Minimum Number of Platforms in DSA Typescript - 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

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

Sorting helps to process events in chronological order, making it easier to track how many trains are at the station at the same time.

beginner

What does the variable 'platforms_needed' represent during the algorithm?

'platforms_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 arrives or departs?

When a train arrives, increment 'platforms_needed'. When a train departs, decrement 'platforms_needed'.

beginner

What is the final answer in the Minimum Number of Platforms problem?

The maximum value of 'platforms_needed' during the process is the minimum number of platforms required.

Why do we need to sort arrival and departure times separately?

A To find the longest train

B To group trains by their platform

C To process events in chronological order

D To count total trains

Sorting arrival and departure times separately allows us to process train events in order of time.

What does an increase in 'platforms_needed' signify?

A A train has departed

B No change

C A platform is freed

D A train has arrived

When a train arrives, 'platforms_needed' increases because one more platform is occupied.

If arrival[i] > departure[j], what should we do in the algorithm?

A Increment platforms_needed

B Decrement platforms_needed

C Do nothing

D Reset platforms_needed

If a train departs before the next arrives, we free a platform by decrementing 'platforms_needed'.

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

A O(n log n)

B O(n^2)

C O(n)

D O(log n)

Sorting takes O(n log n), and the traversal is O(n), so overall O(n log n).

What does the maximum value of 'platforms_needed' represent?

A Minimum platforms required

B Total trains

C Maximum waiting time

D Number of trains departed

The maximum 'platforms_needed' is the minimum number of platforms needed to avoid waiting.

Explain the step-by-step approach to find the minimum number of platforms needed for trains.

Think about processing train events in order of time.

Why is sorting both arrival and departure times separately important in this problem?

Consider how to know when a platform frees up before next train arrives.

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 on the platform

B. The total number of trains arriving in a day

C. The maximum speed of trains on the platform

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

Solution

1. Step 1: Understand the problem goal

   The problem asks for the minimum number of platforms required so that no train has to wait for another to leave.

2. Step 2: Clarify what is being counted

   We count overlapping train schedules to find the peak number of trains at the station simultaneously.

3. Final Answer:

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

4. Quick Check:

   Minimum platforms = max trains overlapping [OK]

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

Common Mistakes:

• Confusing total trains with platforms needed
• Ignoring overlapping times
• Counting total arrival or departure times only

2. Which of the following TypeScript code snippets correctly sorts an array of train arrival times stored as numbers?

easy

A. arrivals.sort();

B. arrivals.sort((a, b) => a - b);

C. arrivals.sort((a, b) => b - a);

D. arrivals.sort((a, b) => a + b);

Solution

1. Step 1: Understand sorting numbers in TypeScript

   Default sort() treats elements as strings, so numeric sort needs a compare function.

2. Step 2: Identify correct compare function

   The function (a, b) => a - b sorts numbers in ascending order correctly.

3. Final Answer:

   arrivals.sort((a, b) => a - b); -> Option B

4. Quick Check:

   Numeric ascending sort uses (a, b) => a - b [OK]

Hint: Use (a, b) => a - b to sort numbers ascending [OK]

Common Mistakes:

• Using sort() without compare function for numbers
• Using (a, b) => a + b which is invalid
• Sorting descending when ascending needed

3. Given arrival times [900, 940, 950, 1100, 1500, 1800] and departure times [910, 1200, 1120, 1130, 1900, 2000], what is the minimum number of platforms needed?

medium

A. 2

B. 3

C. 4

D. 5

Solution

1. Step 1: Sort arrival and departure times

   Arrivals: 900, 940, 950, 1100, 1500, 1800; Departures: 910, 1120, 1130, 1200, 1900, 2000.

2. Step 2: Count platforms needed by comparing arrivals and departures

   At 900 arrive (1 platform), 910 depart (0), 940 arrive (1), 950 arrive (2), 1100 arrive (3), 1120 depart (2), 1130 depart (1), 1200 depart (0), 1500 arrive (1), 1800 arrive (2), 1900 depart (1), 2000 depart (0). Maximum platforms needed is 4.

3. Final Answer:

   4 -> Option C

4. Quick Check:

   Max overlapping trains = 4 [OK]

Hint: Track arrivals and departures to find max overlap [OK]

Common Mistakes:

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

4. The following TypeScript code tries to find the minimum number of platforms but has a bug. What is the bug?

function findPlatforms(arrivals: number[], departures: number[]): number {
  arrivals.sort((a, b) => a - b);
  departures.sort((a, b) => a - b);
  let platformNeeded = 1, maxPlatforms = 1;
  let i = 1, j = 0;
  while (i < arrivals.length && j < departures.length) {
    if (arrivals[i] <= departures[j]) {
      platformNeeded++;
      i++;
    } else {
      platformNeeded--;
      j++;
    }
    if (platformNeeded > maxPlatforms) maxPlatforms = platformNeeded;
  }
  return maxPlatforms;
}

medium

A. Start i from 0 instead of 1 to include first arrival

B. Use < instead of <= in comparison to avoid counting overlaps wrongly

C. Initialize platformNeeded to 0 instead of 1

D. Sort arrivals and departures in descending order

Solution

1. Step 1: Analyze loop initialization

   Variable i starts at 1, skipping the first arrival time, which causes missing counting the first train.

2. Step 2: Correct initialization for accurate counting

   Starting i at 0 ensures all arrivals are considered, giving correct platform count.

3. Final Answer:

   Start i from 0 instead of 1 to include first arrival -> Option A

4. Quick Check:

   Include all arrivals by starting i=0 [OK]

Hint: Start pointers at 0 to include all trains [OK]

Common Mistakes:

• Skipping first arrival by starting i at 1
• Changing comparison operator incorrectly
• Initializing platformNeeded wrongly

5. You have trains arriving and departing as follows: Arrivals: [1000, 1010, 1025, 1030, 1040] Departures: [1015, 1020, 1035, 1045, 1050] If you want to minimize the number of platforms by rescheduling trains without changing their arrival order, which train's departure time should you delay to reduce platform count?

hard

A. Delay the departure of train arriving at 1010

B. Delay the departure of train arriving at 1000

C. Delay the departure of train arriving at 1040

D. Delay the departure of train arriving at 1025

Solution

1. Step 1: Identify overlapping trains causing max platforms

   Trains at 1010 and 1025 overlap because 1010 departs at 1020 and 1025 arrives before that.

2. Step 2: Delay departure of train at 1010 to after 1025 departs

   Delaying 1010's departure reduces overlap with 1025, lowering platform need.

3. Final Answer:

   Delay the departure of train arriving at 1010 -> Option A

4. Quick Check:

   Delay overlapping train's departure to reduce platforms [OK]

Hint: Delay departure of earliest overlapping train to reduce platforms [OK]

Common Mistakes:

• Delaying wrong train's departure
• Changing arrival order which is fixed
• Ignoring overlap timing details