LeetCode 1041. Robot Bounded In Circle【字符串,模拟】中等

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On an infinite plane, a robot initially stands at (0, 0) and faces north. Note that:

The north direction is the positive direction of the y-axis.
The south direction is the negative direction of the y-axis.
The east direction is the positive direction of the x-axis.
The west direction is the negative direction of the x-axis.

The robot can receive one of three instructions:

"G": go straight 1 unit.
"L": turn 90 degrees to the left (i.e., anti-clockwise direction).
"R": turn 90 degrees to the right (i.e., clockwise direction).

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 is initially at (0, 0) facing the north direction.
"G": move one step. Position: (0, 1). Direction: North.
"G": move one step. Position: (0, 2). Direction: North.
"L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: West.
"L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: South.
"G": move one step. Position: (0, 1). Direction: South.
"G": move one step. Position: (0, 0). Direction: South.
Repeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (0, 2) --> (0, 1) --> (0, 0).
Based on that, we return true.

Example 2:

Input: instructions = "GG"
Output: false
Explanation: The robot is initially at (0, 0) facing the north direction.
"G": move one step. Position: (0, 1). Direction: North.
"G": move one step. Position: (0, 2). Direction: North.
Repeating the instructions, keeps advancing in the north direction and does not go into cycles.
Based on that, we return false.

Example 3:

Input: instructions = "GL"
Output: true
Explanation: The robot is initially at (0, 0) facing the north direction.
"G": move one step. Position: (0, 1). Direction: North.
"L": turn 90 degrees anti-clockwise. Position: (0, 1). Direction: West.
"G": move one step. Position: (-1, 1). Direction: West.
"L": turn 90 degrees anti-clockwise. Position: (-1, 1). Direction: South.
"G": move one step. Position: (-1, 0). Direction: South.
"L": turn 90 degrees anti-clockwise. Position: (-1, 0). Direction: East.
"G": move one step. Position: (0, 0). Direction: East.
"L": turn 90 degrees anti-clockwise. Position: (0, 0). Direction: North.
Repeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (-1, 1) --> (-1, 0) --> (0, 0).
Based on that, we return true.

Constraints:

1 <= instructions.length <= 100
instructions[i] is 'G', 'L' or, 'R'.

题意：机器人在一个无限的二维平面上，给它一串移动指令，机器人反复执行这条指令，如果它在平面上重复走一个死循环，就返回 true 。

解法模拟

当机器人执行完指令 instructions 后，它的位置和方向均有可能发生变化。我们先考虑位置，然后考虑其方向。

如果它的位置仍位于原点，那么不管它此时方向是什么，都将永远无法离开。
如果它的位置不在原点，我们分情况讨论此时机器人的方向：
- 如果仍然朝北，那么机器人不会陷入循环。假设执行完一串指令后，机器人的位置是 $(x, y)$ 且不为原点，方向仍然朝北，那么执行完第二串指令后，机器人的位置便成为 $(2\times x, 2\times y)$ ，会不停地往外部移动，不会陷入循环。
- 如果朝南，那么执行第二串指令时，机器人的位移与第一次相反，即第二次的位移是 $(- x, - y)$ ，并且结束后会回到原来的方向。这样一来，每两串指令之后，机器人都会回到原点，并且方向朝北，机器人会陷入循环。
- 如果朝东，即右转了 $90\degree$ 。这样一来，每执行一串指令，机器人都会右转 $90°$ 。那么第一次和第三次指令的方向是相反的，第二次和第四次指令的方向是相反的，位移之和也为 $0$ ，这样一来，每四串指令之后，机器人都会回到原点，并且方向朝北，机器人会陷入循环。如果机器人朝西，也是一样的结果。

因此，机器人想要摆脱循环，在一串指令之后的状态，必须是不位于原点且方向朝北。

class Solution {
public:bool isRobotBounded(string instructions) {int move[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};int x = 0, y = 0, dir = 0; // 0北,1东,2南,3西for (char &c : instructions) {if (c == 'G') x += move[dir][0], y += move[dir][1];else if (c == 'L') dir = (dir + 3) % 4;else dir = (dir + 1) % 4;}return (x == 0 && y == 0) || dir != 0;}
};