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package g0701_0800.s0731_my_calendar_ii;

// #Medium #Binary_Search #Design #Ordered_Set #Segment_Tree
// #2022_03_25_Time_27_ms_(97.74%)_Space_54.6_MB_(48.74%)

import java.util.TreeMap;

/**
 * 731 - My Calendar II\.
 *
 * Medium
 *
 * You are implementing a program to use as your calendar. We can add a new event if adding the event will not cause a **triple booking**.
 *
 * A **triple booking** happens when three events have some non-empty intersection (i.e., some moment is common to all the three 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 `MyCalendarTwo` class:
 *
 * *   `MyCalendarTwo()` 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 **triple booking**. Otherwise, return `false` and do not add the event to the calendar.
 *
 * **Example 1:**
 *
 * **Input** 
 *
 * ["MyCalendarTwo", "book", "book", "book", "book", "book", "book"] 
 *
 * [ [], [10, 20], [50, 60], [10, 40], [5, 15], [5, 10], [25, 55]]
 *
 * **Output:** [null, true, true, true, false, true, true]
 *
 * **Explanation:** 
 *
 *     MyCalendarTwo myCalendarTwo = new MyCalendarTwo(); 
 *     myCalendarTwo.book(10, 20); // return True, The event can be booked. 
 *     myCalendarTwo.book(50, 60); // return True, The event can be booked. 
 *     myCalendarTwo.book(10, 40); // return True, The event can be double booked. 
 *     myCalendarTwo.book(5, 15); // return False, The event ca not be booked, because it would result in a triple booking. 
 *     myCalendarTwo.book(5, 10); // return True, The event can be booked, as it does not use time 10 which is already double booked. 
 *     myCalendarTwo.book(25, 55); // return True, The event can be booked, as the time in [25, 40) will be double booked with the third event, the time [40, 50) will be single booked, and the time [50, 55) will be double booked with the second event.
 *
 * **Constraints:**
 *
 * *   0 <= start < end <= 10⁹
 * *   At most `1000` calls will be made to `book`.
**/
public class MyCalendarTwo {
    private final TreeMap map;
    private final TreeMap overlap;

    public MyCalendarTwo() {
        map = new TreeMap<>();
        overlap = new TreeMap<>();
    }

    public boolean book(int start, int end) {
        Integer ol = overlap.lowerKey(end);
        if (ol == null || overlap.get(ol) <= start) {
            while (true) {
                Integer lower = map.lowerKey(end);
                if (lower == null || map.get(lower) <= start) {
                    break;
                }
                overlap.put(Math.max(start, lower), Math.min(end, map.get(lower)));
                start = Math.min(start, lower);
                end = Math.max(end, map.get(lower));
                map.remove(lower);
            }
            map.put(start, end);
            return true;
        }
        return false;
    }
}

/*
 * Your MyCalendarTwo object will be instantiated and called as such:
 * MyCalendarTwo obj = new MyCalendarTwo();
 * boolean param_1 = obj.book(start,end);
 */