Sponsored
Sponsored
The idea is to simulate the movement of the robot step by step according to the given instructions. We maintain the robot's current position and direction. If after one set of instructions, the robot has not returned to its original position but is not facing north, it must eventually form a circle upon repeated execution of the instructions.
Steps include initializing the position and direction, iterating over the instructions to update the position and direction, and finally checking conditions for cycle existence.
Time Complexity: O(n), where n is the length of the instructions string, because we iterate through the instructions once.
Space Complexity: O(1), since we use constant extra space for variables.
1class Solution:
2 def isRobotBounded(self, instructions: str) -> bool:
3 x, y, direction = 0, 0, 0
4 deltas = [(0, 1), (1, 0), (0, -1), (-1, 0)]
5
6 for inst in instructions:
7 if inst == 'G':
8 x, y = x + deltas[direction][0], y + deltas[direction][1]
9 elif inst == 'L':
10 direction = (direction + 3) % 4
11 elif inst == 'R':
12 direction = (direction + 1) % 4
13
14 return (x == 0 and y == 0) or direction != 0In Python, the approach leverages tuple operations for movement. The instruction processes are similar, adjusting position or direction accordingly. Post-loop checks decide the bounded state.
Here, simulate the robot's actions on the plane for up to four cycles of the input instructions. The observation is that if the robot returns to the starting position or is not facing north, then it will ultimately confine within a bounded circle.
The simulation idea draws from rotational symmetry and periodicity principles in movement patterns over multiple instruction applications.
Time Complexity: O(4n) = O(n); we simulate up to four full instruction loops.
Space Complexity: O(1), as it only uses constant space independent of input size.
The C implementation leverages a nested loop with a fixed cycle count determined by directionality. If the robot returns to (0, 0) within four cycles or isn't facing north, it suggests containment within a circle.