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Find a pair with sum N having minimum absolute difference
  • Last Updated : 19 Mar, 2021

Given an integer N, the task is to find a distinct pair of X and Y such that X + Y = N and abs(X – Y) is minimum.

Examples:

Input: N = 11
Output: 5 6 
Explanation:
X = 5 and Y = 6 satisfy the given equation. 
Therefore, the minimum absolute value of abs(X – Y) = 1.

Input: N = 12 
Output: 5 7

Naive Approach: The simplest approach to solve this problem is to generate all possible values of X and Y with a sum equal to N and print the value of X and Y which gives the minimum absolute value of abs(X – Y).



Time Complexity: O(N2
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized based on the following observations:

If N % 2 == 1, then pairs (N / 2) and (N / 2 + 1) have minimum absolute difference. 
Otherwise, pairs (N / 2 – 1) and (N / 2 + 1) will have the minimum absolute difference.

Follow the steps below to solve the problem:

  • Check if N is odd or not. If found to be true, then print the floor value of (N / 2) and (N / 2 + 1) as the required answer.
  • Otherwise, print the value of (N / 2 – 1) and (N / 2 + 1).

Below is the implementation of the above approach:

C++




// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the value of X and Y
// having minimum value of abs(X - Y)
void findXandYwithminABSX_Y(int N)
{
    // If N is an odd number
    if (N % 2 == 1) {
        cout << (N / 2) << " " << (N / 2 + 1);
    }
 
    // If N is an even number
    else {
        cout << (N / 2 - 1) << " " << (N / 2 + 1);
    }
}
 
// Driver Code
int main()
{
    int N = 12;
    findXandYwithminABSX_Y(N);
}

Java




// Java program to implement
// the above approach
import java.util.*;
class GFG {
 
    // Function to find the value
    // of X and Y having minimum
    // value of Math.abs(X - Y)
    static void findXandYwithminABSX_Y(int N)
    {
        // If N is an odd number
        if (N % 2 == 1) {
            System.out.print((N / 2) + " " + (N / 2 + 1));
        }
 
        // If N is an even number
        else {
            System.out.print((N / 2 - 1) + " "
                             + (N / 2 + 1));
        }
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int N = 12;
        findXandYwithminABSX_Y(N);
    }
}
 
// This code is contributed by gauravrajput1

Python3




# Python3 program to implement
# the above approach
 
# Function to find the value of X and Y
# having minimum value of abs(X - Y)
 
 
def findXandYwithminABSX_Y(N):
 
    # If N is an odd number
    if (N % 2 == 1):
        print((N // 2), (N // 2 + 1))
 
    # If N is an even number
    else:
        print((N // 2 - 1), (N // 2 + 1))
 
 
# Driver Code
if __name__ == '__main__':
 
    N = 12
 
    findXandYwithminABSX_Y(N)
 
# This code is contributed by mohit kumar 29

C#




// C# program to implement
// the above approach
using System;
class GFG {
 
    // Function to find the value
    // of X and Y having minimum
    // value of Math.abs(X - Y)
    static void findXandYwithminABSX_Y(int N)
    {
        // If N is an odd number
        if (N % 2 == 1) {
            Console.Write((N / 2) + " " + (N / 2 + 1));
        }
 
        // If N is an even number
        else {
            Console.Write((N / 2 - 1) + " " + (N / 2 + 1));
        }
    }
 
    // Driver Code
    public static void Main()
    {
        int N = 12;
        findXandYwithminABSX_Y(N);
    }
}
 
// This code is contributed by bgangwar59

PHP




<?php
   
function findXandYwithminABSX_Y($N){
   
    // If N is an odd number
    if ($N % 2 == 1)
  {
    return ($N / 2) . " " . ($N / 2 + 1);
  }
  
  // If N is an even number
  else
  {
    return ($N /2 -1) . " " . ($N / 2 + 1);
  }
   
   
}
 
   
// Driver code  
$N = 12;
echo(findXandYwithminABSX_Y($N));
 
   
?>

Javascript




<script>
 
// JavaScript program to implement the above approach
 
// Function to find the value of X and Y
// having minimum value of abs(X - Y)
function findXandYwithminABSX_Y(N)
{
 
    // If N is an odd number
    if (N % 2 == 1)
    {
        document.write((N / 2) + " " + (N / 2 + 1));
    }
 
    // If N is an even number
    else
    {
        document.write((N / 2 - 1) + " " + (N / 2 + 1));
    }
}
 
 
// Driver Code
 
    let N = 12;
    findXandYwithminABSX_Y(N);
     
    // This code is contributed by susmitakundugoaldanga.
</script>
Output: 
5 7

 

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

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