Maximum Bitwise AND pair (X, Y) from given range such that X and Y can be same

Given a range [L, R], the task is to find a pair (X, Y), not necessarily distinct. Find the maximum possible value of the bitwise AND of the chosen integers.

Examples:

Input: L = 3, R = 7
Output: 7
Explanation:
In all the possible pairs, pair (7, 7) gives the maximum value for bitwise AND.

Input: L = 54, R = 55
Output: 55
Explanation:
In all the possible pairs, pair (55, 55) gives the maximum value for bitwise AND.

Naive Approach: To solve the problem mentioned above the naive method is to iterate from L to R and check the bitwise AND for every possible pair and print the maximum value in the end.



Time Complexity: O(N2)

Efficient Approach:

To optimize the above method we have to observe that here we have to integers L and R and we have to select two integers from the interval [L, R] so that their bitwise AND should be maximum. Bitwise AND of any two numbers between L and R will be always less than or equal to R only. So if we have to select two integers from the interval, we can choose the integers to be R and that’s the only way to maximize the bitwise AND.

Below is the implementation of above approach:

C

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// C implementation to find the
// Maximum Bitwise AND pair (X, Y)
// from given range such that
// X and Y can be same
  
#include <stdio.h>
  
// Function to return the
// maximum bitwise AND
int maximumAND(int L, int R)
{
    return R;
}
  
// Driver code
int main()
{
    int l = 3;
    int r = 7;
  
    printf("%d", maximumAND(l, r));
  
    return 0;
}

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C++

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// C++ implementation to find the
// Maximum Bitwise AND pair (X, Y)
// from given range such that
// X and Y can be same
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the
// maximum bitwise AND
int maximumAND(int L, int R)
{
    return R;
}
  
// Driver code
int main()
{
    int l = 3;
    int r = 7;
  
    cout << maximumAND(l, r);
  
    return 0;
}

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Java

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// Java implementation to find the
// Maximum Bitwise AND pair (X, Y)
// from given range such that
// X and Y can be same
  
class GFG {
  
    // Function to return the
    // maximum bitwise AND
    static int maximumAND(int L, int R)
    {
        return R;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int l = 3;
        int r = 7;
        System.out.print(maximumAND(l, r));
    }
}

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Python3

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# Python3 implementation to find the 
# Maximum Bitwise AND pair (X, Y)
# from given range such that
# X and Y can be same
  
# Function to return the
# maximum bitwise AND 
def maximumAND(L, R):
    return R
  
# Driver code 
if __name__ == '__main__'
    l = 3
    r = 7
    print(maximumAND(l, r)) 

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C#

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// C# implementation to find the
// maximum Bitwise AND pair (X, Y)
// from given range such that
// X and Y can be same
using System;
  
class GFG{
  
// Function to return the
// maximum bitwise AND
static int maximumAND(int L, int R)
{
    return R;
}
  
// Driver code
public static void Main(String[] args)
{
    int l = 3;
    int r = 7;
      
    Console.Write(maximumAND(l, r));
}
}
  
// This code is contributed by amal kumar choubey

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Output:

7

Time Complexity: O(1)

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Improved By : Amal Kumar Choubey