What is the time complexity of Nearest Exit from Entrance in Maze?

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

What is the space complexity of Nearest Exit from Entrance in Maze?

The space complexity is O(m*n).

What data structures are used to solve Nearest Exit from Entrance in Maze?

This problem uses Array, Breadth-First Search, Matrix. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Nearest Exit from Entrance in Maze?

Insight 1: Breadth-First Search (BFS) is suitable for finding the shortest path in an unweighted graph (maze). Insight 2: We can use the maze itself to keep track of visited cells to avoid cycles by marking visited cells as walls (+).

Which companies ask LeetCode 1926. Nearest Exit from Entrance in Maze in interviews?

This problem is frequently asked at Samsung, eBay.

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Nearest Exit from Entrance in Maze - LeetCode 1926 Solution

Nearest Exit from Entrance in Maze - Complete Solution Guide

Nearest Exit from Entrance in Maze is LeetCode problem 1926, 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

You are given an m x n matrix maze ( 0-indexed ) with empty cells (represented as '.' ) and walls (represented as '+' ). You are also given the entrance of the maze, where entrance = [entrance row , entrance col ] denotes the row and column of the cell you are initially standing at. In one step, you can move one cell up , down , left , or right . You cannot step into a cell with a wall, and you cannot step outside the maze. Your goal is to find the nearest exit from the entrance . An exit is def

Detailed Explanation

The problem asks us to find the shortest path (in terms of number of steps) from a given entrance cell in a maze to the nearest exit. The maze is represented by a 2D grid where '.' represents an empty cell and '+' represents a wall. An exit is an empty cell located at the boundary of the maze, excluding the entrance itself. We can move one step up, down, left, or right. If no exit is reachable, we should return -1.

Solution Approach

The solution uses BFS to explore the maze. Starting from the entrance cell, it explores all possible paths one step at a time. For each cell visited, it checks if it is an exit (a boundary cell that is not the entrance). If an exit is found, the number of steps taken to reach that exit is returned. If the BFS completes without finding an exit, it means there is no path to an exit, and -1 is returned. The maze is modified to mark visited cells, preventing cycles and redundant exploration.

Step-by-Step Algorithm

Step 1: Initialize a queue with the entrance cell and its initial step count (0). Mark the entrance as visited by changing its value in the maze to '+'.
Step 2: While the queue is not empty, dequeue a cell (row, col) and its step count from the queue.
Step 3: Explore the four possible directions (up, down, left, right) from the current cell.
Step 4: For each direction, check if the neighboring cell is within the maze bounds, is an empty cell ('.'), and has not been visited yet (not '+').
Step 5: If the neighboring cell meets the criteria in Step 4, check if it is an exit (i.e., is on the boundary of the maze). If it is an exit, return the current step count + 1.
Step 6: If the neighboring cell is not an exit but is a valid cell, mark it as visited by changing its value in the maze to '+', and enqueue it into the queue with an incremented step count (steps + 1).
Step 7: If the queue becomes empty before finding any exit, return -1.

Key Insights

Insight 1: Breadth-First Search (BFS) is suitable for finding the shortest path in an unweighted graph (maze).
Insight 2: We can use the maze itself to keep track of visited cells to avoid cycles by marking visited cells as walls (+).
Insight 3: Checking for exit condition within the BFS traversal improves efficiency; we don't need to explore the entire maze if an exit is found early.

Complexity Analysis

Time Complexity: O(m*n)

Space Complexity: O(m*n)

Topics

This problem involves: Array, Breadth-First Search, Matrix.

Companies

Asked at: Samsung, eBay.

Nearest Exit from Entrance in Maze | LeetCode 1926

Medium

Array Breadth-First Search Matrix

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

Solution Code

Available in:

import java.util.LinkedList;
import java.util.Queue;

class Solution {
    public int nearestExit(char[][] maze, int[] entrance) {
        int m = maze.length;
        int n = maze[0].length;
        int start_r = entrance[0];
        int start_c = entrance[1];
        
        Queue<int[]> q = new LinkedList<>();
        q.offer(new int[]{start_r, start_c, 0});
        maze[start_r][start_c] = '+';

        int[][] directions = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};

        while (!q.isEmpty()) {
            int[] curr = q.poll();
            int r = curr[0];
            int c = curr[1];
            int steps = curr[2];

            for (int[] dir : directions) {
                int dr = dir[0];
                int dc = dir[1];
                int nr = r + dr;
                int nc = c + dc;

                if (0 <= nr && nr < m && 0 <= nc && nc < n && maze[nr][nc] == '.') {
                    if (nr == 0 || nr == m - 1 || nc == 0 || nc == n - 1) {
                        return steps + 1;
                    }
                    
                    maze[nr][nc] = '+';
                    q.offer(new int[]{nr, nc, steps + 1});
                }
            }
        }
        
        return -1;
    }
}

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Problem Info

Description

Problem 1926: Nearest Exit from Entrance in Maze - Detailed explanation and solution approaches.

