1041. Robot Bounded in Circle

Problem Statement

Medium

On an infinite plane, a robot initially stands at (0, 0) and faces north. The robot can receive one of three instructions:

"G": go straight 1 unit;
"L": turn 90 degrees to the left;
"R": turn 90 degrees to the right.

The robot performs the instructions given in order, and repeats them forever.

Return true if and only if there exists a circle in the plane such that the robot never leaves the circle.

Example 1:

Input: instructions = "GGLLGG"
Output: true
Explanation: The robot moves from (0,0) to (0,2), turns 180 degrees, and then returns to (0,0).
When repeating these instructions, the robot remains in the circle of radius 2 centered at the origin.

Example 2:

Input: instructions = "GG"
Output: false
Explanation: The robot moves north indefinitely.

Example 3:

Input: instructions = "GL"
Output: true
Explanation: The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...

Constraints:

1 <= instructions.length <= 100
instructions[i] is 'G', 'L' or, 'R'.

C++

Source file

class Solution {
public:
    bool isRobotBounded(string instructions) {
        array <int, 4> directn; //NESW
        for (int i=0; i<4; i++)
            directn[i]=0;
        int facing = 0;
        for(int k=0; k<4; k++){            
            for (int i=0; i< instructions.length(); i++){
                if(instructions[i]=='G')
                    directn[facing]++;
                else if(instructions[i]=='R')
                    facing++;
                else if(instructions[i]=='L')
                    facing--;
                if (facing>=4)
                    facing %= 4;
                else if(facing<0)
                    facing += 4;
            }
            if(directn[0]==directn[2] && directn[1]==directn[3])    //premature stopping, no need to check further
                return true;    // optimisation, otherwise not reqd
        }
        return (directn[0]==directn[2] && directn[1]==directn[3]);
    }
};