On an infinite plane, a robot initially stands at (0, 0) and faces north. The robot can receive one of three instructions:
"G": go straight 1 unit;
"L": turn 90 degrees to the left;
"R": turn 90 degrees to the right.
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 moves from (0,0) to (0,2), turns 180 degrees, and then returns to (0,0).
When repeating these instructions, the robot remains in the circle of radius 2 centered at the origin.
Example 2:
Input: instructions = "GG"
Output: false
Explanation: The robot moves north indefinitely.
Example 3:
Input: instructions = "GL"
Output: true
Explanation: The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...
Constraints:
1 <= instructions.length <= 100
instructions[i] is 'G', 'L' or, 'R'.
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Approach #1 One Pass
Time: O(N) && Space: O(1)
classSolution {publicbooleanisRobotBounded(String instructions) {int[][] directions =newint[][]{{0,1}, {1,0}, {0,-1}, {-1,0}};int x =0, y =0;int idx =0;for (char i :instructions.toCharArray()) {if (i =='L') { idx = (idx +3) %4; } elseif (i =='R') { idx = (idx +1) %4; } else { x = x + directions[idx][0]; y = y + directions[idx][1]; } }return ( (x ==0&& y ==0) || idx !=0); }}