Problem
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'.
Solution (Java)
class Solution {
public boolean isRobotBounded(String instructions) {
int[][] dir = {{0, 1}, {-1, 0}, {0, -1}, {1, 0}};
int i = 0;
int x = 0;
int y = 0;
for (int s = 0; s < instructions.length(); s++) {
if (instructions.charAt(s) == 'L') {
i = (i + 1) % 4;
} else if (instructions.charAt(s) == 'R') {
i = (i + 3) % 4;
} else {
x = x + dir[i][0];
y = y + dir[i][1];
}
}
return x == 0 && y == 0 || i != 0;
}
}
Explain:
nope.
Complexity:
- Time complexity : O(n).
- Space complexity : O(n).