【leetcode】1041. Robot Bounded In Circle

题目如下：

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) -> ...
Note:

1 <= instructions.length <= 100

instructions[i] is in {'G', 'L', 'R'}

解题思路：看到这个题目，我的感觉就是如果能回到起点，应该是执行instructions一次，两次或者四次。嘿嘿，当然我也不知道怎么证明，反正能AC。

代码如下：

class Solution(object):

    def process(self,start,instructions):

        for i in instructions:

            if i == 'G':

                if start[2] == 'N':start[1] += 1

                elif start[2] == 'S':start[1] -= 1

                elif start[2] == 'E':start[0] += 1

                elif start[2] == 'W':start[0] -= 1

            elif i == 'L':

                if start[2] == 'N':start[2] = 'W'

                elif start[2] == 'S':start[2] = 'E'

                elif start[2] == 'E':start[2] = 'N'

                elif start[2] == 'W':start[2] = 'S'

            elif i == 'R':

                if start[2] == 'N':start[2] = 'E'

                elif start[2] == 'S':start[2] = 'W'

                elif start[2] == 'E':start[2] = 'S'

                elif start[2] == 'W':start[2] = 'N'

        return start

    def isRobotBounded(self, instructions):

        """

        :type instructions: str

        :rtype: bool

        """

        start = [0,0,'N']

        end = self.process(start,instructions)

        if end[0] == end[1] == 0:

            return True

        end = self.process(start, instructions)

        if end[0] == end[1] == 0:

            return True

        end = self.process(start, instructions)

        end = self.process(start, instructions)

        if end[0] == end[1] == 0:

            return True

        return False

巴特西

【leetcode】1041. Robot Bounded In Circle

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