# 1240. Algorithm - CoordinateString and Array

Coordinate questions.

## 1. Coordinate

### 1.1 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'}

### 1.2 Solution:

public boolean isRobotBounded(String instructions) {
int x = 0, y = 0, i = 0, d[][] = \{\{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
for (int j = 0; j < instructions.length(); ++j)
if (instructions.charAt(j) == 'R')
i = (i + 1) % 4;
else if (instructions.charAt(j) == 'L')
i = (i + 3) % 4;
else {
x += d[i][0];
y += d[i][1];
}
return x == 0 && y == 0 || i > 0;
}