Find K such that |A – K| = |B – K|

Given two integers A and B where (A ? B). The task is to find K such that |A – K| = |B – K|. If no such K exists then print -1.

Examples:

Input: A = 2, B = 16 
Output: 9 
|2 – 9| = |16 – 9| = 7

Input: A = 5, B = 2 
Output: -1 

Approach: It is given that A ? B. So let A < B then there are three cases:  

• K < A: This gives A – K = B – K which gives A = B which is false.
• K > B: This gives K – A = K – B which is also false.
• A ? K ? B: This gives K – A = B – K which gives 2 * K = A + B

If A + B is odd, there is thus no solution. If A + B is even then the answer is (A + B) / 2.

Below is the implementation of the above approach:  

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to find k such that
// |a - k| = |b - k|
int find_k(int a, int b)
{
    // If (a + b) is even
    if ((a + b) % 2 == 0)
        return ((a + b) / 2);

    return -1;
}

// Driver code
int main()
{
    int a = 2, b = 16;

    cout << find_k(a, b);

    return 0;
}

Java

// Java implementation of the approach
class GFG
{

// Function to find k such that
// |a - k| = |b - k|
static int find_k(int a, int b)
{
    // If (a + b) is even
    if ((a + b) % 2 == 0)
        return ((a + b) / 2);

    return -1;
}

// Driver code
public static void main(String[] args)
{
    int a = 2, b = 16;

    System.out.println(find_k(a, b));
}
}

// This code is contributed by Code_Mech

Python3

# Python3 implementation of the approach

# Function to find k such that
# |a - k| = |b - k|
def find_k(a, b) :

    # If (a + b) is even
    if ((a + b) % 2 == 0) :
        return ((a + b) // 2);

    return -1;

# Driver code
if __name__ == "__main__" :

    a = 2; b = 16;

    print(find_k(a, b));

# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;

class GFG
{

// Function to find k such that
// |a - k| = |b - k|
static int find_k(int a, int b)
{
    // If (a + b) is even
    if ((a + b) % 2 == 0)
        return ((a + b) / 2);

    return -1;
}

// Driver code
public static void Main()
{
    int a = 2, b = 16;

    Console.Write(find_k(a, b));
}
}

// This code is contributed by chitranayal

Javascript

<script>

// Javascript implementation of the approach

// Function to find k such that
// |a - k| = |b - k|
function find_k(a, b)
{

    // If (a + b) is even
    if ((a + b) % 2 == 0)
        return ((a + b) / 2);

    return -1;
}

// Driver code
var a = 2, b = 16;

document.write( find_k(a, b));

// This code is contributed by akshitsaxenaa09

</script>

Output

9

Time Complexity: O(1)

Auxiliary Space: O(1)