Activity Selection Problem in DSA C - Execution Trace

Concept Flow - Activity Selection Problem

Sort activities by finish time

↓

Select first activity

↓

For each next activity

↓

Check if start >= last selected finish?

No→Skip activity

Yes↓

Select activity

↓

Repeat until all activities checked

↓

Return selected activities

Sort activities by finish time, then pick the earliest finishing compatible activities one by one.

Execution Sample

DSA C

activities = [(1,4),(3,5),(0,6),(5,7),(8,9),(5,9)];
// Sort by finish time
activities.sort(key=lambda x: x[1])
selected = [activities[0]]
last_finish = activities[0][1]
for i in range(1, len(activities)):
    if activities[i][0] >= last_finish:
        selected.append(activities[i])
        last_finish = activities[i][1]

Select maximum number of non-overlapping activities by sorting and greedy selection.

Execution Table

Step	Operation	Current Activity (start, finish)	Last Selected Finish	Selected Activities	Action
1	Sort activities by finish time	-	-	[]	Original: [(1,4),(3,5),(0,6),(5,7),(8,9),(5,9)] sorted by finish time: [(1,4),(3,5),(0,6),(5,7),(8,9),(5,9)]
2	Select first activity	(1,4)	-	[(1,4)]	Select first activity (1,4)
3	Check next activity	(3,5)	4	[(1,4)]	3 < 4? No, skip (3,5)
4	Check next activity	(0,6)	4	[(1,4)]	0 < 4? No, skip (0,6)
5	Check next activity	(5,7)	4	[(1,4)]	5 >= 4? Yes, select (5,7)
6	Check next activity	(8,9)	7	[(1,4),(5,7)]	8 >= 7? Yes, select (8,9)
7	Check next activity	(5,9)	9	[(1,4),(5,7),(8,9)]	5 >= 9? No, skip (5,9)
8	End	-	9	[(1,4),(5,7),(8,9)]	All activities checked

💡 All activities checked, selection complete.

Variable Tracker

Variable	Start	After Step 2	After Step 5	After Step 7	Final
Selected Activities	[]	[(1,4)]	[(1,4),(5,7)]	[(1,4),(5,7),(8,9)]	[(1,4),(5,7),(8,9)]
Last Selected Finish	-	4	7	9	9
Current Activity	-	(1,4)	(5,7)	(5,9)	-

Key Moments - 3 Insights

Why do we sort activities by their finish time first?

Sorting by finish time ensures we always pick the activity that frees the schedule earliest, allowing more activities to fit later. See Step 1 in execution_table.

Why do we compare the start time of the current activity with the finish time of the last selected activity?

To avoid overlapping activities, we only select the current activity if it starts after or exactly when the last selected one finishes. See Steps 3, 5, 6, and 7.

Why do we always select the first activity after sorting?

Because the first activity finishes earliest, selecting it maximizes room for others. This is shown in Step 2.

Visual Quiz - 3 Questions

Look at the execution_table, what is the selected activities list after Step 5?

A [(1,4),(3,5)]

B [(1,4)]

C [(1,4),(5,7)]

D [(5,7)]

💡 Hint

Check the 'Selected Activities' column at Step 5 in execution_table.

At which step does the condition 'start >= last finish' become false for the activity (5,9)?

A Step 4

B Step 7

C Step 6

D Step 3

💡 Hint

Look at Step 7 in execution_table under 'Action' and 'Current Activity'.

If the activity (5,7) was removed, what would be the selected activities after Step 7?

A [(1,4),(8,9)]

B [(1,4),(5,9),(8,9)]

C [(1,4),(5,9)]

D [(3,5),(8,9)]

💡 Hint

Without (5,7), the next compatible activity after (1,4) is (8,9). Check variable_tracker for selected activities.

Concept Snapshot

Activity Selection Problem:
- Sort activities by finish time
- Select first activity
- For each next activity, select if start >= last selected finish
- Repeat until all checked
- Result: max non-overlapping activities

Full Transcript

The Activity Selection Problem finds the maximum number of activities that don't overlap. First, we sort activities by their finish times. Then, we pick the first activity because it finishes earliest. Next, for each activity, we check if its start time is at or after the finish time of the last selected activity. If yes, we select it; if no, we skip it. We repeat this until all activities are checked. The selected activities form the largest set of non-overlapping activities.