# 0729. My Calendar I

https://leetcode.com/problems/my-calendar-i

## 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.

**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.
```

**Constraints:**

* `0 <= start < end <= 109`
* At most `1000` calls will be made to `book`.

## ac1: TreeMap

```java
class MyCalendar {
    TreeMap<Integer, Integer> tmap;
    public MyCalendar() {
        tmap = new TreeMap<>();
    }
    
    public boolean book(int start, int end) {
        Integer f = tmap.floorKey(start);
        Integer c = tmap.ceilingKey(start);
        if (f != null && tmap.get(f) > start || c != null && end > c) {
            return false;
        }
        tmap.put(start, end);
        return true;
    }
}
// O(logN) query and insert
```

Can be more concise:

```java
TreeMap<Integer, Integer> map;
public MyCalendar() {
    map = new TreeMap<>();
}

public boolean book(int start, int end) {
    Integer low = map.lowerKey(end);
    
    if(low == null || map.get(low) <= start) {
        map.put(start, end);
        return true;
    }
    return false;
}
```

## ac2: Doublely LinkedList + Binary Search

* Use Doublely LinkedList to store intervals;
* Binary search find insertion index of start, check if it's valid. Just like above TreeMap approach. Benefit: O(logN) lookup, O(1) insert. The code is lengthy though.
