1041. Robot Bounded In Circle

1041. Robot Bounded In Circle (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 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. 1 <= instructions.length <= 100
2. instructions[i] is in {'G', 'L', 'R'}

Related Topics:
Math

Solution 1.

// OJ: https://leetcode.com/problems/robot-bounded-in-circle/
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
    bool isRobotBounded(string instructions) {
        int x = 0, y = 0, d = 0, dir[4][2] = {{0,1},{-1,0},{0,-1},{1,0}};
        for (int i = 0; i < 4; ++i) {
            for (char c : instructions) {
                if (c == 'G') x += dir[d][0], y += dir[d][1];
                else if (c == 'L') d = (d + 1) % 4;
                else d = (d + 3) % 4;
            }
            if (x == 0 && y == 0) return true;
        }
        return false;
    }
};