What is the time complexity of Most Visited Sector in a Circular Track?

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

What data structures are used to solve Most Visited Sector in a Circular Track?

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

What are the key insights for solving Most Visited Sector in a Circular Track?

Insight 1: The problem can be efficiently solved by tracking the visited sectors. Instead of simulating the entire race, we can directly determine the sectors visited between the starting sector of the first round and the ending sector of the last round. Insight 2: We can use an array to count the visits to each sector. The indices of this array correspond to the sector numbers.

Which companies ask LeetCode 1560. Most Visited Sector in a Circular Track in interviews?

This problem is frequently asked at Expedia.

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Most Visited Sector in a Circular Track - LeetCode 1560 Solution

Most Visited Sector in a Circular Track - Complete Solution Guide

Most Visited Sector in a Circular Track is LeetCode problem 1560, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given an integer n and an integer array rounds . We have a circular track which consists of n sectors labeled from 1 to n . A marathon will be held on this track, the marathon consists of m rounds. The i th round starts at sector rounds[i - 1] and ends at sector rounds[i] . For example, round 1 starts at sector rounds[0] and ends at sector rounds[1] Return an array of the most visited sectors sorted in ascending order. Notice that you circulate the track in ascending order of sector numbers in t

Detailed Explanation

The problem simulates a marathon on a circular track with 'n' sectors. The marathon consists of 'm' rounds. Each round starts and ends at specific sectors given in the `rounds` array. The goal is to identify and return the sector(s) visited most frequently during the entire marathon, sorted in ascending order.

Solution Approach

The solution uses a frequency counting approach. It initializes a count array to store the number of times each sector is visited. Then, it iterates through the sectors visited between the start and end points of the marathon, incrementing the counter for each visited sector. Finally, it finds the maximum count and returns the sectors with that maximum count.

Step-by-Step Algorithm

Step 1: Initialize a count array of size 'n' with zeros. Each index represents a sector, and the value at each index will store the count of visits to that sector.
Step 2: Determine the starting sector (`start`) and ending sector (`end`) from the `rounds` array. Adjust these indices to be 0-based (subtract 1).
Step 3: Handle the circular nature of the track. If `start` <= `end`, iterate from `start` to `end` (inclusive), incrementing the counts for each sector. Otherwise (if `start` > `end`), iterate from `start` to `n-1` and then from 0 to `end`, incrementing counts.
Step 4: Find the maximum count among all sectors.
Step 5: Iterate through the count array again. For each sector with a count equal to the maximum count, add that sector number (index + 1) to the result array.
Step 6: Return the result array containing the most visited sector(s) sorted in ascending order.

Key Insights

Insight 1: The problem can be efficiently solved by tracking the visited sectors. Instead of simulating the entire race, we can directly determine the sectors visited between the starting sector of the first round and the ending sector of the last round.
Insight 2: We can use an array to count the visits to each sector. The indices of this array correspond to the sector numbers.
Insight 3: We need to handle the circular nature of the track. If the starting sector is greater than the ending sector, the marathon covers the end of the track and the beginning.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Simulation.

Companies

Asked at: Expedia.

Most Visited Sector in a Circular Track | LeetCode 1560

Easy

Array Simulation

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

Solution Code

Available in:

import java.util.ArrayList;
import java.util.List;

class Solution {
    public List<Integer> mostVisited(int n, int[] rounds) {
        List<Integer> result = new ArrayList<>();
        int start = rounds[0];
        int end = rounds[rounds.length - 1];

        if (start <= end) {
            for (int i = start; i <= end; i++) {
                result.add(i);
            }
        } else {
            for (int i = 1; i <= end; i++) {
                result.add(i);
            }
            for (int i = start; i <= n; i++) {
                result.add(i);
            }
        }

        return result;
    }
}

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Problem Info

Description

Problem 1560: Most Visited Sector in a Circular Track - Detailed explanation and solution approaches.

Topics

Array Simulation

Companies

Expedia

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1560

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

6 steps

1
Step 1: Initialize a count array of size 'n' with zeros. Each index represents a sector, and the value at each index will store the count of visits to that sector.
2
Step 2: Determine the starting sector (`start`) and ending sector (`end`) from the `rounds` array. Adjust these indices to be 0-based (subtract 1).
3
Step 3: Handle the circular nature of the track. If `start` <= `end`, iterate from `start` to `end` (inclusive), incrementing the counts for each sector. Otherwise (if `start` > `end`), iterate from `start` to `n-1` and then from 0 to `end`, incrementing counts.
4
Step 4: Find the maximum count among all sectors.
5
Step 5: Iterate through the count array again. For each sector with a count equal to the maximum count, add that sector number (index + 1) to the result array.
6
Step 6: Return the result array containing the most visited sector(s) sorted in ascending order.

💡

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 `rounds` array once (O(m)) and then iterates through the count array twice (O(n)). Since m is bounded by n (m <= 100 and n >= 2), the overall time complexity is dominated by the iterations over the count array, making it O(n). The space complexity is O(n) due to the count array.

📖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

Optimized Frequency Counting

Instead of iterating through the count array twice, find the maximum count while building the count array. This slightly improves time complexity.

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

Trade-offs: This optimization offers a minor improvement in runtime but adds a small amount of complexity to the main loop. The difference is negligible for the given constraints.

✨

Key Insights

1Insight 1: The problem can be efficiently solved by tracking the visited sectors. Instead of simulating the entire race, we can directly determine the sectors visited between the starting sector of the first round and the ending sector of the last round.
2Insight 2: We can use an array to count the visits to each sector. The indices of this array correspond to the sector numbers.
3Insight 3: We need to handle the circular nature of the track. If the starting sector is greater than the ending sector, the marathon covers the end of the track and the beginning.

📚

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 starting sector is greater than the ending sector. The solution correctly handles this by traversing the track circularly. For example, `rounds = [4, 2]` on a track with n = 4, correctly identifies sectors 1,2,3,4
Edge case 2: Multiple sectors are visited the most frequently. The solution correctly identifies and returns all of them, sorted in ascending order.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the circular nature of the track, leading to incorrect results when the last sector is smaller than the first sector.

✗Common mistake 2: Not correctly converting between 1-based indexing (sector numbers) and 0-based indexing (array indices).

✅

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: Analyzing website traffic patterns. 'Sectors' could represent different pages on a website, and 'rounds' could represent user sessions. The algorithm can help identify the most popular pages.

🏦Real-world scenario 2: Monitoring sensor data on a circular system. For example, sensors placed around a pipeline or a rotating machine. The algorithm can find the most frequently activated sections.

💡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

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ Watch Out

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

👨‍💻 From Experience

This is one of the first problems I solved when learning Array. It's a great foundation for more complex problems.

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: September 29, 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

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

@DevExpert92Jul 13

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

@AlgoMasterJul 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.

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 "Most Visited Sector in a Circular Track"?

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

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