729. My Calendar I

729. My Calendar I

Implement a MyCalendar class to store your events. A new event can be added if adding the event will not cause a double booking.

Your class will have the 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 double booking happens when two events have some non-empty intersection (ie., there is some time that is common to both events.)

For each call to the method MyCalendar.book, return 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.Your class will be called like this: MyCalendar cal = new MyCalendar(); MyCalendar.book(start, end)

Example 1:

MyCalendar();
MyCalendar.book(10, 20); // returns true
MyCalendar.book(15, 25); // returns false
MyCalendar.book(20, 30); // returns true
Explanation: 
The first event can be booked.  The second can't because time 15 is already booked by another event.
The third event can be booked, as the first event takes every time less than 20, but not including 20.

Note:

The number of calls to MyCalendar.book per test case will be at most 1000.

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

My Solutions：

方法1：对已有的每一个event检查与新event是否重叠。start < c[1] && end > c[0] 代表两个events一定有重叠部分，返回false

（start < c[1]代表在已有event结束前，新event一定已经开始了。end > c[0] 代表新event结束的时间一定在已有的event开始之后。）

时间：O(n)

public class MyCalendar {
    List<int[]> calendar;

    MyCalendar() {
        calendar = new ArrayList();
    }

    public boolean book(int start, int end) {
        for (int[] c: calendar) {
            if (start < c[1] && end > c[0]) return false;
        }
        calendar.add(new int[]{start, end});
        return true;
    }
}

方法2：利用treemap的性质优化

• floorKey(target)方法返回当前Map里小于target的key的最大值。

• ceilingKey(target)返回当前Map里大于target的key的最小值。

class MyCalendar {
    
    TreeMap<Integer, Integer> calendar;

    public MyCalendar() {
        calendar = new TreeMap();
    }

    public boolean book(int start, int end) {
        Integer prev = calendar.floorKey(start), next = calendar.ceilingKey(start);
        if ((prev == null || calendar.get(prev) <= start) //prev is before start
            && (next == null || end <= next)) { //end is before next
            calendar.put(start, end);
            return true;
        }
        return false;
    }
}

时间：O(lgn), For each new event, we search that the event is legal in O(log⁡N) time, then insert it in O(log⁡N) time.