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 public boolean isRobotBounded(String instructions) {
3 int x = 0, y = 0, direction = 0;
4 int[][] deltas = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
5
6 for (char inst : instructions.toCharArray()) {
7 if (inst == 'G') {
8 x += deltas[direction][0];
9 y += deltas[direction][1];
10 } else if (inst == 'L') {
11 direction = (direction + 3) % 4;
12 } else if (inst == 'R') {
13 direction = (direction + 1) % 4;
14 }
15 }
16
17 return (x == 0 && y == 0) || direction != 0;
18 }
19}In this Java solution, the main operation is similar to C/C++. Each character in the instruction updates the robot's position or direction. Finally, the robot's final condition determines if it's bounded in a circle.
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.
This Python variant evaluates robot trajectories across explicitly defined cycles. It verifies termination causes based on repeat position or non-north orientation after multiple loops.