Activity Selection (N Meetings)
A medium Greedy interview guide. Task statement, worked examples, intuition, and step-by-step solutions.
- Topic
- Greedy
- Sheets
- 1
- Core for
- 3 roles
The problem
Given n meetings with their start and end times, find the minimum number of rooms required to accommodate all meetings without overlap.
Example 1
- Input
- meetings = [[0,30],[5,10],[15,20]]
- Output
- 2
- Why
- Meetings [0,30] and [5,10] overlap, and [0,30] and [15,20] overlap. At most 2 meetings happen simultaneously.
Example 2
- Input
- meetings = [[7,10],[2,4]]
- Output
- 1
- Why
- No meetings overlap, so only one room is needed.
Constraints
- 1 <= meetings.length <= 10^5
- meetings[i].length == 2
- 0 <= start < end <= 10^9
How to think about it
Updated 2026-09-29Every meeting must be assigned a room, and a room only becomes available once its earlier meeting finishes. Sorting meetings by start time allows assigning each to the room whose meeting concludes earliest, allocating a new room only when even that room is still occupied.
Approaches, worst first
Chronological event sweep
time O(n log n) · space O(n)
Split intervals into start (+1) and end (-1) events. Sort all events chronologically, breaking ties by placing end events before start events, and track the peak active rooms.
Min-heap of end timesWrite this one
time O(n log n) · space O(n)
Sort meetings by start time. Maintain a min-heap of end times for currently occupied rooms. If the earliest ending room in the heap finishes before or when the new meeting starts, reuse it by popping and pushing the new end time; otherwise allocate an additional room.
Where people lose marks · 2
- Tie-breaking: if meeting A ends at time T and meeting B starts at time T, they can share the same room (`start >= heap.top()`), not requiring a new room.
- Sorting meetings by end time instead of start time breaks the heap simulation because rooms would be evaluated out of chronological start order.
The theory behind it
Greedy — the ground this problem stands on. All Greedy problems
What Greedy is
A greedy algorithm makes the best-looking choice available right now, at every step, without ever looking back or second-guessing its decision. Think of a cashier making change by handing over the largest possible coin first, repeatedly, until the total is reached. Unlike dynamic programming, which saves and compares answers to multiple overlapping paths, a greedy strategy commits to one immediate option and keeps moving forward.
When to reach for it
Reach for greedy when problems ask for minimum jumps, interval scheduling, assigning resources to maximize satisfaction, or finding fractional values. Key signals include sorted orders where greedily taking the next item never hurts future options, or gas station round trips where running balances prove reachability. If you can prove that taking the immediate best choice never leaves you worse off than any alternative, greedy gives the fastest answer.
How the pattern works
Start by sorting the input to bring the most promising candidates to the front. At each position, evaluate your local rule, take the best available piece, and update your running state. The crucial mental step is proving the greedy choice property: demonstrate that picking this immediate winner cannot block a better global solution down the road. If choosing an item now forces you to reconsider past decisions when conditions change later, greedy fails and you must switch to dynamic programming instead.
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