Line Sweep for Max Overlap
Count concurrent intervals with events.
Line Sweep for Max Overlap is a free Coding Interview Prep lesson on CoddyKit — lesson 3 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Coding Interview Prep learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.
The Max Overlap Question
How many intervals cover the same moment at once? The peak count is the maximum overlap, the busiest point on your timeline. 📈
Think in Events
Stop thinking about whole intervals. Split each one into two events: a +1 when it starts and a -1 when it ends.
Build the Event List
For every interval add a start event and an end event to one shared list. Each event carries a position and a delta of plus or minus one.
events = []
for s, e in intervals:
events.append((s, 1)); events.append((e, -1))Sort the Events
Sort every event by position so you can sweep across the timeline from left to right, processing changes in the right order.
events.sort()Sweep and Count
Walk the sorted events keeping a running counter. Add each delta as you pass it, and the counter is how many intervals are active now.
active = 0
for pos, delta in events:
active += deltaTrack the Peak
After each update, compare the counter to your best so far. The largest value the counter ever reaches is the maximum overlap.
best = max(best, active)The Tie-Break Trick
At equal positions, order matters. If an end at x should free the slot before a start at x, sort ends before starts at the same point.
Encode Deltas to Sort Right
A neat way to break ties is choosing deltas so the tuple sort does it for you. Place the -1 delta ahead of +1 when positions match.
events.append((s, 1)); events.append((e, -1)) # -1 sorts first at a tieWhy It Is Fast
You create 2n events, sort them once, and sweep once. The whole method is O(n log n), dominated by that single sort.
Where You See It
Maximum overlap answers classic tasks like the minimum number of rooms needed for meetings, or peak simultaneous users on a server.
Beyond Just Counting
The same sweep extends easily: track total covered length, or find every position where the count changes, all in one linear pass.
Quick Check
You sweep events to find maximum overlap.
Recap
Turn intervals into +1 start and -1 end events, sort them, and sweep a counter to find the peak. Break ties by ending before starting. 🚀
Frequently asked questions
Is the “Line Sweep for Max Overlap” lesson free?
Yes — the full text of “Line Sweep for Max Overlap” is free to read here on the web, and the Coding Interview Prep course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Coding Interview Prep course, upgrade to CoddyKit PRO.
What will I learn in “Line Sweep for Max Overlap”?
Count concurrent intervals with events. You practise Coding Interview Prep with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.
Do I need any experience to start Coding Interview Prep?
No prior experience is required. Coding Interview Prep on CoddyKit is structured for beginners through advanced learners; this is — lesson 3 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Line Sweep for Max Overlap” lesson take?
Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.
Can I write and run code in this Coding Interview Prep lesson?
Yes. Every Coding Interview Prep lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.
All lessons in this course
- Sort Intervals by Start
- Merge Overlapping Intervals
- Line Sweep for Max Overlap
- Minimum Removals for No Overlap