Minimum Number of Platforms in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the problem statement of the Minimum Number of Platforms?

Given arrival and departure times of trains, find the minimum number of platforms needed so that no train waits.

beginner

Why do we sort arrival and departure times separately in the Minimum Number of Platforms problem?

Sorting helps us process events in chronological order to track how many trains are at the station at the same time.

beginner

What does the variable 'platform_needed' represent in the algorithm?

'platform_needed' tracks the current number of trains at the station, indicating how many platforms are occupied at that moment.

beginner

How do we update the count of platforms when a train departs?

When a train departs, we decrease 'platform_needed' by one because a platform becomes free.

intermediate

What is the time complexity of the Minimum Number of Platforms algorithm using sorting?

The time complexity is O(n log n) due to sorting the arrival and departure arrays, where n is the number of trains.

What is the first step in solving the Minimum Number of Platforms problem?

A Sort arrival and departure times separately

B Count total trains

C Assign platforms randomly

D Calculate total waiting time

Sorting arrival and departure times helps process events in order to track platform usage.

If a train arrives at 10:00 and another departs at 10:00, how many platforms are needed at that time?

A 1

B 0

C 2

D Depends on train length

Departure at 10:00 frees a platform before arrival at 10:00, so only 1 platform is needed.

What does increasing 'platform_needed' indicate during the algorithm?

A A train departs

B A platform is freed

C A train arrives

D No trains at station

When a train arrives, 'platform_needed' increases to show one more platform is occupied.

Which data structure is primarily used to solve the Minimum Number of Platforms problem efficiently?

A Stack

B Queue

C Hash map

D Sorted arrays

Sorted arrays of arrival and departure times allow linear traversal to count platforms.

What is the main goal of the Minimum Number of Platforms algorithm?

A Minimize train delays

B Minimize number of platforms needed

C Maximize train speed

D Maximize platform usage

The goal is to find the least number of platforms so no train waits.

Explain the step-by-step approach to find the minimum number of platforms needed for trains given their arrival and departure times.

Think about processing events in order and counting how many trains are at the station simultaneously.

Describe why sorting arrival and departure times separately helps solve the Minimum Number of Platforms problem efficiently.

Consider how to know when trains overlap in time.

Practice

1. What does the "Minimum Number of Platforms" problem ask you to find given train arrival and departure times?

easy

A. The least number of platforms needed so no train waits

B. The total number of trains arriving in a day

C. The longest time a train stays on a platform

D. The earliest train arrival time

Solution

1. Step 1: Understand the problem context

   The problem wants to find how many platforms are needed so that no train has to wait for another to leave.

2. Step 2: Identify the key requirement

   We must find the minimum number of platforms so that all trains can be accommodated without delay.

3. Final Answer:

   The least number of platforms needed so no train waits -> Option A

4. Quick Check:

   Minimum platforms = no waiting trains [OK]

Hint: Focus on overlapping train times to find platform count [OK]

Common Mistakes:

• Confusing total trains with platforms needed
• Ignoring overlapping arrival and departure times
• Thinking about train durations instead of platform count

2. Which of the following Python code snippets correctly sorts the arrival times list named arrivals for the Minimum Number of Platforms problem?

easy

A. arrivals.sort(arrivals)

B. sort(arrivals)

C. arrivals.sort()

D. arrivals.sorted()

Solution

1. Step 1: Recall Python list sorting method

   Python lists have a method called sort() that sorts the list in place.

2. Step 2: Check each option

   arrivals.sort() uses arrivals.sort() which is correct. sort(arrivals) is invalid syntax. arrivals.sorted() uses a non-existent method. arrivals.sort(arrivals) incorrectly passes the list as argument.

