1041-robot-bounded-in-circle.adoc

1041. Robot Bounded In Circle

{leetcode}/problems/robot-bounded-in-circle/[LeetCode - Robot Bounded In Circle^]

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'}

思路分析

Tip	这道题不是要看路径是否相交。

这道题的关键点事找出不存在环路的条件：执行一遍指令后，机器人必须不在原点且方向继续朝北：

• 如果在原点，无论执行多少遍，结果都会在原点。

• 如果方向不是初始化方向，那么多次执行后，就会相互抵消，形成环路。

一刷

link:{sourcedir}/_1041_RobotBoundedInCircle.java[role=include]

参考资料

1. 1041. 困于环中的机器人 - 官方题解

2. 1041. 困于环中的机器人 / 矩阵变换的思路

3. 1041. 困于环中的机器人 - 一题一解：模拟（详细题解）

4. 1041. 困于环中的机器人 - 【宫水三叶】常规模拟题