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 <= 100instructions[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][0];
y += directions[idx][1];
}
}
return (x == 0 && y == 0) || idx != 0;
}
}
Input
instructions = "GGLLGG"
Output
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][0]; y += d[i][1];
}
return x == 0 && y == 0 || i > 0;
};
Input
instructions = "GGLLGG"
Output
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
Input
instructions = "GG"
Output
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[4][] { new int[2] { 0, 1 }, new int[2] { 1, 0 }, new int[2] { 0, -1 }, new int[2] { -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][0];
y += directions[dir][1];
}
}
return (x == 0 && y == 0) || (dir != 0);
}
}
}
Input
instructions = "GG"
Output
false