Maximum OR value of a pair in an Array without using OR operator

Given an array arr[] containing N positive integers, the task is to find the maximum bitwise OR value of a pair in the given array without using the Bitwise OR operator.
Examples:

Input: arr[] = {3, 6, 8, 16} 
Output: 24 
Explanation: 
The pair giving maximum OR value is (8, 16) => 8|16 = 24
Input: arr[] = {8, 7, 3, 12} 
Output: 15 
Explanation: 
There are more than one pair giving us the maximum OR value. One among them => 8|7 = 15

Approach: The idea is to find the two numbers which have the most count of set bits at distinct indices. In this way, the resultant number will have all those indices as a set bit, and this can be done without using the OR operator. 

• Find out the maximum element in the array and then find the particular element in the remaining array that will have the set bit at the indexes where the maximum element has an unset bit.
• To maximize our output we have to find such an element that will have a set bit in such a manner that will maximize our output.
• Calculate the complement of the maximum element in the array and find the maximum AND value with the other numbers.
• The maximum AND value of this complement with other array elements will give us the maximum unset bits that could be set in our answer due to other array elements.
• Adding maximum elements with this maximum AND value will give us our desired maximum OR value pair without using OR operation.

Below is the implementation of the above approach:

// C++ implementation of the approach

#include <bits/stdc++.h>
using namespace std;

// Function to return the maximum bitwise OR
// for any pair of the given array
// without using bitwise OR operation
int maxOR(int arr[], int n)
{

    // find maximum element in the array
    int max_value
        = *max_element(arr, arr + n);

    int number_of_bits
        = floor(log2(max_value)) + 1;

    // finding complement will set
    // all unset bits in a number
    int complement
        = ((1 << number_of_bits) - 1)
          ^ max_value;

    int c = 0;

    // iterate through all other
    // array elements to find
    // maximum AND value
    for (int i = 0; i < n; i++) {
        if (arr[i] != max_value) {
            c = max(c, (complement & arr[i]));
        }
    }

    // c will give the maximum value
    // that could be added to max_value
    // to produce maximum OR value
    return (max_value + c);
}

// Driver code
int main()
{
    int arr[] = { 3, 6, 8, 16 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << maxOR(arr, n);

    return 0;
}

// Java implementation 
// of the approach
import java.util.*;
class GFG{

// Function to return the maximum 
// bitwise OR for any pair of the 
// given array without using bitwise 
// OR operation
static int maxOR(int arr[], int n)
{

    // find maximum element in the array
    int max_value = 
        Arrays.stream(arr).max().getAsInt();

    int number_of_bits = 
        (int)((Math.log(max_value))) + 2;

    // finding complement will set
    // all unset bits in a number
    int complement = ((1 << number_of_bits) - 1) ^ 
                       max_value;

    int c = 0;

    // iterate through all other
    // array elements to find
    // maximum AND value
    for (int i = 0; i < n; i++) 
    {
        if (arr[i] != max_value) 
        {
            c = Math.max(c, 
                         (complement & arr[i]));
        }
    }

    // c will give the maximum value
    // that could be added to max_value
    // to produce maximum OR value
    return (max_value + c);
}

// Driver code
public static void main(String[] args)
{
    int arr[] = {3, 6, 8, 16};
    int n = arr.length;
    System.out.print(maxOR(arr, n));
}
}

// This code is contributed by gauravrajput1 

# Python3 implementation of the approach
from math import log2, floor

# Function to return the maximum bitwise OR
# for any pair of the given array
# without using bitwise OR operation
def maxOR(arr, n):
    
    # Find maximum element in the array
    max_value = max(arr)

    number_of_bits = floor(log2(max_value)) + 1

    # Finding complement will set
    # all unset bits in a number
    complement = (((1 << number_of_bits) - 1) ^ 
                 max_value)
    c = 0

    # Iterate through all other
    # array elements to find
    # maximum AND value
    for i in range(n):
        
        if (arr[i] != max_value):
            c = max(c, (complement & arr[i]))

    # c will give the maximum value
    # that could be added to max_value
    # to produce maximum OR value
    return (max_value + c)

# Driver code
if __name__ == '__main__':
    
    arr = [3, 6, 8, 16]
    n = len(arr)

    print(maxOR(arr, n))

# This code is contributed by Bhupendra_Singh

// C# program for the above approach 
using System;
using System.Linq; 

class GFG{

// Function to return the maximum 
// bitwise OR for any pair of the 
// given array without using bitwise 
// OR operation
static int maxOR(int[] arr, int n)
{

    // Find maximum element in the array
    int max_value = arr.Max();

    int number_of_bits = (int)(Math.Log(max_value)) + 2;

    // Finding complement will set
    // all unset bits in a number
    int complement = ((1 << number_of_bits) - 1) ^ 
                      max_value;

    int c = 0;

    // Iterate through all other
    // array elements to find
    // maximum AND value
    for(int i = 0; i < n; i++) 
    {
        if (arr[i] != max_value) 
        {
            c = Math.Max(c, 
                        (complement & arr[i]));
        }
    }

    // c will give the maximum value
    // that could be added to max_value
    // to produce maximum OR value
    return (max_value + c);
}

// Driver code
public static void Main()
{
    int[] arr = { 3, 6, 8, 16 };
    int n = arr.Length;
    
    Console.Write(maxOR(arr, n));
}
}

// This code is contributed by code_hunt

<script>
// javascript implementation 
// of the approach

    // Function to return the maximum
    // bitwise OR for any pair of the
    // given array without using bitwise
    // OR operation
    function maxOR(arr , n) {

        // find maximum element in the array
        var max_value = Math.max.apply(Math,arr);

        var number_of_bits = parseInt( ((Math.log(max_value)))) + 2;

        // finding complement will set
        // all unset bits in a number
        var complement = ((1 << number_of_bits) - 1) ^ max_value;

        var c = 0;

        // iterate through all other
        // array elements to find
        // maximum AND value
        for (i = 0; i < n; i++) {
            if (arr[i] != max_value) {
                c = Math.max(c, (complement & arr[i]));
            }
        }

        // c will give the maximum value
        // that could be added to max_value
        // to produce maximum OR value
        return (max_value + c);
    }

    // Driver code
    
        var arr = [ 3, 6, 8, 16 ];
        var n = arr.length;
        document.write(maxOR(arr, n));

// This code is contributed by todaysgaurav
</script>

24

Time Complexity: O(N) 

Auxiliary Space: O(1)