Compute maximum of two integers in C/C++ using Bitwise Operators

Given two integers A and B, the task is to find the maximum of two numbers using Bitwise Operators.

Examples:

Input: A = 40, B = 54
Output: 54

Input: A = -1, B = -10
Output: -1

Approach: The idea is to use the Bitwise Operator as well as the Right Shift Operator to find the greatest number between two distinct numbers without using any conditional statements( if … ) and Ternary Operator(?: ). Below are the steps:

• Find the maximum value on the basis of the below expression:

z = A – B
i = (z >> 31) & 1
max = a – (i*z)

• Subtract two numbers and store it in another variable z.
• To get the sign of the number obtained after subtraction, apply Right Shift to the variable z and store it in another variable i and then perform Bitwise AND operation on the variable i with 1 to get values in 1 or 0.
• Perform the following expression to get the largest value among the two given numbers as max = (a – (i * z)).

Illustration:

A = 40, B = 54
z = (A – B) = 40 – 54 = -14
i = -1 & 1 = 1
max = a – (i * z) = (40 – (1 * -14)) = 54

Below is the implementation of the above approach:

C++

// C++ program for above approach
#include <iostream>
using namespace std;

// Function to find the largest number
int findMax(int a, int b)
{
    int z, i, max;

    // Perform the subtraction
    z = a - b;

    // Right shift and Bitwise AND
    i = (z >> 31) & 1;

    // Find the maximum number
    max = a - (i * z);

    // Return the maximum value
    return max;
}

// Driver Code
int main()
{
    int A = 40, B = 54;

    // Function Call
    cout << findMax(A, B);

    return 0;
}

C

// C program for the above approach
#include <stdio.h>

// Function to find the largest number
int findMax(int a, int b)
{
    int z, i, max;

    // Perform the subtraction
    z = a - b;

    // Right shift and Bitwise AND
    i = (z >> 31) & 1;

    // Find the maximum number
    max = a - (i * z);

    // Return the maximum value
    return max;
}

// Driver Code
int main()
{
    int A = 40, B = 54;

    // Function Call
    printf("%d", findMax(A, B));

    return 0;
}

Java

// Java program for above approach
import java.io.*;

class GFG {

  // Function to find the largest number
  public static int findMax(int a, int b)
  {
    int z, i, max;

    // Perform the subtraction
    z = a - b;

    // Right shift and Bitwise AND
    i = (z >> 31) & 1;

    // Find the maximum number
    max = a - (i * z);

    // Return the maximum value
    return max;
  }

  // Driver Code
  public static void main (String[] args)
  {
    int A = 40, B = 54;

    // Function Call
    System.out.println(findMax(A, B));
  }

}

// This code is contributed by Shubham Singh

Python3

# Python program for the above approach

# Function to find the largest number
def findmaxx(a, b):

    # Perform the subtraction
    z = a - b

    # Right shift and Bitwise AND
    i = (z >> 31) & 1

    # Find the maxximum number
    maxx = a - (i * z)

    # Return the maxximum value
    return maxx

# Driver Code
A = 40
B = 54

# Function Call
print(findmaxx(A, B))

# This code is contributed by Shubham Singh

Javascript

<script>
// Javascript program for above approach

// Function to find the largest number
function findMax(a, b)
{
    var z, i, max;

    // Perform the subtraction
    z = a - b;

    // Right shift and Bitwise AND
    i = (z >> 31) & 1;

    // Find the maximum number
    max = a - (i * z);

    // Return the maximum value
    return max;
}

// Driver Code
var A = 40, B = 54;

// Function Call
document.write(findMax(A, B));

// This code is ocntributed by shubham singh
</script>

Output:

54

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