Activity Selection Problem in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of the Activity Selection Problem?

To select the maximum number of activities that don't overlap in time from a given set of activities, each with a start and finish time.

beginner

Which algorithmic approach is commonly used to solve the Activity Selection Problem efficiently?

The greedy algorithm approach, which selects activities based on earliest finish time to maximize the number of non-overlapping activities.

intermediate

Why do we sort activities by their finish times in the Activity Selection Problem?

Sorting by finish times ensures that when we pick an activity, we leave as much room as possible for the remaining activities, maximizing the total count.

intermediate

In the Activity Selection Problem, after selecting an activity, what is the next step?

Skip all activities that start before the selected activity finishes, then select the next activity that starts after the current one finishes.

intermediate

What is the time complexity of the greedy solution to the Activity Selection Problem after sorting?

O(n log n) due to sorting the activities by finish time, where n is the number of activities. The selection process itself is O(n).

What is the first step in solving the Activity Selection Problem using a greedy approach?

A Sort activities by their start times

B Sort activities by their finish times

C Select the longest activity first

D Select activities randomly

Sorting activities by their finish times allows the greedy algorithm to pick the earliest finishing activity first, maximizing the number of activities selected.

After selecting an activity, which activities are skipped in the Activity Selection Problem?

A Activities that start before the selected activity finishes

B Activities that finish before the selected activity starts

C All activities with the same start time

D Activities with the longest duration

We skip activities that start before the current selected activity finishes to avoid overlapping.

What does the Activity Selection Problem aim to maximize?

A Sum of start times

B Total duration of selected activities

C Number of non-overlapping activities selected

D Number of overlapping activities

The goal is to select the maximum number of activities that do not overlap.

Which data structure is most commonly used to store activities for the Activity Selection Problem?

A Queue

B Stack

C Binary tree

D Array or list of pairs (start, finish)

Activities are usually stored as pairs of start and finish times in an array or list.

What is the time complexity of selecting activities after sorting in the Activity Selection Problem?

A O(n)

B O(n^2)

C O(log n)

D O(n log n)

After sorting, selecting activities is done in a single pass, which takes O(n) time.

Explain the greedy approach to solve the Activity Selection Problem step-by-step.

Think about how choosing the earliest finishing activity helps.

Describe why sorting by finish time is crucial in the Activity Selection Problem.

Consider how finish times affect the possibility of selecting more activities.

Practice

1. What is the main goal of the Activity Selection Problem?

easy

A. Select the maximum number of activities that don't overlap in time

B. Find the activity with the longest duration

C. Sort activities by their start time

D. Calculate the total duration of all activities

Solution

1. Step 1: Understand the problem goal

   The Activity Selection Problem aims to choose activities that do not overlap and maximize the count.

2. Step 2: Identify the correct goal

   Among the options, only selecting the maximum number of non-overlapping activities matches the problem's goal.

3. Final Answer:

   Select the maximum number of activities that don't overlap in time -> Option A

4. Quick Check:

   Goal = Max non-overlapping activities [OK]

Hint: Focus on maximizing count without time conflicts [OK]

Common Mistakes:

• Confusing longest duration with maximum count
• Sorting by start time only
• Summing durations instead of counting activities

2. Which of the following C# code snippets correctly sorts activities by their finish time for the Activity Selection Problem?

easy

A. activities.Sort((a, b) => a.Start.CompareTo(b.Start));

B. activities.Sort((a, b) => a.Finish.CompareTo(b.Finish));

C. activities.OrderBy(a => a.Duration);

D. activities.OrderByDescending(a => a.Start);

Solution

1. Step 1: Identify sorting criteria for Activity Selection

   The greedy approach requires sorting activities by their finish time in ascending order.

2. Step 2: Match code with sorting by finish time

   activities.Sort((a, b) => a.Finish.CompareTo(b.Finish)); uses Sort with finish time comparison, which is correct.

