What is the time complexity of Walking Robot Simulation?

The optimal solution has a time complexity of O(n*m).

What data structures are used to solve Walking Robot Simulation?

This problem uses Array, Hash Table, Simulation. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Walking Robot Simulation?

Insight 1: Representing directions: Using an array or list to represent the four directions (North, East, South, West) as (dx, dy) pairs simplifies the turning logic. Insight 2: Using a Hash Set for Obstacles: A hash set (or similar data structure for other languages like C++) provides efficient constant-time lookups to determine if a particular coordinate is an obstacle.

Which companies ask LeetCode 874. Walking Robot Simulation in interviews?

This problem is frequently asked at Jane Street, PhonePe, Shopify.

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Walking Robot Simulation - LeetCode 874 Solution

Q: How to solve Walking Robot Simulation?

The solution involves simulating the robot's movement step by step according to the commands. We keep track of the robot's current position (x, y) and its current direction. We use an array to store the (dx, dy) changes for each direction (North, East, South, West). A hash set stores the coordinates of the obstacles for fast lookup. For each command, we update the robot's direction or move it forward one unit at a time until the commanded distance is reached or an obstacle is encountered. After each command (or move if the command moves the robot), we update the maximum squared Euclidean distance from the origin and return it.

Walking Robot Simulation - Complete Solution Guide

Walking Robot Simulation is LeetCode problem 874, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

A robot on an infinite XY-plane starts at point (0, 0) facing north. The robot receives an array of integers commands , which represents a sequence of moves that it needs to execute. There are only three possible types of instructions the robot can receive: -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 i th obstacle is at grid point obstacles[i] = (x i , y i ) . If the robot runs into an

Detailed Explanation

The problem asks us to simulate a robot moving on an infinite XY-plane from the origin (0, 0). The robot starts facing north and receives a sequence of commands. Commands can be turning left (-2), turning right (-1), or moving forward a specific number of units (1 to 9). The robot needs to avoid obstacles, which are also given as input. If the robot encounters an obstacle while moving, it stops at the location immediately before the obstacle. The goal is to find the maximum squared Euclidean distance the robot reaches from the origin during its path.

Solution Approach

The solution involves simulating the robot's movement step by step according to the commands. We keep track of the robot's current position (x, y) and its current direction. We use an array to store the (dx, dy) changes for each direction (North, East, South, West). A hash set stores the coordinates of the obstacles for fast lookup. For each command, we update the robot's direction or move it forward one unit at a time until the commanded distance is reached or an obstacle is encountered. After each command (or move if the command moves the robot), we update the maximum squared Euclidean distance from the origin and return it.

Step-by-Step Algorithm

Step 1: Initialize robot's position (x, y) to (0, 0), direction index (dir_idx) to 0 (North), and maximum squared distance (max_dist_sq) to 0.
Step 2: Create a directions array or list to store the (dx, dy) changes for each direction: North (0, 1), East (1, 0), South (0, -1), West (-1, 0).
Step 3: Create a hash set (or similar data structure) to store the obstacle coordinates for fast lookup.
Step 4: Iterate through the commands array:
Step 5: If the command is -1 (turn right), increment the direction index (dir_idx = (dir_idx + 1) % 4).
Step 6: If the command is -2 (turn left), decrement the direction index (dir_idx = (dir_idx + 3) % 4). We use addition by 3 and modulo to ensure a positive result.
Step 7: If the command is a positive integer (move forward), get the (dx, dy) changes for the current direction from the directions array.
Step 8: Move the robot forward one unit at a time until the commanded distance is reached or an obstacle is encountered. For each unit moved, check if the next coordinate (x + dx, y + dy) is in the obstacle set. If it is, break the inner loop.
Step 9: Update the robot's position (x += dx, y += dy).
Step 10: Update the maximum squared distance (max_dist_sq = max(max_dist_sq, x*x + y*y)).
Step 11: After iterating through all the commands, return the maximum squared distance (max_dist_sq).

Key Insights

Insight 1: Representing directions: Using an array or list to represent the four directions (North, East, South, West) as (dx, dy) pairs simplifies the turning logic.
Insight 2: Using a Hash Set for Obstacles: A hash set (or similar data structure for other languages like C++) provides efficient constant-time lookups to determine if a particular coordinate is an obstacle.
Insight 3: Step-by-Step Movement: Moving the robot one unit at a time within the move command allows for obstacle detection and immediate stopping if an obstacle is encountered.

Complexity Analysis

Time Complexity: O(n*m)

Space Complexity: O(k)

Topics

This problem involves: Array, Hash Table, Simulation.

Companies

Asked at: Jane Street, PhonePe, Shopify.

