# 1041. Robot Bounded In Circle

## Description

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'.

## Solutions

• class Solution {
public boolean isRobotBounded(String instructions) {
int k = 0;
int[] dist = new int[4];
for (int i = 0; i < instructions.length(); ++i) {
char c = instructions.charAt(i);
if (c == 'L') {
k = (k + 1) % 4;
} else if (c == 'R') {
k = (k + 3) % 4;
} else {
++dist[k];
}
}
return (dist[0] == dist[2] && dist[1] == dist[3]) || (k != 0);
}
}

• class Solution {
public:
bool isRobotBounded(string instructions) {
int dist[4]{};
int k = 0;
for (char& c : instructions) {
if (c == 'L') {
k = (k + 1) % 4;
} else if (c == 'R') {
k = (k + 3) % 4;
} else {
++dist[k];
}
}
return (dist[0] == dist[2] && dist[1] == dist[3]) || k;
}
};

• class Solution:
def isRobotBounded(self, instructions: str) -> bool:
k = 0
dist = [0] * 4
for c in instructions:
if c == 'L':
k = (k + 1) % 4
elif c == 'R':
k = (k + 3) % 4
else:
dist[k] += 1
return (dist[0] == dist[2] and dist[1] == dist[3]) or k != 0


• func isRobotBounded(instructions string) bool {
dist := [4]int{}
k := 0
for _, c := range instructions {
if c == 'L' {
k = (k + 1) % 4
} else if c == 'R' {
k = (k + 3) % 4
} else {
dist[k]++
}
}
return (dist[0] == dist[2] && dist[1] == dist[3]) || k != 0
}

• function isRobotBounded(instructions: string): boolean {
const dist: number[] = new Array(4).fill(0);
let k = 0;
for (const c of instructions) {
if (c === 'L') {
k = (k + 1) % 4;
} else if (c === 'R') {
k = (k + 3) % 4;
} else {
++dist[k];
}
}
return (dist[0] === dist[2] && dist[1] === dist[3]) || k !== 0;
}