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: 54Input: 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 numberint 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 Codeint 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 numberint 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 Codeint main(){ int A = 40, B = 54; // Function Call printf("%d", findMax(A, B)); return 0;} |
Java
// Java program for above approachimport 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 numberdef 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 CodeA = 40B = 54# Function Callprint(findmaxx(A, B))# This code is contributed by Shubham Singh |
Javascript
<script>// Javascript program for above approach// Function to find the largest numberfunction 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 Codevar A = 40, B = 54;// Function Calldocument.write(findMax(A, B));// This code is ocntributed by shubham singh</script> |
Output:
54
Time Complexity: O(1)
Auxiliary Space: O(1)
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