Find the minimum sum of distance to A and B from any integer point in a ring of size N

Given a circular ring which has marking from 1 to N. Given two numbers A and B, you can stand at any place(say X) and count the total sum of the distance(say Z i.e., distance from X to A + distance from X to B). The task is to choose X in such a way that Z is minimized. Print the value of Z thus obtained. Note that X cannot neither be equal to A nor be equal to B.

Examples:

Input: N = 6, A = 2, B = 4
Output: 2
Choose X as 3, so that distance from X to A is 1, and distance from X to B is 1.

Input: N = 4, A = 1, B = 2
Output: 3
Choose X as 3 or 4, both of them gives distance as 3.

Approach: There are two paths between the positions A and B on the circle, one in clockwise direction and another in anti-clockwise. An optimal value for Z is to choose X as any point on the minimum path between A and B then Z will be equal to the minimum distance between the positions except for the case when both the positions are adjacent to each other i.e. the minimum distance is 1. In that case, X cannot be chosen as the point between them as it must be different from both A and B and the result will be 3.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the minimum value of Z
int findMinimumZ(int n, int a, int b)
{
  
    // Change elements such that a < b
    if (a > b)
        swap(a, b);
  
    // Distance from (a to b)
    int distClock = b - a;
  
    // Distance from (1 to a) + (b to n)
    int distAntiClock = (a - 1) + (n - b + 1);
  
    // Minimum distance between a and b
    int minDist = min(distClock, distAntiClock);
  
    // If both the positions are
    // adjacent on the circle
    if (minDist == 1)
        return 3;
  
    // Return the minimum Z possible
    return minDist;
}
  
// Driver code
int main()
{
    int n = 4, a = 1, b = 2;
    cout << findMinimumZ(n, a, b);
  
    return 0;
}

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Java

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// Java implementation of the approach
class GFG 
{
  
    // Function to return the minimum value of Z
    static int findMinimumZ(int n, int a, int b) 
    {
  
        // Change elements such that a < b
        if (a > b)
        {
            swap(a, b);
        }
  
        // Distance from (a to b)
        int distClock = b - a;
  
        // Distance from (1 to a) + (b to n)
        int distAntiClock = (a - 1) + (n - b + 1);
  
        // Minimum distance between a and b
        int minDist = Math.min(distClock, distAntiClock);
  
        // If both the positions are
        // adjacent on the circle
        if (minDist == 1
        {
            return 3;
        }
  
        // Return the minimum Z possible
        return minDist;
    }
  
    private static void swap(int x, int y)
    {
        int temp = x;
        x = y;
        y = temp;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int n = 4, a = 1, b = 2;
        System.out.println(findMinimumZ(n, a, b));
    }
}
  
/* This code contributed by PrinciRaj1992 */

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Python3

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# Python 3 implementation of the approach
# Function to return the minimum value of Z
def findMinimumZ(n, a, b):
      
    # Change elements such that a < b
    if (a > b):
        temp = a
        a = b
        b = temp
  
    # Distance from (a to b)
    distClock = b - a
  
    # Distance from (1 to a) + (b to n)
    distAntiClock = (a - 1) + (n - b + 1)
  
    # Minimum distance between a and b
    minDist = min(distClock, distAntiClock)
  
    # If both the positions are
    # adjacent on the circle
    if (minDist == 1):
        return 3
  
    # Return the minimum Z possible
    return minDist
  
# Driver code
if __name__ == '__main__':
    n = 4
    a = 1
    b = 2
    print(findMinimumZ(n, a, b))
      
# This code is contributed by
# Surendra_Gangwar

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C#

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// C# implementation of the approach
using System;
  
class GFG
{
      
    // Function to return the minimum value of Z
    static int findMinimumZ(int n, int a, int b) 
    {
  
        // Change elements such that a < b
        if (a > b)
        {
            swap(a, b);
        }
  
        // Distance from (a to b)
        int distClock = b - a;
  
        // Distance from (1 to a) + (b to n)
        int distAntiClock = (a - 1) + (n - b + 1);
  
        // Minimum distance between a and b
        int minDist = Math.Min(distClock, distAntiClock);
  
        // If both the positions are
        // adjacent on the circle
        if (minDist == 1) 
        {
            return 3;
        }
  
        // Return the minimum Z possible
        return minDist;
    }
  
    private static void swap(int x, int y)
    {
        int temp = x;
        x = y;
        y = temp;
    }
  
    // Driver code
    static public void Main ()
    {
        int n = 4, a = 1, b = 2;
        Console.WriteLine(findMinimumZ(n, a, b));
    }
  
}
  
/* This code contributed by ajit*/

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PHP

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<?php
//PHP implementation of the approach
// Function to return the minimum value of Z
function findMinimumZ($n, $a, $b)
{
  
    // Change elements such that a < b
    if ($a > $b)
          
        $a = $a ^ $b
        $b = $a ^ $b
        $a = $a ^ $b;
  
    // Distance from (a to b)
    $distClock = $b - $a;
  
    // Distance from (1 to a) + (b to n)
    $distAntiClock = ($a - 1) + ($n - $b + 1);
  
    // Minimum distance between a and b
    $minDist = min($distClock, $distAntiClock);
  
    // If both the positions are
    // adjacent on the circle
    if ($minDist == 1)
        return 3;
  
    // Return the minimum Z possible
    return $minDist;
}
  
// Driver code
  
$n = 4;
$a = 1;
$b = 2;
echo findMinimumZ($n, $a, $b);
  
  
// This code is contributed by akt_mit
?>

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Output:

3


My Personal Notes arrow_drop_up

Striver(underscore)79 at Codechef and codeforces D

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