Algorithms / Interval Overlap Meeting Rooms
Least You Need to Know: Interval Overlap, Meeting Rooms, and End-Time Heaps
Some interval problems are not about choosing one compatible subset. Instead they ask for the **maximum number of overlapping intervals** at any moment, or equivalently the minimum number of rooms needed to host them all. A min-heap of end times tracks how many intervals are active right now.
جو کم از کم جاننا ضروری ہے
- Meeting rooms asks for the maximum simultaneous overlap, not the size of one non-overlapping subset.
- Sort intervals by start time, then compare each new start against the earliest ending active interval.
- If the earliest end time is finished before the new start, one room can be reused.
- A min-heap of active end times tracks current overlap efficiently.
- This is a different goal from interval scheduling maximize-count.
اہم علامتیں
[s, f)
interval starting at s and ending at f
active interval
an interval whose end time has not yet passed
min-heap of end times
earliest finishing active interval at the root
مختصر حل شدہ مثال
- Sort meetings by start time.
- Push the first meeting's end time into a min-heap.
- For each new meeting, compare its start to the smallest current end time.
- If that room is free, pop it; then push the new end time.
- The maximum heap size seen is the number of rooms needed.
عام غلطیاں
- Students often reuse earliest-finish interval scheduling even though the objective changed.
- Students often compare with the latest end time instead of the earliest one.
- Students often ignore interval endpoint conventions when deciding whether touching intervals overlap.
اس قسم کے سوال کو کیسے پہچانیں
- The prompt asks for minimum rooms, servers, or resources to host all intervals.
- You care about simultaneous activity, not one chosen subset.
- Each new interval should be compared to the earliest resource release time.
Next recommended lesson
Continue through this topic with Least You Need to Know: Interval Scheduling and Earliest-Finish Greedy.
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