Interval partitioning problem : Greedy algorithm – Algorithms and Me


Interval partitioning problem : Greedy algorithm – Algorithms and Me
There are n lectures to be schedules and there are certain classrooms. Each lecture has a start time si and finish time fi. Task is to schedule all lectures in minimum number of classes and there cannot be more than one lecture in a classroom at a given time.

1. Sort all lectures based on start time in ascending order.
2. Number of initial classrooms = 0
3. While lecture to be scheduled:
   3.1 Take first lecture yet not scheduled,
   3.2 If there a already a class available for lecture's start time
       Assign lecture to the class.
   3.3 If not, then allocate a new classroom
       number of classroom = number of classroom + 1
4. Return number of classrooms.
    1. from PriorityQueue import PriorityQueue
    2. from Classroom import Classroom
    3.  
    4. jobs = [(1, 930, 1100), (2, 930, 1300), (3, 930, 1100), (5, 1100, 1400),(4, 1130, 1300), (6, 1330, 1500), (7, 1330, 1500), (8,1430,1700), (9, 1530, 1700), (10, 1530, 1700)]
    5.  
    6. def find_num_classrooms():
    7. num_classrooms = 0;
    8. priority_queue = PriorityQueue()
    9.  
    10. for job in jobs:
    11. # we have job here, now pop the classroom with least finishing time
    12. classroom = priority_queue.pop();
    13. if(classroom == None) :
    14. #allocate a new class
    15. num_classrooms+= 1;
    16. priority_queue.push(Classroom(num_classrooms,job[2]),job[2]);
    17. else:
    18. #check if finish time of current classroom is
    19. #less than start time of this lecture
    20. if(classroom.finish_time <= job[1]):
    21. classroom.finish_time = job[2]
    22. priority_queue.push(classroom,job[2])
    23. else:
    24. num_classrooms+= 1;
    25. #Since last classroom needs to be compared again, push it back
    26. priority_queue.push(classroom,job[2])
    27. #Push the new classroom in list
    28. priority_queue.push(Classroom(num_classrooms,job[2]),job[2])
    29.  
    30. return num_classrooms
    31.  
    32. print "Number of classrooms required: " + find_num_classrooms();

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