How to Solve Most Visited Sector in a Circular Track

This problem requires simulating a circular track marathon and counting visits per sector using an array. By iterating through each round and incrementing visits, you can determine which sectors are most frequently visited. Sorting the resulting sectors in ascending order ensures the correct output format while handling the circular nature of the track.

Problem Statement

You are given an integer n representing a circular track with sectors labeled from 1 to n and an array rounds representing a marathon with multiple rounds. Each round starts at rounds[i - 1] and ends at rounds[i], moving through sectors in ascending order and wrapping around the track if necessary.

Return an array of the sectors visited most frequently during the marathon, sorted in ascending order. The goal is to track visit counts efficiently using array simulation techniques while accounting for circular traversal of the track.

Examples

Example 1

Input: n = 4, rounds = [1,3,1,2]

Output: [1,2]

The marathon starts at sector 1. The order of the visited sectors is as follows: 1 --> 2 --> 3 (end of round 1) --> 4 --> 1 (end of round 2) --> 2 (end of round 3 and the marathon) We can see that both sectors 1 and 2 are visited twice and they are the most visited sectors. Sectors 3 and 4 are visited only once.

Example 2

Input: n = 2, rounds = [2,1,2,1,2,1,2,1,2]

Output: [2]

Example details omitted.

Example 3

Input: n = 7, rounds = [1,3,5,7]

Output: [1,2,3,4,5,6,7]

Example details omitted.

Constraints

• 2 <= n <= 100
• 1 <= m <= 100
• rounds.length == m + 1
• 1 <= rounds[i] <= n
• rounds[i] != rounds[i + 1] for 0 <= i < m

Solution Approach

Simulate Sector Visits with an Array

Initialize an array of size n to count visits for each sector. For each round, iterate from the start sector to the end sector, incrementing the corresponding counts. Use modulo arithmetic to wrap around the circular track, ensuring all visited sectors are correctly counted.

Identify Maximum Visit Count

After simulating all rounds, scan the array to find the maximum visit count. This step isolates the sectors that were visited most frequently, reflecting the core array simulation pattern of this problem.

Collect and Sort Most Visited Sectors

Iterate through the count array to collect sectors with the maximum visits. Sort the resulting list in ascending order to meet the output requirement. This step ensures clarity in results while preserving the original circular traversal logic.

Complexity Analysis

Time complexity is O(n + m) where n is the number of sectors and m is the number of rounds, as each round is simulated efficiently. Space complexity is O(n) for the array storing visit counts of each sector.

What Interviewers Usually Probe

• Ask about simulating rounds efficiently without revisiting sectors unnecessarily.
• Check if the candidate handles circular wrap-around correctly using modulo arithmetic.
• Listen for reasoning about using an array to count visits versus more complex data structures.

Common Pitfalls or Variants

Common pitfalls

• Failing to account for circular wrap-around, causing incorrect visit counts.
• Using nested loops unnecessarily, which increases time complexity.
• Forgetting to sort the result array, leading to incorrect output order.

Follow-up variants

• Return the least visited sectors instead of the most visited sectors.
• Simulate a track with variable-length rounds or weighted visits.
• Handle a dynamic number of sectors added or removed between rounds.

How GhostInterview Helps

• GhostInterview guides through building the visit count array for each sector efficiently.
• It ensures proper handling of circular traversal to avoid off-by-one errors.
• The solver highlights sorting and final collection of sectors with maximum visits automatically.

Topic Pages

• Array
• Simulation

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FAQ

What is the easiest way to simulate the circular track visits?

Use an array of size n and increment counts for each sector visited, applying modulo arithmetic to handle wrap-around.

Why does the problem require sorting the result array?

Sorting ensures the sectors are returned in ascending order, which is explicitly required in the problem statement.

Can this problem be solved without simulating each sector visit?

Yes, by using range counting between start and end sectors, but explicit simulation aligns with the array plus simulation pattern.

How do I handle rounds that wrap around from n to 1?

Use modulo arithmetic to loop back to sector 1 when the end sector index exceeds n, maintaining correct visit counts.

Which pattern does this problem emphasize for interview solutions?

This problem emphasizes the Array plus Simulation pattern, focusing on visit counting and circular traversal handling.