Topics

Array Breadth-First Search Matrix

Companies

SamsungeBay

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:1926

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

7 steps

1
Step 1: Initialize a queue with the entrance cell and its initial step count (0). Mark the entrance as visited by changing its value in the maze to '+'.
2
Step 2: While the queue is not empty, dequeue a cell (row, col) and its step count from the queue.
3
Step 3: Explore the four possible directions (up, down, left, right) from the current cell.
4
Step 4: For each direction, check if the neighboring cell is within the maze bounds, is an empty cell ('.'), and has not been visited yet (not '+').
5
Step 5: If the neighboring cell meets the criteria in Step 4, check if it is an exit (i.e., is on the boundary of the maze). If it is an exit, return the current step count + 1.
6
Step 6: If the neighboring cell is not an exit but is a valid cell, mark it as visited by changing its value in the maze to '+', and enqueue it into the queue with an incremented step count (steps + 1).
7
Step 7: If the queue becomes empty before finding any exit, return -1.

💡

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(m*n)

💾

Space Complexity

O(m*n)

📝

Why?

The time complexity is determined by the number of cells visited during the BFS. Since each cell is visited at most once, the time complexity is proportional to the number of cells, which is m*n. The space complexity is mainly determined by the size of the queue. In the worst case, all empty cells might be added to the queue, leading to a space complexity of O(m*n).

📖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

Depth-First Search (DFS)

DFS could be used but it's not guaranteed to find the shortest path first. You'd need to explore all possible paths and then find the minimum length path.

Time: O(m*n) in the worst case (exploring all paths).Space: O(m*n) in the worst case due to recursion depth.

Trade-offs: BFS is generally preferred over DFS for shortest path problems in unweighted graphs because BFS guarantees finding the shortest path, while DFS does not and requires more complex logic to find the shortest path.

Dijkstra's Algorithm

Dijkstra's algorithm can be applied, treating each step as having a weight of 1. However, since all edges have the same weight, BFS is a simpler and more efficient approach.

Time: O(m*n log(m*n)) if using a priority queue implementation, or O((m*n)^2) with array-based implementation.Space: O(m*n)

Trade-offs: Dijkstra's algorithm is more complex than BFS and is generally used for weighted graphs. Since our maze is an unweighted graph, BFS is the better choice.

✨

Key Insights

1Insight 1: Breadth-First Search (BFS) is suitable for finding the shortest path in an unweighted graph (maze).
2Insight 2: We can use the maze itself to keep track of visited cells to avoid cycles by marking visited cells as walls (+).
3Insight 3: Checking for exit condition within the BFS traversal improves efficiency; we don't need to explore the entire maze if an exit is found early.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: The maze contains only walls, resulting in no possible paths and therefore no exits. The algorithm correctly returns -1 as no paths are explored.
Edge case 2: The entrance is surrounded by walls, meaning there are no adjacent empty cells to start exploring. The algorithm correctly returns -1 as the queue becomes empty immediately.
Edge case 3: The exit is right next to the entrance. The algorithm handles this correctly and returns 1.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not marking visited cells, leading to infinite loops in the BFS.

✗Common mistake 2: Incorrectly defining the exit condition, such as not checking for boundary cells or including the entrance as an exit.

✗Common mistake 3: Using DFS instead of BFS, which might not find the shortest path directly.

✗Common mistake 4: Not considering the case where no exit is reachable, resulting in incorrect output.

✅

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: Pathfinding in robotics, where a robot needs to navigate a maze-like environment to reach a specific destination.

🏦Real-world scenario 2: Network routing, where finding the shortest path between two nodes in a network is crucial for efficient data transmission.

🎮Real-world scenario 3: Game development, where AI agents need to find the shortest path to a target in a game world.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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: October 5, 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

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 6

❓

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 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 "Nearest Exit from Entrance in Maze"?

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 breadth-first search techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?