LWC 59：731. My Calendar II

LWC 59：731. My Calendar II

传送门：729. My Calendar II

Problem:

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

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.

A triple booking happens when three events have some non-empty intersection (ie., there is some time that is common to all 3 events.)

For each call to the method MyCalendar.book, return 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.

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(50, 60); // returns true
MyCalendar.book(10, 40); // returns true
MyCalendar.book(5, 15); // returns false
MyCalendar.book(5, 10); // returns true
MyCalendar.book(25, 55); // returns true
Explanation:
The first two events can be booked. The third event can be double booked.
The fourth event (5, 15) can’t be booked, because it would result in a triple booking.
The fifth event (5, 10) can be booked, as it does not use time 10 which is already double booked.
The sixth event (25, 55) 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.

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].

思路：
水过，当新加入一个区间时，如果在该区间内，出现重复的区间时，则认为是a triple booking，关键在于如何求出两个区间的重叠区间，画个图就能明白，重叠区间为：

s = max(s1, s2), si = 区间i的开始坐标e = min(e1, e2), ei = 区间i的结束坐标

首先排除一部分冗余区间，左侧的与候选区间的不重叠区间和右侧的不重叠区间均可以排除，而中间那一部分，则需要以O(n2)的时间复杂度来计算每两个区间的重叠区域，是否与候选区域发生重叠。

代码如下：

class MyCalendarTwo {    class Interval implements Comparable<Interval>{        int s;        int e;        Interval(int s, int e){            this.s = s;            this.e = e;        }        @Override        public int compareTo(Interval o) {            return this.s == o.s ? this.e - o.e : this.s - o.s;        }        @Override        public String toString() {            return "[" + s + ", " + e +"]";        }    }    List<Interval> mem;    public MyCalendarTwo() {        mem = new ArrayList<>();    }    public boolean book(int start, int end) {        Interval candicate = new Interval(start, end);        if (tripleOverlap(candicate)) {            return false;        }        else {            mem.add(candicate);            return true;        }    }    boolean tripleOverlap(Interval candicate) {        Collections.sort(mem);        int n = mem.size();        int left = 0;        int right = n - 1;        while (left < n && candicate.s >= mem.get(left).e) left ++;        while (right >= 0 && candicate.e <= mem.get(right).s) right --;        for (int i = left; i <= right; ++i) {            for (int j = left; j < i; ++j){                Interval ans = new Interval(-1, -1);                if (overlap(mem.get(j), mem.get(i), ans)) {                    if (overlap(ans, candicate, new Interval(-1, -1))) return true;                }            }        }        return false;    }    boolean overlap(Interval a, Interval b, Interval ans) {        if (b.s >= a.s && b.s < a.e || b.e <= a.e && b.e > a.s || b.s <= a.s && b.e >= a.e) {            ans.s = Math.max(b.s, a.s);            ans.e = Math.min(a.e, b.e);            return true;        }        return false;    }}

再来一种积分的思路，时间复杂度为O(n2)，加入新的区间后，判断当前区间的累积值是否超过3，超过3则说明该区间不该被加入，重新去除。

具体查看imos 累积法。

JAVA代码超时，C++则AC，代码如下：

class MyCalendarTwo {public:    map<int, int> m;    MyCalendarTwo() {    }    bool book(int start, int end) {        m[start] ++;        m[end] --;        int s = 0;        for (auto it : m) {            s += it.second;            if (s >= 3) {                m[end] ++;                m[start] --;                return false;            }        }        return true;    }};