# Reaching a point using clockwise or anticlockwise movements

• Last Updated : 20 Feb, 2023

Given starting and ending position and a number N. Given that we are allowed to move in only four directions as shown in the image below. The directions of moves are U(), R, Dand L. We need to write a program to determine if starting from the given starting position we can reach the given end position in exactly N moves in moving about any direction(Clockwise or Anticlockwise).

Examples :

Input: start = U , end = L , N = 3
Output: Clockwise
Explanation: Step 1: move clockwise to reach R
Step 2: move clockwise to reach D
Step 3: move clockwise to reach L
So we reach from U to L in 3 steps moving in
clockwise direction.

Input: start = R , end = L , N = 3
Output: Not possible
Explanation: It is not possible to start from
R and end at L in 3 steps moving about in any
direction.

Input: start = D , end = R , N = 7
Output: Clockwise
Explanation: Starting at D, we complete one
complete clockwise round in 4 steps to reach D
again, then it takes 3 step to reach R 

The idea to solve this problem is to observe that we can complete one round in 4 steps by traveling in any direction (clockwise or anti-clockwise), so taking n%4 steps is equivalent to taking n steps from the starting point. Therefore n is reduced to n%4. Consider the values of ‘U’ as 0, ‘R’ as 1, ‘D’ as 2 and ‘L’ as 3. If the abs(value(a)-value(b)) is 2 and n is also 2, then we can move either in clockwise or anticlockwise direction to reach the end position from the start position. If moving k steps in clockwise direction take us to the end position from start position then we can say that the condition for clockwise move will be (value(a)+k)%4==value(b). Similarly, the condition for anticlockwise move will be (value(a)+k*3)%4==value(b) since taking k step from position a in clockwise direction is equivalent to taking (a + k*3)%4 steps in anticlockwise direction.
Below is the implementation of the above approach:

## C++

 // CPP program to determine if // starting from the starting // position we can reach the  // end position in N moves // moving about any direction#include using namespace std;  // function that returns mark // up value of directionsint value(char a){    if (a == 'U')        return 0;    if (a == 'R')        return 1;    if (a == 'D')        return 2;    if (a == 'L')        return 3;}  // function to print// the possible movevoid printMove(char a, char b, int n){    // mod with 4 as completing     // 4 steps means completing     // one single round    n = n % 4;      // when n is 2 and the     // difference between moves is 2    if (n == 2 and abs(value(a) -                        value(b)) == 2)        cout << "Clockwise or Anticlockwise";      // anticlockwise condition    else if ((value(a) + n * 3) % 4 == value(b))        cout << "Anticlockwise";      // clockwise condition    else if ((value(a) + n) % 4 == value(b))        cout << "Clockwise";    else        cout << "Not Possible";}  // Driver Codeint main(){    char a = 'D', b = 'R';    int n = 7;    printMove(a, b, n);      return 0;}

## Java

 // Java program to determine if // starting from the starting // position we can reach the // end position in N moves // moving about any directionclass GFG{    // function that returns mark     // up value of directions    static int value(char a)    {        if (a == 'U')            return 0;        if (a == 'R')            return 1;        if (a == 'D')            return 2;        if (a == 'L')            return 3;                          return -1;    }      // function to print    // the possible move    static void printMove(char a,                           char b,                           int n)    {        // mod with 4 as completing         // 4 steps means completing        // one single round        n = n % 4;              // when n is 2 and         // the difference        // between moves is 2        if (n == 2 && Math.abs(value(a) -                                value(b)) == 2)            System.out.println("Clockwise " +                        " or Anticlockwise");              // anticlockwise condition        else if ((value(a) + n * 3) %                       4 == value(b))            System.out.println("Anticlockwise");              // clockwise condition        else if ((value(a) + n) % 4 == value(b))            System.out.println("Clockwise");        else            System.out.println("Not Possible");    }      // Driver Code    public static void main(String args[])    {        char a = 'D', b = 'R';        int n = 7;        printMove(a, b, n);    }}  // This code is contributed by Sam007

## Python3

 # python program to determine # if starting from the starting# position we can reach the end # position in N moves moving  # any direction  # function that returns mark# up value of directionsdef value(a):          if (a == 'U'):        return 0    if (a == 'R'):        return 1    if (a == 'D'):        return 2    if (a == 'L'):        return 3  # function to print # the possible movedef printMove(a, b, n):          # mod with 4 as completing    # 4 steps means completing    # one single round    n = n % 4;      # when n is 2 and     # the difference    # between moves is 2    if (n == 2 and        abs(value(a) - value(b)) == 2):        print ("Clockwise or Anticlockwise")      # anticlockwise condition    elif ((value(a) + n * 3) % 4 == value(b)):        print ("Anticlockwise")      # clockwise condition    elif ((value(a) + n) % 4 == value(b)):        print ("Clockwise")    else:        print ("Not Possible")    # Driver Codea = 'D'b = 'R'n = 7printMove(a, b, n)  # This code is contributed by Sam007.

## C#

 // C# program to determine// if starting from the // starting position we // can reach the end position// in N moves moving about // any directionusing System;  class GFG{    // function that returns mark     // up value of directions    static int value(char a)    {        if (a == 'U')            return 0;        if (a == 'R')            return 1;        if (a == 'D')            return 2;        if (a == 'L')            return 3;                      return -1;    }      // function to print    // the possible move    static void printMove(char a,                           char b,                           int n)    {        // mod with 4 as completing         // 4 steps means completing        // one single round        n = n % 4;              // when n is 2 and         // the difference        // between moves is 2        if (n == 2 && Math.Abs(value(a) -                                value(b)) == 2)            Console.Write("Clockwise " +                    "or Anticlockwise");              // anticlockwise condition        else if ((value(a) + n * 3) %                         4 == value(b))            Console.Write("Anticlockwise");              // clockwise condition        else if ((value(a) + n) %                     4 == value(b))            Console.WriteLine("Clockwise");        else            Console.WriteLine("Not Possible");    }      // Driver Code    public static void Main()    {    char a = 'D', b = 'R';    int n = 7;    printMove(a, b, n);    }}  // This code is contributed by Sam007

## PHP

 

## Javascript

 

Output :

Clockwise

Time Complexity: O(1), as we are not using any loop or recursion to traverse.

Auxiliary Space: O(1), as we are not using any extra space.

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