Walking Robot Simulation II

The Walking Robot Simulation II problem challenges you to simulate robot movements and track its position and direction in a grid.

design simulation

Problem Statement

You are given a grid of size width x height on an XY-plane, where the bottom-left corner is at (0, 0) and the top-right corner is at (width - 1, height - 1). The robot starts at position (0, 0) facing the 'East' direction. You need to simulate the robot's movement based on a set of commands. The robot can move a specific number of steps, turning when it reaches a boundary of the grid.

Each movement command directs the robot to move in the current facing direction. If the robot reaches the edge of the grid, it turns 90 degrees clockwise and continues moving. After executing the steps, the robot must report its position and direction. Your task is to implement this simulation and efficiently track the robot’s state during the execution of each command.

Examples

Example 1

Input: See original problem statement.

Output: See original problem statement.

Input ["Robot", "step", "step", "getPos", "getDir", "step", "step", "step", "getPos", "getDir"] [[6, 3], [2], [2], [], [], [2], [1], [4], [], []] Output [null, null, null, [4, 0], "East", null, null, null, [1, 2], "West"]

Explanation Robot robot = new Robot(6, 3); // Initialize the grid and the robot at (0, 0) facing East. robot.step(2); // It moves two steps East to (2, 0), and faces East. robot.step(2); // It moves two steps East to (4, 0), and faces East. robot.getPos(); // return [4, 0] robot.getDir(); // return "East" robot.step(2); // It moves one step East to (5, 0), and faces East. // Moving the next step East would be out of bounds, so it turns and faces North. // Then, it moves one step North to (5, 1), and faces North. robot.step(1); // It moves one step North to (5, 2), and faces North (not West). robot.step(4); // Moving the next step North would be out of bounds, so it turns and faces West. // Then, it moves four steps West to (1, 2), and faces West. robot.getPos(); // return [1, 2] robot.getDir(); // return "West"

Constraints

2 <= width, height <= 100
1 <= num <= 105
At most 104 calls in total will be made to step, getPos, and getDir.

Solution Approach

Grid Boundary Handling

To handle robot movement within grid boundaries, keep track of the robot’s current position and facing direction. When the robot moves out of bounds, adjust its direction by rotating 90 degrees clockwise. Using modulus operations can simplify this adjustment to determine the next valid direction or position without exceeding the grid's limits.

Efficient State Tracking

You must efficiently update the robot's position and direction with each command. This can be done by maintaining a state that tracks the robot's current coordinates and direction. For each movement command, update the state and check for boundary conditions to decide when to turn the robot.

Handling Multiple Commands

The robot will execute multiple commands in sequence. After each step, the robot must either change direction or stop at its current position. Efficiently handling and simulating multiple commands involves ensuring that each step is processed correctly, and the robot’s state is updated after each movement.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the number of commands processed and the grid's size. For each command, we update the robot’s state in constant time. The space complexity is O(1) as we only need to store the robot's position and direction.

What Interviewers Usually Probe

Looking for a clean approach to handle boundary conditions and direction changes.
Check if the candidate can optimize the position tracking with modulus for wrapping around the grid.
Evaluate the candidate’s ability to simulate multiple commands without unnecessary complexity.

Common Pitfalls or Variants

Common pitfalls

Not handling the boundary conditions properly, causing the robot to move out of bounds.
Overcomplicating the direction changes, leading to inefficient code.
Failing to correctly update the robot’s state after each command.

Follow-up variants

Add more complex movement patterns with obstacles in the grid.
Simulate robot movements in a 3D grid or more complex environments.
Introduce time-based movements, where the robot’s speed varies depending on the command.

FAQ

What is the main challenge in the Walking Robot Simulation II problem?

The challenge lies in handling grid boundaries efficiently and ensuring that the robot correctly updates its position and direction after each move.

How can modulus operations help in this problem?

Modulus operations can help quickly compute which direction the robot should face after reaching a boundary, simplifying the logic for turning and wrapping around the grid.

What happens when the robot reaches the edge of the grid?

When the robot reaches the edge of the grid, it turns 90 degrees clockwise and continues moving in the new direction.

How do I handle multiple commands in the simulation?

You can handle multiple commands by updating the robot's position and direction after each command, ensuring the state reflects the robot's movements sequentially.

What is the significance of the 'getPos' and 'getDir' commands?

The 'getPos' command returns the robot’s current position, while 'getDir' returns the current facing direction, both crucial for verifying the robot’s state after executing commands.

terminal

Solution

Solution 1: Case Analysis

Let $mx = width - 1$ and $my = height - 1$. The robot's trajectory forms the boundary of a rectangle with $(0, 0)$ as the bottom-left corner and $(mx, my)$ as the top-right corner. We can divide the robot's trajectory into four segments:

class Robot:

    def __init__(self, width: int, height: int):
        self.mx = width - 1
        self.my = height - 1
        self.p = 2 * self.mx + 2 * self.my
        self.cur = 0
        self.moved = False

    def step(self, num: int) -> None:
        self.moved = True
        self.cur = (self.cur + num) % self.p

    def getPos(self) -> List[int]:
        d = self.cur
        mx, my = self.mx, self.my
        if 0 <= d <= mx:
            return [d, 0]
        if mx < d <= mx + my:
            return [mx, d - mx]
        if mx + my < d <= 2 * mx + my:
            return [mx - (d - (mx + my)), my]
        return [0, my - (d - (2 * mx + my))]

    def getDir(self) -> str:
        d = self.cur
        mx, my = self.mx, self.my
        if not self.moved:
            return "East"
        if 1 <= d <= mx:
            return "East"
        elif mx < d <= mx + my:
            return "North"
        elif mx + my < d <= 2 * mx + my:
            return "West"
        return "South"


# Your Robot object will be instantiated and called as such:
# obj = Robot(width, height)
# obj.step(num)
# param_2 = obj.getPos()
# param_3 = obj.getDir()

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