# 1041. Robot Bounded In Circle 困于环中的机器人

@TOC

## # 题目描述

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'}`

## # 解题方法

### # 找规律

Python代码如下：

``````class Solution(object):
def isRobotBounded(self, instructions):
"""
:type instructions: str
:rtype: bool
"""
dirs = [(0, 1), (-1, 0), (0, -1), (1, 0)]
x, y = 0, 0
curd = 0
for i in instructions:
if i == "G":
x += dirs[curd][0]
y += dirs[curd % 4][1]
elif i == "L":
curd = (curd + 1) % 4
elif i == "R":
curd = (curd - 1) % 4
return (x == 0 and y == 0) or curd != 0
``````

``````class Solution(object):
def isRobotBounded(self, instructions):
"""
:type instructions: str
:rtype: bool
"""
dirs = [(0, 1), (-1, 0), (0, -1), (1, 0)]
x, y = 0, 0
curd = 0
for i in instructions * 4:
if i == "G":
x += dirs[curd][0]
y += dirs[curd % 4][1]
elif i == "L":
curd = (curd + 1) % 4
elif i == "R":
curd = (curd - 1) % 4
return x == 0 and y == 0
``````

## # 日期

2019 年 6 月 15 日 —— 今天这个题有意思