Maximum OR value of a pair in an Array | Set 2

Given an array arr[] of N positive elements, the task is to find the maximum bitwise OR value of a pair from the given array.

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.
8|7 = 15

Naive Approach: Refer to Maximum OR value of a pair in an array for the naive approach.



Efficient Approach: In this article, we will discuss an optimized solution for the given problem.

Follow the steps below to solve the problem:

  • Find the largest element from the array.
  • Perform Bitwise OR between the largest element and the remaining array elements one by one. This is because the arrangement of set bits in the largest element will contribute to maximum OR value possible from array elements.
  • Print the maximum OR value obtained performing the above step.

Below is the implementation of the above approach:

C++

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// C++ implementation of
// the approach above
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the maximum
// bitwise OR for any pair of the
// given array in O(n) time complexity.
int maxOR(int arr[], int n)
{
    // Find the maximum
    // element in the array
    int max_value
        = *max_element(arr,
                       arr + n);
  
    // Stores the maximum
    // OR value
    int ans = 0;
  
    // Traverse the array and
    // perform Bitwise OR
    // between every array element
    // with the maximum element
    for (int i = 0; i < n; i++) {
        ans = max(ans, (max_value
                        | arr[i]));
    }
    return ans;
}
  
// Driver Code
int main()
{
    int arr[] = { 3, 6, 8, 16 };
    int n = sizeof(arr)
            / sizeof(arr[0]);
  
    cout << maxOR(arr, n);
  
    return 0;
}

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Java

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// Java implementation of
// the approach above
import java.util.Arrays;
class GFG{
      
// Function to return the maximum
// bitwise OR for any pair of the
// given array in O(n) time complexity.
static int maxOR(int []arr, int n)
{
    // Find the maximum
    // element in the array
    int max_value = Arrays.stream(arr).max().getAsInt();
  
    // Stores the maximum
    // OR value
    int ans = 0;
  
    // Traverse the array and
    // perform Bitwise OR
    // between every array element
    // with the maximum element
    for (int i = 0; i < n; i++) 
    {
        ans = Math.max(ans, (max_value | arr[i]));
    }
    return ans;
}
  
// Driver Code
public static void main(String[] args)
{
    int arr[] = new int[]{ 3, 6, 8, 16 };
    int n = 4;
  
    System.out.print(maxOR(arr, n));
}
}
  
// This code is contributed by Ritik Bansal

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C#

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// C# implementation of
// the approach above
using System;
using System.Linq;
  
class GFG{
      
// Function to return the maximum
// bitwise OR for any pair of the
// given array in O(n) time complexity.
static int maxOR(int []arr, int n)
{
      
    // Find the maximum
    // element in the array
    int max_value = arr.Max();
  
    // Stores the maximum
    // OR value
    int ans = 0;
  
    // Traverse the array and
    // perform Bitwise OR
    // between every array element
    // with the maximum element
    for(int i = 0; i < n; i++) 
    {
        ans = Math.Max(ans, (max_value | 
                             arr[i]));
    }
    return ans;
}
  
// Driver Code
public static void Main(String[] args)
{
    int []arr = { 3, 6, 8, 16 };
    int n = 4;
  
    Console.Write(maxOR(arr, n));
}
}
  
// This code is contributed by 29AjayKumar

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Output:

24

Time Complexity: O(N)
Auxiliary Space: O(1)

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