Watch 5 video solutions for Most Visited Sector in a Circular Track, a easy level problem involving Array, Simulation. This walkthrough by Programming Live with Larry has 2,056 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
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 ith 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 the counter-clockwise direction (See the first example).
Example 1:
Input: n = 4, rounds = [1,3,1,2] Output: [1,2] Explanation: 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 3:
Input: n = 7, rounds = [1,3,5,7] Output: [1,2,3,4,5,6,7]
Constraints:
2 <= n <= 1001 <= m <= 100rounds.length == m + 11 <= rounds[i] <= nrounds[i] != rounds[i + 1] for 0 <= i < mProblem Overview: You have n sectors arranged in a circular track labeled from 1 to n. A runner completes several rounds defined by the rounds array. Each element marks the sector where a round starts and the next element marks where it ends. The task is to determine which sectors are visited the most during the entire run.
Approach 1: Direct Traversal Using Modulo (Simulation) (Time: O(k), Space: O(n))
This approach simulates the runner's movement step by step. Start at rounds[0], then repeatedly move to the next sector using modulo arithmetic: sector = (sector % n) + 1. Maintain a frequency array to count how many times each sector is visited. For every segment from rounds[i] to rounds[i+1], iterate forward across the circular track and update counts. After processing all rounds, scan the frequency array to find sectors with the maximum visit count.
This method is straightforward and mirrors the real movement on the track. It works well when constraints are small and you want a clear simulation of the process. However, it performs unnecessary work because many visits follow a predictable pattern.
Approach 2: Efficient Range Computation (Time: O(n), Space: O(1) excluding output)
The key observation: the most visited sectors are simply the sectors encountered in the final stretch from the first round's start to the last round's end. Earlier rounds add equal counts to intermediate sectors, so they do not affect which sectors end up with the maximum frequency.
If rounds[0] <= rounds[m-1], the most visited sectors are the continuous range [rounds[0], rounds[m-1]]. If the path wraps around the circle (rounds[0] > rounds[m-1]), the answer becomes two ranges: [1, rounds[m-1]] and [rounds[0], n]. Construct the result in ascending order as required by the problem.
This works because the runner repeatedly passes through sectors in the same direction. The sectors between the first and last positions receive one additional visit compared to others. The solution relies on simple array traversal rather than full simulation, making it both cleaner and faster.
Recommended for interviews: The efficient range computation approach is what interviewers expect. It shows you identified the repeating traversal pattern instead of brute‑forcing the simulation. Walking through the simulation approach first can demonstrate understanding, but deriving the range insight proves stronger algorithmic reasoning.
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Direct Traversal Using Modulo (Simulation) | O(k) where k is total sector moves | O(n) | When you want a straightforward simulation of the runner's movement |
| Efficient Range Computation | O(n) | O(1) excluding output | Preferred solution when recognizing the circular traversal pattern |