Activity Selection Problem using Greedy Algorithm in C++

There are n different activities are given with their starting time and ending time. Select maximum number of activities to solve by a single person.

We will use the greedy approach to find the next activity whose finish time is minimum among rest activities, and the start time is more than or equal with the finish time of the last selected activity.

• The complexity of this problem is O(n log n) when the list is not sorted. When the sorted list is provided the complexity will be O(n).

Input

A list of different activities with starting and ending times.

{(5,9), (1,2), (3,4), (0,6), (5,7), (8,9)}

Output

Selected Activities are −

Activity: 0 , Start: 1 End: 2
Activity: 1 , Start: 3 End: 4
Activity: 3 , Start: 5 End: 7
Activity: 5 , Start: 8 End: 9

Algorithm

maxActivity(act, size)

Input - A list of activity, and the number of elements in the list.
Output - The order of activities how the have been chosen.

Begin
   initially sort the given activity List
   set i := 1
   display the i-th activity //in this case it is the first activity
   for j := 1 to n-1 do
      if start time of act[j] >= end of act[i] then
         display the jth activity
         i := j
   done
End

Example

 Live Demo

#include<iostream>
#include<algorithm>
using namespace std;
   struct Activitiy {
      int start, end;
   };
   bool comp(Activitiy act1, Activitiy act2) {
      return (act1.end < act2.end);
   }
   void maxActivity(Activitiy act[], int n) {
   sort(act, act+n, comp); //sort activities using compare function
   cout << "Selected Activities are: " << endl;
   int i = 0;// first activity as 0 is selected
   cout << "Activity: " << i << " , Start: " <<act[i].start << " End: " << act[i].end <<endl;
   for (int j = 1; j < n; j++) { //for all other activities
      if (act[j].start >= act[i].end) { //when start time is >=end time, print the activity
         cout << "Activity: " << j << " , Start: " <<act[j].start << " End: " << act[j].end <<endl;
         i = j;
      }
   }
}
int main() {
   Activitiy actArr[] = {{5,9},{1,2},{3,4},{0,6},{5,7},{8,9}};
   int n = 6;
   maxActivity(actArr,n);
   return 0;
}

Output

Selected Activities are:
Activity: 0 , Start: 1 End: 2
Activity: 1 , Start: 3 End: 4
Activity: 3 , Start: 5 End: 7
Activity: 5 , Start: 8 End: 9