What is the time complexity of Path Crossing?

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

What data structures are used to solve Path Crossing?

This problem uses Hash Table, String. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Path Crossing?

Insight 1: Using a set (or hash table) to efficiently track visited coordinates is crucial for achieving an optimal time complexity. Sets provide constant-time average complexity for insertion and lookup. Insight 2: The problem can be solved by iterating through the path string, updating the current coordinates based on each direction, and checking if the new coordinates have already been visited. This requires keeping track of the coordinates' history.

Which companies ask LeetCode 1496. Path Crossing in interviews?

This problem is frequently asked at Yandex.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Path Crossing - LeetCode 1496 Solution

Path Crossing - Complete Solution Guide

Path Crossing is LeetCode problem 1496, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp.

Problem Statement

Given a string path , where path[i] = 'N' , 'S' , 'E' or 'W' , each representing moving one unit north, south, east, or west, respectively. You start at the origin (0, 0) on a 2D plane and walk on the path specified by path . Return true if the path crosses itself at any point, that is, if at any time you are on a location you have previously visited . Return false otherwise. Example 1: Input: path = "NES" Output: false Explanation: Notice that the path doesn't cross any point more than once. Ex

Detailed Explanation

The problem asks whether a path, represented by a string of 'N', 'S', 'E', and 'W' characters (North, South, East, West), crosses itself. The path starts at the origin (0, 0) on a 2D plane. Each character in the string represents a movement of one unit in the corresponding direction. The path crosses itself if it visits the same coordinate more than once. The output should be a boolean value: `true` if the path crosses itself, and `false` otherwise.

Solution Approach

The provided solutions use a set (or hash set in Java, unordered set in C++) to store the visited coordinates as (x, y) pairs. The algorithm iterates through the path string: For each direction, it updates the x and y coordinates accordingly. Before adding the new coordinates to the set, it checks if the coordinates are already present. If a duplicate is found, it means the path has crossed itself, and the function immediately returns `true`. If the loop completes without finding any duplicates, it means the path does not cross itself, and the function returns `false`.

Step-by-Step Algorithm

Step 1: Initialize a set `visited` to store the coordinates visited so far. Add the origin (0, 0) to `visited`.
Step 2: Initialize the current coordinates `x` and `y` to 0.
Step 3: Iterate through each character `c` in the input string `path`.
Step 4: Based on the character `c`, update `x` and `y` accordingly ('N': y++, 'S': y--, 'E': x++, 'W': x--).
Step 5: Check if the new coordinates `(x, y)` are already in the `visited` set. If they are, return `true` (path crossing detected).
Step 6: Add the new coordinates `(x, y)` to the `visited` set.
Step 7: After iterating through all characters, return `false` (no path crossing).

Key Insights

Insight 1: Using a set (or hash table) to efficiently track visited coordinates is crucial for achieving an optimal time complexity. Sets provide constant-time average complexity for insertion and lookup.
Insight 2: The problem can be solved by iterating through the path string, updating the current coordinates based on each direction, and checking if the new coordinates have already been visited. This requires keeping track of the coordinates' history.
Insight 3: The origin (0,0) is considered a visited point from the beginning, because the path starts there.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Hash Table, String.

Companies

Asked at: Yandex.

Path Crossing | LeetCode 1496

Easy

Hash Table String

Time: O(n)Space: O(n)

Solution Code

Available in:

class Solution {
    public boolean isPathCrossing(String path) {
        Set<String> visited = new HashSet<>();
        visited.add("0,0");
        int x = 0, y = 0;
        for (char c : path.toCharArray()) {
            if (c == 'N') y++;
            else if (c == 'S') y--;
            else if (c == 'E') x++;
            else x--;
            String coord = x + "," + y;
            if (visited.contains(coord)) return true;
            visited.add(coord);
        }
        return false;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 1496: Path Crossing - Detailed explanation and solution approaches.

Topics

Hash Table String

Companies

Yandex

Stats

Difficulty:Easy

Languages:3

Companies:1

Problem #:1496

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 set `visited` to store the coordinates visited so far. Add the origin (0, 0) to `visited`.
2
Step 2: Initialize the current coordinates `x` and `y` to 0.
3
Step 3: Iterate through each character `c` in the input string `path`.
4
Step 4: Based on the character `c`, update `x` and `y` accordingly ('N': y++, 'S': y--, 'E': x++, 'W': x--).
5
Step 5: Check if the new coordinates `(x, y)` are already in the `visited` set. If they are, return `true` (path crossing detected).
6
Step 6: Add the new coordinates `(x, y)` to the `visited` set.
7
Step 7: After iterating through all characters, return `false` (no path crossing).

💡

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)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The algorithm iterates through the path string once, which takes O(n) time, where n is the length of the path. In the worst case, the number of unique coordinates visited could be equal to the length of the path. Therefore, the space used by the `visited` set is also O(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

Using a 2D array

Instead of a set, you could use a 2D boolean array to represent the plane. The array size would need to be large enough to accommodate the maximum possible coordinates based on the path length. Each cell would indicate if that coordinate has been visited.

Time: O(n)Space: O(m*m), where 'm' is the maximum possible coordinate value (dependent on n). This approach is less efficient space-wise if the path covers a large area.

Trade-offs: This approach is simpler to understand for beginners but less efficient in space compared to using a hash set, especially for large paths that don't densely fill the space.

✨

Key Insights

1Insight 1: Using a set (or hash table) to efficiently track visited coordinates is crucial for achieving an optimal time complexity. Sets provide constant-time average complexity for insertion and lookup.
2Insight 2: The problem can be solved by iterating through the path string, updating the current coordinates based on each direction, and checking if the new coordinates have already been visited. This requires keeping track of the coordinates' history.
3Insight 3: The origin (0,0) is considered a visited point from the beginning, because the path starts there.

📚

Key Terms Explained

For Students

Hash Table

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

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Empty path string. The solution correctly handles this by immediately returning `false` as no crossing can occur.
Edge case 2: Path that returns to the origin. The solution correctly identifies this as a crossing.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to add the starting point (0, 0) to the `visited` set. This leads to incorrect results if the path crosses itself at the origin.

✗Common mistake 2: Using a list or array instead of a set to store visited points. Checking for existence in a list takes O(n) time, resulting in a total time complexity of O(n^2), which is inefficient.

✅

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 for robots to avoid collisions. This algorithm can be adapted to check for self-intersections in a robot's planned trajectory.

🏦Real-world scenario 2: GPS tracking: Analyzing a GPS trace to detect if a vehicle or person has revisited a location, possibly indicating a change in direction or a loop in the route.

💡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

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate values.

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: July 27, 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 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.

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) complexity.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

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 "Path Crossing"?

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

🤖 Need help with this problem?