3. Final Answer:

   activities.Sort((a, b) => a.Finish.CompareTo(b.Finish)); -> Option B

4. Quick Check:

   Sort by finish time = activities.Sort((a, b) => a.Finish.CompareTo(b.Finish)); [OK]

Hint: Sort activities by finish time ascending [OK]

Common Mistakes:

• Sorting by start time instead of finish time
• Using OrderBy without assignment
• Sorting descending instead of ascending

3. Given the following activities with start and finish times:
var activities = new List<Activity> { new Activity(1, 4), new Activity(3, 5), new Activity(0, 6), new Activity(5, 7), new Activity(8, 9) };
What is the maximum number of non-overlapping activities selected by the greedy algorithm?

medium

A. 5

B. 4

C. 2

D. 3

Solution

1. Step 1: Sort activities by finish time

   Sorted activities by finish time: (1,4), (3,5), (0,6), (5,7), (8,9)

2. Step 2: Select activities greedily

   Select (1,4) first, skip (3,5) and (0,6) because they overlap, select (5,7), then (8,9). Total selected = 3.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   Max non-overlapping = 3 [OK]

Hint: Pick earliest finishing activities first [OK]

Common Mistakes:

• Counting overlapping activities
• Not sorting by finish time
• Selecting activities by start time only

4. Consider this buggy C# code for Activity Selection:

activities.Sort((a, b) => a.Start.CompareTo(b.Start));
var selected = new List<Activity>();
selected.Add(activities[0]);
foreach(var act in activities) {
  if(act.Start >= selected.Last().Finish) {
    selected.Add(act);
  }
}

What is the main error causing incorrect results?

medium

A. Looping over activities incorrectly

B. Using >= instead of > in condition

C. Sorting by start time instead of finish time

D. Not initializing selected list before adding

Solution

1. Step 1: Check sorting criteria

   The code sorts activities by start time, but greedy algorithm requires sorting by finish time.

2. Step 2: Understand impact of wrong sorting

   Sorting by start time can select overlapping activities, causing incorrect results.

3. Final Answer:

   Sorting by start time instead of finish time -> Option C

4. Quick Check:

   Sort by finish time needed, not start time [OK]

Hint: Always sort by finish time for correct selection [OK]

Common Mistakes:

• Sorting by start time
• Confusing condition operators
• Forgetting to add first activity

5. You have activities with start and finish times:
[(1,3), (2,5), (4,7), (6,9), (8,10), (9,11)]
Using the Activity Selection Problem approach, which set of activities maximizes the number of non-overlapping activities?

hard

A. [(1,3), (4,7), (8,10)]

B. [(1,3), (4,7), (6,9), (9,11)]

C. [(1,3), (6,9), (9,11)]

D. [(2,5), (6,9), (9,11)]

Solution

1. Step 1: Sort activities by finish time

   Sorted by finish time: (1,3), (2,5), (4,7), (6,9), (8,10), (9,11)

2. Step 2: Select activities greedily

   Select (1,3), skip (2,5) because it overlaps with (1,3), select (4,7) (4 >= 3), select (6,9) overlaps with (4,7)? No, 6 < 7 so skip (6,9), select (8,10) (8 >= 7), select (9,11) overlaps with (8,10)? 9 < 10 so skip (9,11). But this conflicts with options, so let's re-check carefully.

3. Step 2 corrected:

   Select (1,3), skip (2,5), select (4,7), skip (6,9) (6 < 7), select (8,10), skip (9,11) (9 < 10). Total 3 activities: (1,3), (4,7), (8,10).

4. Step 3: Verify options

   [(1,3), (4,7), (8,10)] matches the selected activities: [(1,3), (4,7), (8,10)].

5. Final Answer:

   [(1,3), (4,7), (8,10)] -> Option A

6. Quick Check:

   Greedy selection = [(1,3), (4,7), (8,10)] [OK]

Hint: Pick earliest finishing compatible activities stepwise [OK]

Common Mistakes:

• Choosing overlapping activities
• Ignoring sorting by finish time
• Selecting more activities that overlap