## Algorithm

Problem Name: 1041. Robot Bounded In Circle

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'`.

## Code Examples

### #1 Code Example with Java Programming

```Code - Java Programming```

``````
class Solution {
public boolean isRobotBounded(String instructions) {
int[][] directions = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
int x = 0;
int y = 0;
int idx = 0;
for (char c : instructions.toCharArray()) {
if (c == 'L') {
idx = (idx + 3) % 4;
}
else if (c == 'R') {
idx = (idx + 1) % 4;
}
else {
x += directions[idx];
y += directions[idx];
}
}
return (x == 0 && y == 0) || idx != 0;
}
}
``````
Copy The Code &

Input

cmd
instructions = "GGLLGG"

Output

cmd
true

### #2 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const isRobotBounded = function(instructions) {
let x = 0, y = 0, i = 0, d = [[0, 1], [1, 0], [0, -1], [ -1, 0]];
for (let 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]; y += d[i];
}
return x == 0 && y == 0 || i > 0;
};
``````
Copy The Code &

Input

cmd
instructions = "GGLLGG"

Output

cmd
true

### #3 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def isRobotBounded(self, instructions: str) -> bool:
x, y, dx, dy = 0, 0, 0, 1
for _ in range(4):
for ins in instructions:
if ins == 'G':
x += dx
y += dy
elif ins == 'L':
dx, dy = -dy, dx
else:
dx, dy = dy, -dx
return x == y == 0
``````
Copy The Code &

Input

cmd
instructions = "GG"

Output

cmd
false

### #4 Code Example with C# Programming

```Code - C# Programming```

``````
namespace LeetCode
{
public class _1041_RobotBoundedInCircle
{
public bool IsRobotBounded(string instructions)
{
var directions = new int[] { new int { 0, 1 }, new int { 1, 0 }, new int { 0, -1 }, new int { -1, 0 } };
int x = 0, y = 0, dir = 0;

foreach (var ch in instructions)
{
if (ch == 'L')
dir = (dir + 3) % 4;
else if (ch == 'R')
dir = (dir + 1) % 4;
else
{
x += directions[dir];
y += directions[dir];
}
}

return (x == 0 && y == 0) || (dir != 0);
}
}
}
``````
Copy The Code &

Input

cmd
instructions = "GG"

Output

cmd
false