Activity Selection Problem in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to sort activities by their finish time.

DSA Python

activities.sort(key=lambda x: x[[1]])

Drag options to blanks, or click blank then click option'

A1

B0

C2

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Sorting by start time instead of finish time.

Using wrong index like 0 or 2.

We sort activities by their finish time, which is at index 1 in each activity tuple.

2fill in blank

medium

Complete the code to select the first activity after sorting.

DSA Python

selected = [activities[[1]]]

Drag options to blanks, or click blank then click option'

A1

B0

C-1

Dlen(activities)

Attempts:

3 left

💡 Hint

Common Mistakes

Using index 1 which is the second activity.

Using negative or out of range indices.

The first activity after sorting is at index 0.

3fill in blank

hard

Fix the error in the loop condition to check if the next activity can be selected.

DSA Python

for i in range(1, len(activities)):
    if activities[i][[1]] >= activities[last_selected][1]:
        selected.append(activities[i])
        last_selected = i

Drag options to blanks, or click blank then click option'

A-1

B2

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Comparing finish time with finish time.

Using wrong indices like 1 or 2.

We compare the start time (index 0) of the current activity with the finish time of the last selected activity.

4fill in blank

hard

Complete the code to create a dictionary of selected activities with start time as key and finish time as value.

DSA Python

result = {: {BLANK_2}} for start, finish in selected

Drag options to blanks, or click blank then click option'

Astart

Bfinish

C{

D}

Attempts:

3 left

💡 Hint

Common Mistakes

Using square brackets instead of curly braces.

Swapping start and finish in keys and values.

We create a dictionary comprehension with curly braces and use finish as the value.

5fill in blank

hard

Fill all three blanks to print the selected activities in order with format 'start -> finish'.

DSA Python

for start, finish in selected:
    print(str(start) + [1] + str(finish) + [2])
print([3])

Drag options to blanks, or click blank then click option'

A ' -> '

B ' -> '

C '\n'

D''

Attempts:

3 left

💡 Hint

Common Mistakes

Forgetting spaces around arrow.

Printing newline inside loop causing extra blank lines.

We join start and finish with ' -> ' and print without extra newline, then print a newline separately.

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 times

D. Calculate the total duration of all activities

Solution

1. Step 1: Understand the problem goal

   The Activity Selection Problem aims to choose the largest set of activities that do not overlap in their time intervals.

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 non-overlapping activities [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 is the correct Python syntax to sort a list of activities by their finish times stored as tuples (start, finish)?

easy

A. activities.sort(key=lambda x: x[0])

B. activities.sort(key=lambda x: x[1])

C. activities.sort(reverse=True)

D. activities.sort(key=lambda x: x[0], reverse=True)

Solution

1. Step 1: Identify sorting key for finish times

   Finish time is the second element in the tuple, so index 1 is used as the key.

2. Step 2: Choose correct sort syntax

   Using activities.sort(key=lambda x: x[1]) sorts by finish time ascending, which is required.

3. Final Answer:

   activities.sort(key=lambda x: x[1]) -> Option B

4. Quick Check:

   Sort by finish time = key index 1 [OK]

Hint: Sort by finish time using key=lambda x: x[1] [OK]

Common Mistakes:

• Sorting by start time instead of finish time
• Using reverse sort without reason
• Incorrect lambda index for key

3. What is the output of the following code?

activities = [(1, 4), (3, 5), (0, 6), (5, 7), (8, 9), (5, 9)]
activities.sort(key=lambda x: x[1])
selected = []
last_finish = 0
for start, finish in activities:
    if start >= last_finish:
        selected.append((start, finish))
        last_finish = finish
print(selected)

medium

A. [(1, 4), (3, 5), (5, 7), (8, 9)]

B. [(0, 6), (8, 9)]

C. [(1, 4), (5, 7), (8, 9)]

D. [(1, 4), (5, 9)]

Solution

1. Step 1: Sort activities by finish time

   Sorted list: [(1,4), (3,5), (0,6), (5,7), (8,9), (5,9)]

2. Step 2: Select activities greedily

   Start with last_finish=0
   - (1,4): start=1 >=0, select, last_finish=4
   - (3,5): start=3 <4, skip
   - (0,6): start=0 <4, skip
   - (5,7): start=5 >=4, select, last_finish=7
   - (8,9): start=8 >=7, select, last_finish=9
   - (5,9): start=5 <9, skip

3. Final Answer:

   [(1, 4), (5, 7), (8, 9)] -> Option C

4. Quick Check:

   Greedy selection = [(1,4),(5,7),(8,9)] [OK]

Hint: Pick earliest finishing activities first [OK]

Common Mistakes:

• Selecting overlapping activities
• Not updating last_finish correctly
• Sorting incorrectly

4. Find the error in this code snippet for the Activity Selection Problem:

activities = [(1, 4), (4, 5), (2, 6)]
activities.sort(key=lambda x: x[1])
selected = []
last_finish = 0
for start, finish in activities:
    if start > last_finish:
        selected.append((start, finish))
        last_finish = finish
print(selected)

medium

A. Using 'start > last_finish' instead of 'start >= last_finish'

B. Missing parentheses in print statement

C. Not initializing selected list

D. Sorting by start time instead of finish time

Solution

1. Step 1: Check sorting key

   Correctly sorts activities by finish time (second element, index 1).

2. Step 2: Check condition in if statement

   Condition uses 'start > last_finish' which excludes activities starting exactly at last_finish time, missing valid selections. It should be 'start >= last_finish'.

3. Final Answer:

   Using 'start > last_finish' instead of 'start >= last_finish' -> Option A

4. Quick Check:

   Condition must allow equal start time [OK]

Hint: Use >= to allow back-to-back activities [OK]

Common Mistakes:

• Using > excludes valid activities
• Sorting by start time only
• Forgetting to update last_finish

5. Given activities with start and finish times:
[(1, 2), (3, 4), (0, 6), (5, 7), (8, 9), (5, 9)]
How many activities can be selected to maximize the count without overlap, and which are they?

hard

A. 2 activities: (0, 6), (8, 9)

B. 3 activities: (0, 6), (5, 7), (8, 9)

C. 5 activities: (1, 2), (3, 4), (5, 7), (8, 9), (5, 9)

D. 4 activities: (1, 2), (3, 4), (5, 7), (8, 9)

Solution

1. Step 1: Sort activities by finish time

   Sorted list: [(1,2), (3,4), (0,6), (5,7), (8,9), (5,9)]

2. Step 2: Select activities greedily

   Start last_finish=0
   - (1,2): start=1 >=0, select, last_finish=2
   - (3,4): start=3 >=2, select, last_finish=4
   - (0,6): start=0 <4, skip
   - (5,7): start=5 >=4, select, last_finish=7
   - (8,9): start=8 >=7, select, last_finish=9
   - (5,9): start=5 <9, skip
   Total selected = 4 activities

3. Final Answer:

   4 activities: (1, 2), (3, 4), (5, 7), (8, 9) -> Option D

4. Quick Check:

   Max count = 4 selected activities [OK]

Hint: Sort by finish time, pick earliest finishing activities [OK]

Common Mistakes:

• Including overlapping activities
• Counting all activities without checking overlap
• Choosing activities with longer duration instead of earliest finish