Max of two numbers without conditional statements, ternary operator or relational operators

Given two integers a and b, the task is to find the greatest of two given numbers without using any conditional statements (such as if and switch), the ternary operator ((condition X)? if X is true: if X is false;) or relational operators (such as <, >, <=, >=, ==, !=).

Examples:

Input: a = 86, b = 34
Output: 86

Input: a = -56, b = -78
Output: -56

Input: a = 789, b = 789
Output: 789

Approach: To solve the problem follow the below idea:

The approach is to use coordinate geometry to find the mid-point of the line drawn by adding the distance from the higher point to the lower point and also adding the distance from the lower point to the higher point. This can be done by using the mathematical expression given below:
f(x, y) = {(|x – y|) + (x + y)} ÷ 2

Implementation of this mathematical expression into a function that takes two integers and returns the greater integer:

C++

// Program to find the greater integer
// among 2 integers
#include <iostream>
using namespace std;

// Function to find the greater integer
int GreaterOfTwo(int x, int y)
{

    // mid-point
    return (abs(x - y) + (x + y)) / 2;
}

// Driver function
int main()
{
    int a, b;
    a = 86, b = 34;

    // Function Call
    cout << GreaterOfTwo(a, b);
    return 0;
}
// This code is contributed by Shashank Kothari(Johnny).

Java

import java.lang.Math;

// Class to find the greater integer among 2 integers
public class GreaterOfTwo {

    // Function to find the greater integer
    public static int greaterOfTwo(int x, int y) {
        // Calculate the mid-point
        return (Math.abs(x - y) + (x + y)) / 2;
    }

    // Main method (Driver function)
    public static void main(String[] args) {
        int a, b;
        a = 86;
        b = 34;

        // Function Call and Print the result
        System.out.println(greaterOfTwo(a, b));
    }
}
//Contributed by Aditi Tyagi

Python3

# Function to find the greater integer among 2 integers
def greater_of_two(x, y):
    # mid-point
    return (abs(x - y) + (x + y)) // 2

# Driver function
def main():
    a, b = 86, 34

    # Function Call
    print(greater_of_two(a, b))

if __name__ == "__main__":
    main()

C#

using System;

namespace CodeTranslation
{
    class Program
    {
        // Function to find the greater integer
        static int GreaterOfTwo(int x, int y)
        {
            // mid-point
            return (Math.Abs(x - y) + (x + y)) / 2;
        }

        static void Main(string[] args)
        {
            int a, b;
            a = 86;
            b = 34;
            // Function Call
            Console.WriteLine(GreaterOfTwo(a, b));
        }
    }
}

Javascript

// Function to find the greater integer
function greaterOfTwo(x, y) {
    // mid-point
    return Math.floor((Math.abs(x - y) + (x + y)) / 2);
}

// Driver function
    let a = 86, b = 34;

    // Function Call
    console.log(greaterOfTwo(a, b));


// This code is contributed by - Dwaipayan Bandyopadhyay

Output

86

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