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1041. Robot Bounded In Circle

Description

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'.

Solutions

Solution 1

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class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        k = 0
        dist = [0] * 4
        for c in instructions:
            if c == 'L':
                k = (k + 1) % 4
            elif c == 'R':
                k = (k + 3) % 4
            else:
                dist[k] += 1
        return (dist[0] == dist[2] and dist[1] == dist[3]) or k != 0

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class Solution {
    public boolean isRobotBounded(String instructions) {
        int k = 0;
        int[] dist = new int[4];
        for (int i = 0; i < instructions.length(); ++i) {
            char c = instructions.charAt(i);
            if (c == 'L') {
                k = (k + 1) % 4;
            } else if (c == 'R') {
                k = (k + 3) % 4;
            } else {
                ++dist[k];
            }
        }
        return (dist[0] == dist[2] && dist[1] == dist[3]) || (k != 0);
    }
}

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class Solution {
public:
    bool isRobotBounded(string instructions) {
        int dist[4]{};
        int k = 0;
        for (char& c : instructions) {
            if (c == 'L') {
                k = (k + 1) % 4;
            } else if (c == 'R') {
                k = (k + 3) % 4;
            } else {
                ++dist[k];
            }
        }
        return (dist[0] == dist[2] && dist[1] == dist[3]) || k;
    }
};

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func isRobotBounded(instructions string) bool {
    dist := [4]int{}
    k := 0
    for _, c := range instructions {
        if c == 'L' {
            k = (k + 1) % 4
        } else if c == 'R' {
            k = (k + 3) % 4
        } else {
            dist[k]++
        }
    }
    return (dist[0] == dist[2] && dist[1] == dist[3]) || k != 0
}

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function isRobotBounded(instructions: string): boolean {
    const dist: number[] = new Array(4).fill(0);
    let k = 0;
    for (const c of instructions) {
        if (c === 'L') {
            k = (k + 1) % 4;
        } else if (c === 'R') {
            k = (k + 3) % 4;
        } else {
            ++dist[k];
        }
    }
    return (dist[0] === dist[2] && dist[1] === dist[3]) || k !== 0;
}

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