每日经典
《静夜思》 ——李白（唐）
床前明月光，疑是地上霜。
举头望明月，低头思故乡。
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 degrees 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: instructions = "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: instructions = "GG"
Output: false
Explanation: The robot moves north indefinitely.
Example 3:
Input: instructions = "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 'G', 'L' or, 'R'.
解析
根据题意，在平面上有一个机器人最初站在 (0, 0) 并面向北方。 机器人可以接收以下三种指令之一：
- “G”：直走 1 个单位；
- “L”：向左转 90 度；
- “R”：向右转 90 度。
机器人按顺序执行指令，并永远重复它们。当且仅当平面中存在一个循环的路径使得机器人在执行完 n 遍 instructions 永远能够回到原点并且仍然面向北方返回 True ，否则返回 False 。我们经过找规律可以发现，想要返回 True ，最多执行 4 遍 instructions 之后可能会回到原点并面向北方，如例 3 ；但是也可能最多执行 2 遍 instructions 之后可能回到原点并面向北方，如例 1 。所以我们遍历 4 倍长度的 instructions ，并且对指令数量进行计数，当遇到 G 时位置 cur 发生变化，当遇到 L 或者 R 的时候方向 d 发生变化，如果在遍历过程中满足 count%len(instructions)==0 and d%4==0 and cur==[0,0] 直接返回 True ，否则遍历结束直接返回 False 即可。
解答
class Solution(object):
def isRobotBounded(self, instructions):
"""
:type instructions: str
:rtype: bool
"""
dirs = [(0, 1), (-1, 0), (0, -1), (1, 0)]
cur = [0,0]
d = 0
count = 0
for c in instructions*4:
count += 1
if c == 'G':
cur[0] += dirs[d%4][0]
cur[1] += dirs[d%4][1]
elif c == 'L':
d += 1
else:
d -= 1
if count%len(instructions)==0 and d%4==0 and cur==[0,0]:
return True
return False
运行结果
Runtime: 34 ms, faster than 8.06% of Python online submissions for Robot Bounded In Circle.
Memory Usage: 13.5 MB, less than 28.85% of Python online submissions for Robot Bounded In Circle.
原题链接：leetcode.com/problems/ro…
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