Check if a given sequence of moves for a robot is circular or not - GeeksforGeeks

Check if a given sequence of moves for a robot is circular or not - GeeksforGeeks
Given a sequence of moves for a robot, check if the sequence is circular or not. A sequence of moves is circular if first and last positions of robot are same. A move can be on of the following.

  G - Go one unit
  L - Turn left
  R - Turn right 

Input: path[] = "GLGLGLG"
Output: Given sequence of moves is circular 

Input: path[] = "GLLG"
Output: Given sequence of moves is circular 

The idea is to consider the starting position as (0, 0) and direction as East (We can pick any values for these). If after the given sequence of moves, we come back to (0, 0), then given sequence is circular, otherwise not.

           N
           |
           |
   W -------------- E
           |
           |
           S 

The move ‘G’ changes either x or y according to following rules.
a) If current direction is North, then ‘G’ increments y and doesn’t change x.
b) If current direction is East, then ‘G’ increments x and doesn’t change y.
c) If current direction is South, then ‘G’ decrements y and doesn’t change x.
d) If current direction is West, then ‘G’ decrements x and doesn’t change y.

The moves ‘L’ and ‘R’, do not change x and y coordinates, they only change direction according to following rule.
a) If current direction is North, then ‘L’ changes direction to West and ‘R’ changes to East
b) If current direction is East, then ‘L’ changes direction to North and ‘R’ changes to South
c) If current direction is South, then ‘L’ changes direction to East and ‘R’ changes to West
d) If current direction is West, then ‘L’ changes direction to South and ‘R’ changes to North.

O(N)

bool isCircular(char path[])

{

  // Initialize starting point for robot as (0, 0) and starting

  // direction as N North

  int x = 0, y = 0;

  int dir = N;

  // Travers the path given for robot

  for (int i=0; path[i]; i++)

  {

      // Find current move

      char move = path[i];

      // If move is left or right, then change direction

      if (move == 'R')

        dir = (dir + 1)%4;

      else if (move == 'L')

        dir = (4 + dir - 1)%4;

      // If move is Go, then change  x or y according to

      // current direction

      else // if (move == 'G')

      {

         if (dir == N)

            y++;

         else if (dir == E)

            x++;

         else if (dir == S)

            y--;

         else // dir == W

            x--;

      }

  }

   // If robot comes back to (0, 0), then path is cyclic

  return (x == 0 && y == 0);

}

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