DEV Community

Cover image for 874. Walking Robot Simulation
MD ARIFUL HAQUE
MD ARIFUL HAQUE

Posted on

874. Walking Robot Simulation

874. Walking Robot Simulation

Difficulty: Medium

Topics: Array, Hash Table, Simulation

A robot on an infinite XY-plane starts at point (0, 0) facing north. The robot can receive a sequence of these three possible types of commands:

  • -2: Turn left 90 degrees.
  • -1: Turn right 90 degrees.
  • 1 <= k <= 9: Move forward k units, one unit at a time.

Some of the grid squares are obstacles. The ith obstacle is at grid point obstacles[i] = (xi, yi). If the robot runs into an obstacle, then it will instead stay in its current location and move on to the next command.

Return _the maximum Euclidean distance that the robot ever gets from the origin squared (i.e. if the distance is 5, return 25).

Note:

  • North means +Y direction.
  • East means +X direction.
  • South means -Y direction.
  • West means -X direction.
  • There can be obstacle in [0,0].

Example 1:

  • Input: commands = [4,-1,3], obstacles = []
  • Output: 25
  • Explanation: The robot starts at (0, 0):
    1. Move north 4 units to (0, 4).
    2. Turn right.
    3. Move east 3 units to (3, 4).
    4. The furthest point the robot ever gets from the origin is (3, 4), which squared is 32 + 42 = 25 units away.

Example 2:

  • Input: commands = [4,-1,4,-2,4], obstacles = [[2,4]]
  • Output: 65
  • Explanation: The robot starts at (0, 0):
    1. Move north 4 units to (0, 4).
    2. Turn right.
    3. Move east 1 unit and get blocked by the obstacle at (2, 4), robot is at (1, 4).
    4. Turn left.
    5. Move north 4 units to (1, 8).
    6. The furthest point the robot ever gets from the origin is (1, 8), which squared is 12 + 82 = 65 units away.

Example 3:

  • Input: commands = [6,-1,-1,6], obstacles = []
  • Output: 36
  • Explanation: The robot starts at (0, 0):
    1. Move north 6 units to (0, 6).
    2. Turn right.
    3. Turn right.
    4. Move south 6 units to (0, 0).
    5. The furthest point the robot ever gets from the origin is (0, 6), which squared is 62 = 36 units away.

Constraints:

  • 1 <= commands.length <= 104
  • commands[i] is either -2, -1, or an integer in the range [1, 9].
  • 0 <= obstacles.length <= 104
  • -3 * 104 <= xi, yi <= 3 * 104
  • The answer is guaranteed to be less than 231

Solution:

We need to simulate the robot's movement on an infinite 2D grid based on a sequence of commands and avoid obstacles if any. The goal is to determine the maximum Euclidean distance squared that the robot reaches from the origin.

Approach

  1. Direction Handling:

    • The robot can face one of four directions: North, East, South, and West.
    • We can represent these directions as vectors:
      • North: (0, 1)
      • East: (1, 0)
      • South: (0, -1)
      • West: (-1, 0)
  2. Turning:

    • A left turn (-2) will shift the direction counterclockwise by 90 degrees.
    • A right turn (-1) will shift the direction clockwise by 90 degrees.
  3. Movement:

    • For each move command, the robot will move in its current direction, one unit at a time. If it encounters an obstacle, it stops moving for that command.
  4. Tracking Obstacles:

    • Convert the obstacles list into a set of tuples for quick lookup, allowing the robot to quickly determine if it will hit an obstacle.
  5. Distance Calculation:

    • Track the maximum distance squared from the origin that the robot reaches during its movements.

Let's implement this solution in PHP: 874. Walking Robot Simulation

<?php
/**
 * @param Integer[] $commands
 * @param Integer[][] $obstacles
 * @return Integer
 */
function robotSim($commands, $obstacles) {
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Test cases
echo robotSim([4,-1,3], []) . "\n"; // Output: 25
echo robotSim([4,-1,4,-2,4], [[2,4]]) . "\n"; // Output: 65
echo robotSim([6,-1,-1,6], []) . "\n"; // Output: 36
?>
Enter fullscreen mode Exit fullscreen mode

Explanation:

  • Direction Management: We use a list of vectors to represent the directions, allowing easy calculation of the next position after moving.
  • Obstacle Detection: By storing obstacles in a set, we achieve O(1) time complexity for checking if a position is blocked by an obstacle.
  • Distance Calculation: We continuously update the maximum squared distance the robot reaches as it moves.

Test Cases

  • The example test cases provided are used to validate the solution:
    • [4,-1,3] with no obstacles should return 25.
    • [4,-1,4,-2,4] with obstacles [[2,4]] should return 65.
    • [6,-1,-1,6] with no obstacles should return 36.

This solution efficiently handles the problem constraints and calculates the maximum distance squared as required.

Contact Links

If you found this series helpful, please consider giving the repository a star on GitHub or sharing the post on your favorite social networks ๐Ÿ˜. Your support would mean a lot to me!

If you want more helpful content like this, feel free to follow me:

Top comments (0)