729. My Calendar I

1. Description

You are implementing a program to use as your calendar. We can add a new event if adding the event will not cause a double booking.
A double booking happens when two events have some non-empty intersection (i.e., some moment is common to both events.).
The event can be represented as a pair of integers start and end that represents a booking on the half-open interval [start, end), the range of real numbers x such that start <= x < end.
Implement the MyCalendar class:

• MyCalendar() Initializes the calendar object.
• boolean book(int start, int end) Returns true if the event can be added to the calendar successfully without causing a double booking. Otherwise, return false and do not add the event to the calendar.

2. Example

Example 1:
Input
[“MyCalendar”, “book”, “book”, “book”]
[[], [10, 20], [15, 25], [20, 30]]
Output
[null, true, false, true]

Explanation
MyCalendar myCalendar = new MyCalendar();
myCalendar.book(10, 20); // return True
myCalendar.book(15, 25); // return False, It can not be booked because time 15 is already booked by another event.
myCalendar.book(20, 30); // return True, The event can be booked, as the first event takes every time less than 20, but not including 20.

3. Constraints

• 0 <= start < end <= $10^9$
• At most 1000 calls will be made to book.

4. Solutions

Binary Search & Ordered Set

n is the times of book function call

class MyCalendar {
    set<pair<int, int>> calendar;

public:
    bool book(int start, int end) {
        // Time complexity: O(nlogn)  
        // Space complexity: O(n)
        auto lower_it = calendar.lower_bound({end, 0});
        if (lower_it == calendar.begin() || (--lower_it)->second <= start) {
            calendar.emplace(start, end);
            return true;
        }

        return false;
    }
};