Problem description
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 indefinetely.
Example 3:
Input: "GL"
Output: true
Explanation:
The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...
Solution
- We notice after 4 sets of instructions, we always face the original direction (north). If at this time, we are at origin. Then we are bounded. If not, then we are unbounded.
- We can keep track of the current position and current direction. as (x, y), (directionx, directiony). Turn left, we just mutiply the direction by ((0,1),(-1,0)). Turn right, we just mutiply the direction by matrix ((0,-1),(1,0)). Move, we just add x + directionx, y + directiony
Below is my python implementation
class Solution:
def isRobotBounded(self, instructions: str) -> bool:
instructions = instructions * 4
x, y = 0, 0
directionx, directiony = 0, 1
for c in instructions:
#print(x,y,directionx, directiony)
if c == 'G':
x += directionx
y += directiony
elif c == 'L':
newdirectionx = -directiony
newdirectiony = directionx
directionx = newdirectionx
directiony = newdirectiony
else:
newdirectionx = directiony
newdirectiony = -directionx
directionx = newdirectionx
directiony = newdirectiony
return x == 0 and y == 0