Occurrences

Your task is to implement a class that maintains a list of numbers and has a method that reports how many distinct occurrence counts the numbers on the list have. The occurrence count of a number tells how many times that number occurs on the list.

For example, the list $[1,2,3,1,2,3]$ has just one occurrence count because each number occurs twice on the list. The list $[1,2,2,3,3,3]$ has three occurrence counts, because the number $1$ occurs once, the number $2$ occurs twice and the number $3$ occurs three times.

In a file occurrences.py, implement the class OccurrenceTracker with the following methods:

• append(number): add number to the end of the list
• count(): return the number of distinct occurrence counts

Both methods should work in $O(1)$ time.

class OccurrenceTracker:
    def __init__(self):
        # TODO

    def append(self, number):
        # TODO

    def count(self):
        # TODO

if __name__ == "__main__":
    tracker = OccurrenceTracker()

    tracker.append(1)
    tracker.append(2)
    tracker.append(1)
    tracker.append(3)
    print(tracker.count()) # 2

    tracker.append(2)
    tracker.append(3)
    print(tracker.count()) # 1

    tracker.append(2)
    tracker.append(3)
    tracker.append(3)
    print(tracker.count()) # 3

You can test the efficiency of your solution with the following code. In this case too the code should finish almost immediately.

    tracker = OccurrenceTracker()
    total = 0
    for i in range(10**5):
        tracker.append(i % 100 + 1)
        total += tracker.count()
    print(total) # 198901