Minimum Number of Platforms in DSA C# - 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 required so that no train waits.

beginner

Which data structures are commonly used to solve the Minimum Number of Platforms problem?

Arrays or lists to store arrival and departure times, and sorting algorithms to order these times.

intermediate

Explain the main idea behind the two-pointer approach for Minimum Number of Platforms.

Sort arrival and departure times separately. Use two pointers to traverse both arrays. Increase platform count when a train arrives before or at the earliest departure, decrease when a train departs.

intermediate

What is the time complexity of the optimal solution for Minimum Number of Platforms?

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

beginner

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

Sorting separately helps to efficiently compare the next arriving train with the earliest departing train to decide platform allocation.

What does the Minimum Number of Platforms problem aim to minimize?

A Train arrival times

B Number of trains

C Number of platforms

D Train departure times

The problem aims to find the minimum number of platforms needed so that no train waits.

Which step is essential before applying the two-pointer technique in this problem?

A Reverse the arrival times

B Sort arrival and departure times separately

C Merge arrival and departure times

D Use a queue for trains

Sorting arrival and departure times separately allows efficient comparison using two pointers.

If a train arrives after the earliest departure, what should we do with the platform count?

A Decrease platform count

B Increase platform count

C Keep platform count same

D Reset platform count

If a train arrives after the earliest departure, a platform is freed, so we decrease the count.

What is the main reason for using two pointers in this problem?

A To traverse arrival and departure arrays simultaneously

B To sort the arrays

C To store platform numbers

D To count trains

Two pointers help traverse arrival and departure arrays to compare times efficiently.

What is the overall time complexity of the optimal solution?

A O(n)

B O(n^2)

C O(log n)

D O(n log n)

Sorting takes O(n log n), which dominates the overall time complexity.

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

Think about how to compare arrival and departure times efficiently.

Explain why sorting arrival and departure times separately is important in solving the Minimum Number of Platforms problem.

Consider how sorted times help in deciding platform usage.

Practice

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

easy

A. The total time trains spend at the station

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

C. The maximum speed of any train

D. The total number of trains arriving in a day

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 output

   The output is the minimum number of platforms required to handle all trains without delay.

3. Final Answer:

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

4. Quick Check:

   Minimum platforms = no waiting trains [OK]

Hint: Count overlapping trains to find minimum platforms needed [OK]

Common Mistakes:

• Confusing total trains with platforms needed
• Ignoring overlapping arrival and departure times
• Thinking about train speed or duration instead

2. Which of the following C# code snippets correctly declares arrays for arrival and departure times for the Minimum Number of Platforms problem?

easy

A. int arrival = [900, 940, 950]; int departure = [910, 1200, 1120];

B. int arrival[] = (900, 940, 950); int departure[] = (910, 1200, 1120);

C. int[] arrival = {900, 940, 950}; int[] departure = {910, 1200, 1120};

D. int[] arrival = (900, 940, 950); int[] departure = (910, 1200, 1120);

Solution

1. Step 1: Recall C# array declaration syntax

   In C#, arrays are declared with type[], and values inside curly braces {}.

2. Step 2: Check each option for correct syntax

   int[] arrival = {900, 940, 950}; int[] departure = {910, 1200, 1120}; uses int[] and curly braces {}, which is correct. Others use parentheses or wrong syntax.

3. Final Answer:

   int[] arrival = {900, 940, 950}; int[] departure = {910, 1200, 1120}; -> Option C

4. Quick Check:

   C# arrays use type[] and {} [OK]

Hint: Use int[] and curly braces {} for arrays in C# [OK]

Common Mistakes:

• Using parentheses () instead of curly braces {}
• Declaring arrays without [] after type
• Using square brackets [] for initialization

3. What is the output of the following C# code snippet that calculates minimum platforms?

int[] arrival = {900, 940, 950, 1100, 1500, 1800};
int[] departure = {910, 1200, 1120, 1130, 1900, 2000};

int platforms = CalculateMinPlatforms(arrival, departure);
Console.WriteLine(platforms);

// Assume CalculateMinPlatforms correctly implements the algorithm.

medium

A. 5

B. 4

C. 2

D. 3

Solution

1. Step 1: Sort arrival and departure times

   Arrival: 900, 940, 950, 1100, 1500, 1800 Departure: 910, 1120, 1130, 1200, 1900, 2000

2. Step 2: Count overlapping trains to find max platforms

   At 950, trains at 900, 940, 950 overlap (3 trains). Later overlaps are fewer.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   Max overlap = 3 platforms [OK]

Hint: Find max overlapping intervals for minimum platforms [OK]

Common Mistakes:

• Not sorting times before counting overlaps
• Counting total trains instead of overlaps
• Mixing arrival and departure arrays

4. Identify the error in this C# code snippet for calculating minimum platforms:

int[] arrival = {900, 940, 950};
int[] departure = {910, 1200, 1120};

Array.Sort(arrival);
Array.Sort(departure);

int i = 0, j = 0, platforms = 0, maxPlatforms = 0;
while (i < arrival.Length && j < departure.Length) {
    if (arrival[i] <= departure[j]) {
        platforms++;
        i++;
    } else {
        platforms--;
        j++;
    }
    maxPlatforms = Math.Max(maxPlatforms, platforms);
}
Console.WriteLine(maxPlatforms);

medium

A. The comparison should be 'arrival[i] < departure[j]' instead of '<='

B. The loop condition should be 'i < arrival.Length || j < departure.Length'

C. The arrays should not be sorted before processing

D. The platforms variable should not be incremented

Solution

1. Step 1: Analyze the comparison operator in the loop

   Using '<=' causes counting a train as arriving exactly when another departs, increasing platforms unnecessarily.

2. Step 2: Correct comparison to '<' to avoid overlap at exact departure time

   Changing to '<' means a train arriving at the same time another departs does not increase platform count.

3. Final Answer:

   The comparison should be 'arrival[i] < departure[j]' instead of '<=' -> Option A

4. Quick Check:

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

Hint: Use '<' not '<=' when comparing arrival and departure [OK]

Common Mistakes:

• Using '<=' causes overcounting platforms
• Not sorting arrays before processing
• Incorrect loop condition causing missed trains

5. Given arrival times [900, 940, 950, 1100, 1500, 1800] and departure times [910, 1200, 1120, 1130, 1900, 2000], how would you modify the algorithm to also return the time intervals when the maximum number of platforms are needed?

hard

A. Track intervals when platform count equals max during iteration and store them

B. Return only the maximum platform count without intervals

C. Sort only arrival times and ignore departure times

D. Count total trains without checking overlaps

Solution

1. Step 1: Modify algorithm to track platform count changes

   While iterating, record start time when platforms reach max and end time when count drops.

2. Step 2: Store intervals where platform count equals maximum

   Keep a list of intervals with max platforms to return after processing all times.

3. Final Answer:

   Track intervals when platform count equals max during iteration and store them -> Option A

4. Quick Check:

   Record max platform intervals during count updates [OK]

Hint: Save start/end times when platform count hits max [OK]

Common Mistakes:

• Ignoring time intervals, returning only counts
• Not updating intervals when platform count changes
• Sorting only one array causing wrong intervals