When solving scheduling problems, a powerful technique is to think about events rather than intervals. Instead of focusing on complete time ranges, we break each interval into two events: a start event and an end event.
This approach transforms complex interval overlap problems into simpler chronological processing. The key insight is that at any point in time, we only need to know how many intervals are currently active, not which specific intervals they are.
Consider tracking hotel room occupancy. Rather than managing complex checkout/checkin combinations, we can process all checkins and checkouts chronologically. When someone checks in, occupancy increases. When someone checks out, occupancy decreases. The peak occupancy tells us the maximum rooms needed.
The two-pointer technique is perfect for this pattern. We maintain separate sorted lists of start events and end events, then use two pointers to process them in chronological order. This gives us O(n log n) time complexity - much better than checking every pair of intervals.
This event-based thinking applies to many real-world problems: server capacity planning (when do we need the most servers?), resource allocation (what's the peak memory usage?), or traffic analysis (when is the busiest time?). The pattern remains the same: convert intervals to events, process chronologically, track the running count.
1def max_concurrent_users(login_times, logout_times):
2 """Find peak number of concurrent users"""
3 logins = sorted(login_times)
4 logouts = sorted(logout_times)
5
6 login_ptr = logout_ptr = 0
7 current_users = peak_users = 0
8
9 while login_ptr < len(logins):
10 if logins[login_ptr] < logouts[logout_ptr]:
11 current_users += 1 # User logs in
12 login_ptr += 1
13 else:
14 current_users -= 1 # User logs out
15 logout_ptr += 1
16
17 peak_users = max(peak_users, current_users)
18
19 return peak_users