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package g1001_1100.s1041_robot_bounded_in_circle;

// #Medium #String #Math #Simulation #2022_02_27_Time_0_ms_(100.00%)_Space_39.9_MB_(14.49%)

/**
 * 1041 - Robot Bounded In Circle\.
 *
 * Medium
 *
 * 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 <= 100`
 * *   `instructions[i]` is `'G'`, `'L'` or, `'R'`.
**/
public 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;
    }
}