Skip to content
Related Articles

Related Articles

Improve Article

Maximum OR sum of sub-arrays of two different arrays

  • Difficulty Level : Easy
  • Last Updated : 12 Apr, 2021

Given two arrays of positive integers. Select two sub-arrays of equal size from each array and calculate maximum possible OR sum of the two sub-arrays. 
Note: Let f(x, l, r) is the OR sum of all the elements in the range [l, r] in array x. 
Examples : 
 

Input : A[] = {1, 2, 4, 3, 2}
        B[] = {2, 3, 3, 12, 1}
Output : 22
Explanation: Here, one way to get maximum
sum is to select sub-array [l = 2, r = 4]
f(A, 2, 4) = 2|4|3 = 7
f(B, 2, 4) = 3|3|12 = 15
So, f(A, 2, 4) + f(B, 2, 4) = 7 + 15 = 22.
This sum can be achieved in many other ways.

Input : A[] = {1, 2, 2}
        B[] = {2, 1, 3}
Output : 6

 

Observe the operation of Bitwise OR operator. If we take two integers X and Y, then (X|Y >= X). It can be proved by taking some examples. Lets derive a formula using the above equation. 
f(a, 1, i-1) | f(a, i, j) | f(a, j+1, n) >= f(a, i, j)
and also f(a, 1, i-1) | f(a, i, j) | f(a, j+1, n) = f(a, 1, n)
from the above two equations, f(a, 1, n) >= f(a, i, j).
So, we get maximum sum when we take the OR of the whole array -> f(a, 1, n) + f(b, 1, n)
Below is the implementation of above approach: 
 

C++




// CPP program to find maximum OR sum
#include <bits/stdc++.h>
using namespace std;
 
// function to find maximum OR sum
void MaximumSum(int a[], int b[], int n)
{
    int sum1 = 0, sum2 = 0;
     
    // OR sum of all the elements
    // in both arrays
    for (int i = 0; i < n; i++) {
        sum1 |= a[i];
        sum2 |= b[i];
    }
    cout << sum1 + sum2 << endl;
}
 
// Driver Code
int main()
{
    int A[] = { 1, 2, 4, 3, 2 };
    int B[] = { 2, 3, 3, 12, 1 };
    int n = sizeof(A) / sizeof(A[0]);
    MaximumSum(A, B, n);
    return 0;
}

Java




// Java program to find maximum OR sum
 
class GFG {
     
// function to find maximum OR sum
static void MaximumSum(int a[], int b[], int n)
{
    int sum1 = 0, sum2 = 0;
 
    // OR sum of all the elements
    // in both arrays
    for (int i = 0; i < n; i++) {
    sum1 |= a[i];
    sum2 |= b[i];
    }
    System.out.println(sum1 + sum2);
}
 
// Driver code
public static void main(String arg[])
{
    int A[] = {1, 2, 4, 3, 2};
    int B[] = {2, 3, 3, 12, 1};
    int n = A.length;
    MaximumSum(A, B, n);
}
}
 
// This code is contributed by Anant Agarwal.

Python3




# Python 3 program to
# find maximum OR sum
 
# function to find
# maximum OR sum
def MaximumSum(a, b, n):
 
    sum1 = 0
    sum2 = 0
     
    # OR sum of all the
    # elements in both arrays
    for i in range(0, n):
        sum1 |= a[i]
        sum2 |= b[i]
     
    print(sum1 + sum2)
 
# Driver Code
A = [ 1, 2, 4, 3, 2 ]
B = [ 2, 3, 3, 12, 1 ]
n = len(A)
 
MaximumSum(A, B, n)
 
# This code is contributed by Smitha Dinesh Semwal

C#




// C# program to find maximum OR sum
using System;
 
class GFG {
     
    // function to find maximum OR sum
    static void MaximumSum(int []a, int []b, int n)
    {
        int sum1 = 0, sum2 = 0;
     
        // OR sum of all the elements
        // in both arrays
        for (int i = 0; i < n; i++)
        {
            sum1 |= a[i];
            sum2 |= b[i];
        }
        Console.WriteLine(sum1 + sum2);
    }
     
    // Driver code
    public static void Main()
    {
        int []A = {1, 2, 4, 3, 2};
        int []B = {2, 3, 3, 12, 1};
        int n = A.Length;
        MaximumSum(A, B, n);
    }
}
 
// This code is contributed by Vt_m.

PHP




<?php
// PHP program to find maximum OR sum
 
// function to find maximum OR sum
function MaximumSum($a, $b, $n)
{
    $sum1 = 0;
    $sum2 = 0;
     
    // OR sum of all the elements
    // in both arrays
    for ($i = 0; $i < $n; $i++)
    {
        $sum1 |= $a[$i];
        $sum2 |= $b[$i];
    }
    echo ($sum1 + $sum2)."\n";
}
 
// Driver Code
$A = array(1, 2, 4, 3, 2 );
$B = array(2, 3, 3, 12, 1 );
$n = sizeof($A) / sizeof($A[0]);
MaximumSum($A, $B, $n);
 
// This code is contributed by mits
 
?>

Javascript




<script>
 
// JavaScript program to find maximum OR sum
 
// function to find maximum OR sum
function MaximumSum(a, b, n)
{
    let sum1 = 0, sum2 = 0;
   
    // OR sum of all the elements
    // in both arrays
    for (let i = 0; i < n; i++) {
    sum1 |= a[i];
    sum2 |= b[i];
    }
    document.write(sum1 + sum2);
}
 
// Driver code
         
    let A = [1, 2, 4, 3, 2];
    let B = [2, 3, 3, 12, 1];
    let n = A.length;
    MaximumSum(A, B, n);
                   
</script>

Output : 

 22

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :