Travelling

 Travelling

Problem Statement

Given N cities in a line and your initial position, you want to visit all the cities at least once. You can go to one coordinate P to P+D or P-D where D is the number of steps which you choose initially. Your task is to find the maximum value of D such that you can visit all the cities at least once.

import java.io.*; // for handling input/output

import java.util.*; // contains Collections framework

// don't change the name of this class

// you can add inner classes if needed

class Main {

    public static void main (String[] args) {

                      // Your code here

        Scanner scn = new Scanner(System.in);

        int n = scn.nextInt();

        int x = scn.nextInt();

        int[] city = new int[n];

        for(int i=0; i<n; i++){

            city[i] = Math.abs(scn.nextInt()-x);

        }

        //now solve the problem

        int gcd_=gcd(city[0],city[1]);

        for(int i=2; i<n; i++){

            gcd_= gcd(gcd_,city[i]);

        }

        System.out.println(gcd_);

    }

    //method to find gcd

    static int gcd(int m, int n){

        if(m==0){

            return n;

        }

        if(n==0){

            return m;

        }

        if(m==n){

            return m;

        }

        if(m>n){

            return gcd(m%n, n);

        }

        return gcd(n%m, m);

    }

}