My Calendar III
Sweep Line
, TreeMap
, Interval
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
.
AK-bookinghappens 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 methodMyCalendar.book
, return an integer K
representing the largest integer such that there exists aK
-booking in the calendar.
Your class will be called like this:
MyCalendarThree cal = new MyCalendarThree();
MyCalendarThree.book(start, end)
Example 1:
MyCalendarThree();
MyCalendarThree.book(10, 20); // returns 1
MyCalendarThree.book(50, 60); // returns 1
MyCalendarThree.book(10, 40); // returns 2
MyCalendarThree.book(5, 15); // returns 3
MyCalendarThree.book(5, 10); // returns 3
MyCalendarThree.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.
Note:
The number of calls to
MyCalendarThree.book
per test case will be at most400
.In calls to
MyCalendarThree.book(start, end)
,start
andend
are integers in the range[0, 10^9]
.
Solution & Analysis
理解 k-booking:
A K-booking happens when K events have some non-empty intersection (ie., there is some time that is common to all K events.)
Approach: Boundary Count - TreeMap - Sweep Line
基本思想和My Calendar II一样,这里问的变成了k-booking的值,每次新加入的booking不会被拒绝,那也就是说返回所有booking的重叠次数的最大值。完全套用TreeMap based扫描线做法即可。
Time: each booking() operation - O(n + logn), total for n booking(): O(n^2 + nlogn) ~ O(n^2)
Space: O(n)
class MyCalendarThree {
TreeMap<Integer, Integer> calendar;
public MyCalendarThree() {
calendar = new TreeMap<>();
}
public int book(int start, int end) {
calendar.put(start, calendar.getOrDefault(start, 0) + 1);
calendar.put(end, calendar.getOrDefault(end, 0) - 1);
int ongoing = 0;
int maxBooking = 0;
for (int v: calendar.values()) {
ongoing += v;
https://leetcode.com/problems/my-calendar-iii/ = Math.max(maxBooking, ongoing);
}
return maxBooking;
}
}
/**
* Your MyCalendarThree object will be instantiated and called as such:
* MyCalendarThree obj = new MyCalendarThree();
* int param_1 = obj.book(start,end);
*/
Reference
https://leetcode.com/problems/my-calendar-iii/discuss/109556/JavaC%2B%2B-Clean-Code
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