My calendar III

Time: O(N^2); Space: O(N); hard

Implement a MyCalendarThree class to store your events. A new event can always be added. Your class will have one method, book(int start, int end). Formally, this represents a booking on the half open interval [start, end), the range of real numbers x such that start <= x < end. A K-booking happens when K events have some non-empty intersection (ie., there is some time that is common to all K events.) For each call to the method MyCalendar.book, return an integer K representing the largest integer such that there exists a K-booking in the calendar.

Your class will be called like this: cal = new MyCalendarThree() cal.book(start, end)

Example 1:

Input/Output:

cal = MyCalendarThree(); cal.book(10, 20) # returns 1 cal.book(50, 60) # returns 1 cal.book(10, 40) # returns 2 cal.book(5, 15) # returns 3 cal.book(5, 10) # returns 3 cal.book(25, 55) # returns 3 Explanation:

  • The first two events can be booked and are disjoint, so the maximum K-booking is a 1-booking.

  • The third event [10, 40) intersects the first event, and the maximum K-booking is a 2-booking.

  • The remaining events cause the maximum K-booking to be only a 3-booking.

  • Note that the last event locally causes a 2-booking, but the answer is still 3 because eg. [10, 20), [10, 40), and [5, 15) are still triple booked.

Notes:

  • The number of calls to MyCalendarThree.book per test case will be at most 400.

  • In calls to MyCalendarThree.book(start, end), start and end are integers in the range [0, 10^9].

[2]:

import bisect

class MyCalendarThree(object):

    def __init__(self):
        self.__books = []

    def book(self, start, end):
        """
        :type start: int
        :type end: int
        :rtype: int
        """
        i = bisect.bisect_left(self.__books, (start, 1))
        if i < len(self.__books) and self.__books[i][0] == start:
            self.__books[i] = (self.__books[i][0], self.__books[i][1]+1)
        else:
            self.__books.insert(i, (start, 1))

        j = bisect.bisect_left(self.__books, (end, 1))

        if j < len(self.__books) and self.__books[j][0] == end:
            self.__books[j] = (self.__books[j][0], self.__books[j][1]-1)
        else:
            self.__books.insert(j, (end, -1))

        result, cnt = 0, 0

        for book in self.__books:
            cnt += book[1]
            result = max(result, cnt)

        return result

[3]:

cal = MyCalendarThree()
assert cal.book(10, 20) ==  1
assert cal.book(50, 60) ==  1
assert cal.book(10, 40) ==  2
assert cal.book(5, 15) ==  3
assert cal.book(5, 10) ==  3
assert cal.book(25, 55) ==  3