Walking Robot Simulation | LeetCode 874

Medium

Array Hash Table Simulation

Time: O(n*m)Space: O(k)

Solution Code

Available in:

import java.util.HashSet;
import java.util.Set;

class Solution {
    public int robotSim(int[] commands, int[][] obstacles) {
        int x = 0, y = 0;
        // 0: North, 1: East, 2: South, 3: West
        int dir_idx = 0;
        int[][] directions = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};

        Set<String> obstacle_set = new HashSet<>();
        for (int[] obstacle : obstacles) {
            obstacle_set.add(obstacle[0] + "," + obstacle[1]);
        }

        int max_dist_sq = 0;

        for (int cmd : commands) {
            if (cmd == -1) { // Turn right
                dir_idx = (dir_idx + 1) % 4;
            } else if (cmd == -2) { // Turn left
                dir_idx = (dir_idx + 3) % 4;
            } else { // Move forward
                int dx = directions[dir_idx][0];
                int dy = directions[dir_idx][1];
                for (int i = 0; i < cmd; i++) {
                    if (obstacle_set.contains((x + dx) + "," + (y + dy))) {
                        break;
                    }
                    x += dx;
                    y += dy;
                }
            }

            max_dist_sq = Math.max(max_dist_sq, x * x + y * y);
        }

        return max_dist_sq;
    }
}

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Problem Info

Description

Problem 874: Walking Robot Simulation - Detailed explanation and solution approaches.

Topics

Array Hash Table Simulation

Companies

Jane StreetPhonePeShopify

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:874

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

11 steps

1
Step 1: Initialize robot's position (x, y) to (0, 0), direction index (dir_idx) to 0 (North), and maximum squared distance (max_dist_sq) to 0.
2
Step 2: Create a directions array or list to store the (dx, dy) changes for each direction: North (0, 1), East (1, 0), South (0, -1), West (-1, 0).
3
Step 3: Create a hash set (or similar data structure) to store the obstacle coordinates for fast lookup.
4
Step 4: Iterate through the commands array:
5
Step 5: If the command is -1 (turn right), increment the direction index (dir_idx = (dir_idx + 1) % 4).
6
Step 6: If the command is -2 (turn left), decrement the direction index (dir_idx = (dir_idx + 3) % 4). We use addition by 3 and modulo to ensure a positive result.
7
Step 7: If the command is a positive integer (move forward), get the (dx, dy) changes for the current direction from the directions array.
8
Step 8: Move the robot forward one unit at a time until the commanded distance is reached or an obstacle is encountered. For each unit moved, check if the next coordinate (x + dx, y + dy) is in the obstacle set. If it is, break the inner loop.
9
Step 9: Update the robot's position (x += dx, y += dy).
10
Step 10: Update the maximum squared distance (max_dist_sq = max(max_dist_sq, x*x + y*y)).
11
Step 11: After iterating through all the commands, return the maximum squared distance (max_dist_sq).

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n*m)

💾

Space Complexity

O(k)

📝

Why?

The time complexity is dominated by the nested loop structure: the outer loop iterates through commands, and the inner loop iterates through the movement steps until an obstacle is hit or movement is complete. The space complexity is primarily from storing the obstacles in the hash set to enable O(1) lookups during the simulation.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

No Alternative Approaches, current one is most optimal

The provided solution is already quite efficient. Any alternative approach, such as sorting the obstacles or using a different data structure for them, would likely increase the complexity or be less efficient for the specific constraints of the problem.

Time: N/ASpace: N/A

Trade-offs: N/A

✨

Key Insights

1Insight 1: Representing directions: Using an array or list to represent the four directions (North, East, South, West) as (dx, dy) pairs simplifies the turning logic.
2Insight 2: Using a Hash Set for Obstacles: A hash set (or similar data structure for other languages like C++) provides efficient constant-time lookups to determine if a particular coordinate is an obstacle.
3Insight 3: Step-by-Step Movement: Moving the robot one unit at a time within the move command allows for obstacle detection and immediate stopping if an obstacle is encountered.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Edge Cases

Edge case 1: Obstacle at the origin (0, 0): The code correctly handles this case because the robot will move off the origin first. The check `(x + dx, y + dy) in obstacle_set` happens *before* the position is updated.
Edge case 2: Multiple turns in a row: The modulo operator (%) ensures that the direction index always stays within the valid range (0 to 3) even with multiple consecutive turns left or right.
Edge case 3: No obstacles: The code will correctly simulate the robot's movement even if the `obstacles` array is empty.
Edge case 4: Commands with large values which causes integer overflow: The problem statement guarantees that the answer is less than 2^31. So, integer overflow is not a concern here.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly handling the direction index after turning: Failing to use the modulo operator (%) can lead to an index out of bounds.

✗Common mistake 2: Not updating the maximum distance after *every* valid move: The maximum distance should be updated after each successful step.

✗Common mistake 3: Assuming obstacle collision on same coordinates when performing turns. Obstacle check should be only done during moving.

✗Common mistake 4: Failing to stop the robot's movement immediately upon encountering an obstacle: Continuing to move after hitting an obstacle will lead to incorrect results.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Robotics path planning: This problem is a simplified version of path planning in robotics, where a robot needs to navigate through an environment with obstacles.

🏦Real-world scenario 2: Video game AI: AI characters in video games often need to navigate through game environments, avoiding obstacles and reaching specific goals. This problem demonstrates some of the core logic involved.

🎮Real-world scenario 3: Autonomous vehicle navigation: Similar to robotics, autonomous vehicles need to plan routes and avoid obstacles while driving.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: November 2, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 14

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 7

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Walking Robot Simulation"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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