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# 1041.Robot-Bounded-In-Circle

## 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 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) -> ...
Constraints:
1 <= instructions.length <= 100
instructions[i] is 'G', 'L' or, 'R'.

## 代码

### Approach #1 One Pass

Time: O(N) && Space: O(1)
class Solution {
public boolean isRobotBounded(String instructions) {
int[][] directions = new int[][]{{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
int x = 0, y = 0;
int idx = 0;
for (char i : instructions.toCharArray()) {
if (i == 'L') {
idx = (idx + 3) % 4;
} else if (i == 'R') {
idx = (idx + 1) % 4;
} else {
x = x + directions[idx];
y = y + directions[idx];
}
}
return ( (x == 0 && y == 0) || idx != 0);
}
}