Minimum Platforms Required
A medium Greedy problem included in Love Babbar 450, Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Greedy
- Sheets
- 2
- Core for
- 3 roles
- Platform
- GeeksforGeeks
The problem
Given arrival and departure times of all trains at a railway station, find the minimum number of platforms required so that no train has to wait.
Example 1
- Input
- arrival = [900,940,950,1100,1500,1800], departure = [910,1200,1100,1130,1900,2000]
- Output
- 3
- Why
- At time 950, three trains are at the station simultaneously, requiring 3 platforms.
Example 2
- Input
- arrival = [900,1100,1235], departure = [1000,1200,1240]
- Output
- 1
- Why
- No trains overlap in schedule, so only one platform is needed.
Constraints
- 1 <= arrival.length == departure.length <= 10^5
- 0 <= arrival[i] < departure[i] <= 2 * 10^9
How to think about it
Updated 2026-09-09The identity of which specific train is on which platform does not matter. The required number of platforms is the peak number of trains present at any single moment in time, which can be tracked as arrivals and departures along a common timeline.
Approaches, worst first
Pairwise overlap count
time O(n^2) · space O(1)
For each train interval, iterate over all other train intervals to count how many overlap with it simultaneously. Quadratic runtime becomes prohibitive on 10^5 intervals.
Two pointers on sorted event endpointsWrite this one
time O(n log n) · space O(1)
Sort arrival and departure arrays independently. Use two pointers to walk through both in chronological order. An arrival increments the platform count, while a departure decrements it. Track the maximum count reached throughout the sweep.
Where people lose marks · 3
- Sorting arrivals and departures independently seems counter-intuitive because individual train pairs break, but train identity is irrelevant when measuring peak occupancy.
- Handling simultaneous events: if an arrival and departure happen at the exact same timestamp, verify whether the departure clears the platform before the arrival docks.
- Forgetting to update max platforms before decrementing count on train departures.
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.
What each operation costs
| Operation | Time |
|---|---|
| sort elements to enable greedy selection | O(n log n) |
| greedy single-pass scan through sorted input | O(n) |
| greedy choice using a priority queue | O(n log n) |
What usually goes wrong with Greedy
- Applying a greedy choice without proving it yields the global optimum, such as picking the largest coin first for arbitrary denominations where dynamic programming was required.
- Forgetting to sort the input before running the greedy loop, making local decisions on unordered elements that produce invalid answers.
- Picking items based on only one attribute when the optimal decision depends on a ratio or combination of multiple attributes.
Which roles need this problem
Greedy is a core topic for these 3 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 4 more roles, including Site Reliability Engineer, Search Engineer, Quant Developer.
Companies that have asked it
Tags taken from the problem's own GeeksforGeeks page — not a copied list.
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