Largest of two distinct numbers without using any conditional statements or operators

Given two positive and distinct numbers, the task is to find the greatest of two given numbers without using any conditional statements(if...) and operators(?: in C/C++/Java).

Examples:  

Input: a = 14, b = 15
Output: 15

Input: a = 14, b = 14
Output: 14

Input: a = 1233133, b = 124
Output: 1233133

The Approach is to return the value on the basis of the below expression: 

c = a - b
flag = (c >> 31) & 1
(a * (1 - flag)) + (b * flag)

Mathematical Explanation:

Let's break down the mathematical operations step by step:

1. Difference Calculation:
   • c=a−b
2. Sign Check:
   • Right shift the sign bit of c to the least significant bit:
     • flag=(c>>31)&1
   • This operation checks the sign of the integer:
     • If c is positive or zero, flag will be 0.
     • If c is negative, flag will be 1.
   • Result Selection:
     • Use the flag to determine the result:
       • result=(a ×! flag) + (b × flag)
     • Simplifying this:
       • If flag=0
         • result=(a ×1 ) + (b × 0) = a
       • If flag=0
         • result=(a × 0) + (b × 1) = b

#include <stdio.h>

// Function to find the largest number
int max(int a, int b)
{
    int c = a - b;
    int flag = (c >> 31) & 1;
    return (a * !flag) + (b * flag);
}

int main()
{
    int a = 78;
    int b = 68;
    printf("The maximum of %d and %d is %d\n", a, b, max(a, b));

    a = 1233133;
    b = 124;
    printf("The maximum of %d and %d is %d\n", a, b, max(a, b));

    a = 14;
    b = 14;
    printf("The maximum of %d and %d is %d\n", a, b, max(a, b));

    return 0;
}

public class MaxOfTwoNumbers {
    public static int max(int a, int b) {
        int c = a - b;
        int flag = (c >> 31) & 1;
        return (a * (1 - flag)) + (b * flag);
    }

    public static void main(String[] args) {
        int a = 78;
        int b = 68;
        System.out.println("The maximum of " + a + " and " + b + " is " + max(a, b));

        a = 68;
        b = 78;
        System.out.println("The maximum of " + a + " and " + b + " is " + max(a, b));

        a = 78;
        b = 78;
        System.out.println("The maximum of " + a + " and " + b + " is " + max(a, b));
    }
}
//coded by anuja_mishra

def max(a, b):
    c = a - b
    flag = (c >> 31) & 1
    return (a * (1 - flag)) + (b * flag)

a = 78
b = 68
print(f"The maximum of {a} and {b} is {max(a, b)}")

a = 68
b = 78
print(f"The maximum of {a} and {b} is {max(a, b)}")

a = 78
b = 78
print(f"The maximum of {a} and {b} is {max(a, b)}")
#coded by anuja_mishra

function max(a, b) {
    var c = a - b;
    var flag = (c >> 31) & 1;
    return (a * (1 - flag)) + (b * flag);
}

let a = 78;
let b = 68;
console.log(`The maximum of ${a} and ${b} is ${max(a, b)}`);

a = 68;
b = 78;
console.log(`The maximum of ${a} and ${b} is ${max(a, b)}`);

a = 78;
b = 78;
console.log(`The maximum of ${a} and ${b} is ${max(a, b)}`);

//coded by anuja_mishra

The maximum of 78 and 68 is 78
The maximum of 1233133 and 124 is 1233133
The maximum of 14 and 14 is 14

Time complexity: O(1)
Auxiliary space: O(1)