Activity Selection Problem in DSA Typescript - 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

↓

Select activity

↓

Repeat

↓

Done

Sort activities by finish time, then pick the earliest finishing activity that doesn't overlap with previously selected ones.

Execution Sample

DSA Typescript

interface Activity {
  start: number;
  finish: number;
}

function selectActivities(activities: Activity[]): Activity[] {
  activities.sort((a, b) => a.finish - b.finish);
  const selected: Activity[] = [];
  let lastFinish = 0;
  for (const act of activities) {
    if (act.start >= lastFinish) {
      selected.push(act);
      lastFinish = act.finish;
    }
  }
  return selected;
}

This code sorts activities by finish time and selects the maximum number of non-overlapping activities.

Execution Table

Step	Operation	Current Activity (start, finish)	Last Selected Finish	Selected Activities	Action	Visual State
1	Sort activities by finish time	-	-	[]	Sorted activities	[ (1,4), (3,5), (0,6), (5,7), (8,9), (5,9) ]
2	Select first activity	(1,4)	0	[]	Select (1,4)	[(1,4)]
3	Check next activity	(3,5)	4	[(1,4)]	Skip (3,5) because 3 < 4	[(1,4)]
4	Check next activity	(0,6)	4	[(1,4)]	Skip (0,6) because 0 < 4	[(1,4)]
5	Check next activity	(5,7)	4	[(1,4)]	Select (5,7) because 5 >= 4	[(1,4), (5,7)]
6	Check next activity	(8,9)	7	[(1,4), (5,7)]	Select (8,9) because 8 >= 7	[(1,4), (5,7), (8,9)]
7	Check next activity	(5,9)	9	[(1,4), (5,7), (8,9)]	Skip (5,9) because 5 < 9	[(1,4), (5,7), (8,9)]
8	End of activities	-	9	[(1,4), (5,7), (8,9)]	Done selecting	[(1,4), (5,7), (8,9)]

💡 All activities checked; selection complete.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	Final
lastFinish	0	4	4	4	7	9	9	9
selected	[]	[(1,4)]	[(1,4)]	[(1,4)]	[(1,4), (5,7)]	[(1,4), (5,7), (8,9)]	[(1,4), (5,7), (8,9)]	[(1,4), (5,7), (8,9)]
currentActivity	-	(1,4)	(3,5)	(0,6)	(5,7)	(8,9)	(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 up time earliest, allowing more activities to fit later. See Step 1 in execution_table where activities are sorted.

Why do we skip activities that start before the last selected activity finishes?

Because they overlap and can't be done together. For example, at Step 3 and 4, activities starting before lastFinish are skipped to avoid overlap.

Why do we update lastFinish only when we select an activity?

Because lastFinish marks the end time of the last chosen activity, helping to check overlap for future activities. See variable_tracker for lastFinish updates after selection steps.

Visual Quiz - 3 Questions

Look at the execution_table at Step 5, what is the lastFinish value after selecting activity (5,7)?

A 4

B 7

C 5

D 9

💡 Hint

Check the 'Last Selected Finish' column at Step 5 in execution_table.

At which step does the condition 'act.start >= lastFinish' become false for the first time?

A Step 3

B Step 2

C Step 5

D Step 6

💡 Hint

Look at the 'Action' column in execution_table where activities are skipped due to overlap.

If the activity (3,5) was changed to (4,5), how would the selection change at Step 3?

A It would cause an error

B It would still be skipped

C It would be selected instead of skipped

D It would be selected but lastFinish would not update

💡 Hint

Compare 'currentActivity' start time with 'lastFinish' at Step 3 in variable_tracker.

Concept Snapshot

Activity Selection Problem:
- Sort activities by finish time
- Select first activity
- For each next activity, select if start >= last selected finish
- Update last selected finish time
- Result: maximum set of non-overlapping activities

Full Transcript

The Activity Selection Problem involves choosing the maximum number of activities that don't overlap. We start by sorting activities by their finish times. Then, we pick the first activity and keep track of its finish time. For each next activity, if its start time is equal or after the last selected finish time, we select it and update the finish time. Otherwise, we skip it. This process continues until all activities are checked. The final selected list contains the maximum number of compatible activities.