1041. Robot Bounded In Circle.cpp

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 degress 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: "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: "GG"
Output: false
Explanation:
The robot moves north indefinitely.
Example 3:

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


Note:

1 <= instructions.length <= 100
instructions[i] is in {'G', 'L', 'R'}
   Hide Hint #1
Calculate the final vector of how the robot travels after executing all instructions once - it consists of a change in position plus a change in direction.
   Hide Hint #2
The robot stays in the circle iff (looking at the final vector) it changes direction (ie. doesn't stay pointing north), or it moves 0.











class Solution {
public:
    bool isRobotBounded(string instructions) {
        int n=instructions.length();
        int dir=0; // 0-N, 1-E, 2-S, 3-W
        int x=0, y=0;
        for(int i=0;i<n;i++){
            if(instructions[i]=='G'){
                if(dir==0) y++;
                else if(dir==1) x--;
                else if(dir==2) y--;
                else x++;
            } else if(instructions[i]=='L'){
                if(dir==0) dir=1;
                else if(dir==1) dir=2;
                else if(dir==2) dir=3;
                else dir=0;
            } else if(instructions[i]=='R'){
                if(dir==0) dir=3;
                else if(dir==1) dir=0;
                else if(dir==2) dir=1;
                else dir=2;
            }
        }


        if(x==0 && y==0) return true;
        else if(dir!=0) return true;
        else return false;
    }
};