Solution Explanation: Walking Robot Simulation

This problem simulates a robot's movement on a grid based on a sequence of commands and obstacles. The goal is to find the maximum squared Euclidean distance the robot reaches from the origin (0, 0).

Approach:

The solution uses a simulation approach combined with a hash table (or set) for efficient obstacle checking.

1. Data Structures:

   • dirs: An array representing the direction vectors (dx, dy) for North (0, 1), East (1, 0), South (0, -1), and West (-1, 0). This simplifies direction changes.
   • s: A hash set (or dictionary in Python) storing obstacle coordinates for O(1) lookup. We use a custom hash function f(x, y) in some languages to handle the coordinate pairs as a single key in the set. This hash function maps coordinate pairs (x,y) into unique integers.

2. Simulation Loop:

   • The code iterates through the commands array.
   • Turning: Commands -2 (left) and -1 (right) update the current direction k using modular arithmetic (% 4).
   • Movement: For move commands (positive integers), the code simulates the movement step-by-step:
     • It calculates the next position (nx, ny).
     • It checks if (nx, ny) is an obstacle using the s set. If it's an obstacle, the robot stops at the current position.
     • If it's not an obstacle, the robot moves to (nx, ny), and the maximum squared distance ans is updated.

3. Result: Finally, the function returns the ans, which represents the maximum squared Euclidean distance.

Time and Space Complexity:

• Time Complexity: O(C * n + m), where:
  • C is the maximum value in commands (maximum steps in a single move command). In the worst-case scenario, the robot could move up to 9 units in a single command.
  • n is the length of the commands array.
  • m is the number of obstacles. The obstacle check takes O(1) time due to the hash set.
• Space Complexity: O(m) to store the obstacles in the hash set s.

Code Examples:

Python:

class Solution:
    def robotSim(self, commands: List[int], obstacles: List[List[int]]) -> int:
        dirs = [(0, 1), (1, 0), (0, -1), (-1, 0)]  # North, East, South, West
        obstacle_set = set(map(tuple, obstacles)) #Convert to set of tuples for efficient lookup
        x, y, direction = 0, 0, 0
        max_distance_squared = 0
 
        for command in commands:
            if command == -2:
                direction = (direction - 1) % 4 #Turn left
            elif command == -1:
                direction = (direction + 1) % 4 #Turn right
            else:
                for _ in range(command):
                    next_x, next_y = x + dirs[direction][0], y + dirs[direction][1]
                    if (next_x, next_y) not in obstacle_set:
                        x, y = next_x, next_y
                        max_distance_squared = max(max_distance_squared, x**2 + y**2)
                    else:
                        break #Obstacle encountered, stop moving in this direction
 
        return max_distance_squared
 

The other language examples (Java, C++, Go, TypeScript) follow a very similar structure, using a hash set or equivalent data structure for obstacle checking and the dirs array for efficient direction handling. The key difference lies in the syntax and data structure implementations specific to each language. Refer to the original response for complete code in those languages.