e it doesn’t matter how many times an element comes, it’s ORing will be counted as one only. Thus our problem boils down to finding the OR of all the elements of the array.
Below is the implementation of above approach.

C++

// C++ program to find OR of all the sub-arrays 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to return OR of sub-arrays 
int OR(int a[], int n) 
{ 
    int ans = a[0]; 
    for (int i = 1; i < n; ++i)  
         ans |= a[i];     
  
    return ans; 
} 
  
// Driver program 
int main() 
{ 
    int a[] = { 1, 4, 6 }; 
    int n = sizeof(a) / sizeof(a[0]); 
  
    // print OR of all subarrays 
    cout << OR(a, n); 
  
    return 0; 
} 

Java

// Java program to find OR of 
// all the sub-arrays  
class GFG  
{ 
      
// function to return OR  
// of sub-arrays  
static int OR(int a[],int n) 
{ 
    int ans = a[0]; 
    int i; 
    for(i = 1; i < n; i++) 
    { 
        ans |= a[i]; 
    } 
    return ans; 
} 
  
// Driver Code  
public static void main(String args[]) 
{ 
    int a[] = { 1, 4, 6}; 
      
    int n = a.length; 
      
    // print OR of all subarrays  
    System.out.println(OR(a, n)); 
} 
} 
  
// This code is contributed  
// by ANKITRAI1 

Python3

# Python3 program to find OR of all the sub-arrays 
  
# function to return OR of sub-arrays  
def OR(a, n): 
      
    ans = a[0] 
    for i in range(1,n): 
        ans |= a[i] 
      
    return ans 
      
# Driver Code 
if __name__=='__main__': 
    a = [1, 4, 6] 
    n = len(a) 
  
# print OR of all subarrays 
    print(OR(a, n)) 
  
# This code is contributed  
# by Shashank_Sharma 

C#

// C# program to find OR of 
// all the sub-arrays  
using System; 
  
class GFG  
{ 
      
// function to return OR  
// of sub-arrays  
static int OR(int[] a, int n) 
{ 
    int ans = a[0]; 
    int i; 
    for(i = 1; i < n; i++) 
    { 
        ans |= a[i]; 
    } 
    return ans; 
} 
  
// Driver Code  
public static void Main() 
{ 
    int[] a = { 1, 4, 6}; 
      
    int n = a.Length; 
      
    // print OR of all subarrays  
    Console.Write(OR(a, n)); 
} 
} 
  
// This code is contributed 
// by ChitraNayal 

PHP

<?php 
// PHP program to find OR  
// of all the sub-arrays 
  
// function to return OR 
// of sub-arrays 
function O_R($a, $n) 
{ 
    $ans = $a[0]; 
    for ($i = 1; $i < $n; ++$i)  
        $ans |= $a[$i];  
  
    return $ans; 
} 
  
// Driver Code 
$a = array( 1, 4, 6 ); 
$n = count($a); 
  
// print OR of all subarrays 
echo O_R($a, $n); 
  
// This code is contributed 
// by inder_verma 
?> 

Output:

Time Complexity: O(N)

My Personal Notes

Suggest a Topic

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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