3. Final Answer:

   arrivals.sort() -> Option C

4. Quick Check:

   List.sort() is correct method [OK]

Hint: Use list.sort() to sort lists in place [OK]

Common Mistakes:

• Using sort() as a standalone function
• Trying to call sorted() as a method
• Passing the list as argument to sort()

3. What is the minimum number of platforms needed for the following train schedule?
arrivals = [900, 940, 950, 1100, 1500, 1800]
departures = [910, 1200, 1120, 1130, 1900, 2000]

medium

A. 4

B. 2

C. 3

D. 1

Solution

1. Step 1: Sort arrival and departure times

   Arrivals sorted: [900, 940, 950, 1100, 1500, 1800]
   Departures sorted: [910, 1120, 1130, 1200, 1900, 2000]

2. Step 2: Use two pointers to count platforms

   Start with i=0 (arrivals), j=0 (departures), platforms=0, max_platforms=0.
   At 900 (arrival), platforms=1.
   At 910 (departure), platforms=0.
   At 940 (arrival), platforms=1.
   At 950 (arrival), platforms=2.
   At 1100 (arrival), platforms=2 (since departure at 1120 is after 1100 but 1130 and 1200 are later).
   Max platforms needed = 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Max overlapping trains = 2 [OK]

Hint: Count overlapping trains using sorted arrivals and departures [OK]

Common Mistakes:

• Not sorting times before counting
• Mixing arrival and departure pointers
• Counting platforms incorrectly at overlaps

4. Identify the error in this Python code snippet for finding minimum platforms:

arrivals = [900, 940, 950]
departures = [910, 1200, 1120]
arrivals.sort()
departures.sort()
i = j = 0
platforms = max_platforms = 0
while i < len(arrivals) and j < len(departures):
    if arrivals[i] <= departures[j]:
        platforms += 1
        i += 1
    else:
        platforms -= 1
        j += 1
    max_platforms = max(max_platforms, platforms)
print(max_platforms)

medium

A. The comparison should be arrivals[i] < departures[j], not <=.

B. The loop condition should use 'or' instead of 'and'.

C. The platforms variable should not be incremented.

D. The departures list should not be sorted.

Solution

1. Step 1: Understand the comparison logic

   Using <= means if arrival time equals departure time, it counts as needing a new platform, but usually a train leaving at time t frees the platform for a train arriving at time t.

2. Step 2: Correct the comparison

   Changing <= to < ensures that if arrival equals departure, platform count decreases first, avoiding unnecessary extra platform.

3. Final Answer:

   The comparison should be arrivals[i] < departures[j], not <=. -> Option A

4. Quick Check:

   Use < to avoid counting simultaneous arrival and departure as overlap [OK]

Hint: Use strict less than for arrival vs departure comparison [OK]

Common Mistakes:

• Using <= causes overcounting platforms
• Changing loop condition wrongly to 'or'
• Not sorting departure times

5. Given multiple trains with arrival and departure times, how would you efficiently find the minimum number of platforms needed if the times are in 24-hour format and some trains arrive and depart at the same time? For example:
arrivals = [900, 940, 950, 1100, 1500, 1800, 1800]
departures = [910, 1200, 1120, 1130, 1900, 2000, 1800]
Choose the best approach.

hard

A. Use a dictionary to map arrival times to departure times and count keys.

B. Count trains arriving at each time and sum them directly without sorting.

C. Sort arrivals only and count unique times.

D. Sort arrivals and departures, then use two pointers with strict less than comparison for arrival vs departure.

Solution

1. Step 1: Sort both arrival and departure lists

   Sorting helps to process events in chronological order, which is essential for counting overlapping trains.

2. Step 2: Use two pointers with strict comparison

   Use two pointers to traverse arrivals and departures. Use arrivals[i] < departures[j] to decide when to increase or decrease platform count, handling same-time arrivals and departures correctly.

3. Final Answer:

   Sort arrivals and departures, then use two pointers with strict less than comparison for arrival vs departure. -> Option D

4. Quick Check:

   Sorting + two pointers + < comparison = correct approach [OK]

Hint: Sort both lists and use two pointers with strict comparison [OK]

Common Mistakes:

• Ignoring sorting of departures
• Using <= causing overcount
• Trying to count without sorting or pointers