leetcode 732. My Calendar III(线段树)

最新推荐文章于 2022-07-23 17:30:58 发布

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最新推荐文章于 2022-07-23 17:30:58 发布

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本文介绍了一种优化的MyCalendarThree实现方法，使用线段树和BST存储区间信息，有效提高了book方法的时间效率，从O(n*logn)降低到O(logn)，适用于大量事件预订场景。

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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.

A K-booking happens 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 method MyCalendar.book, return an integer K representing the largest integer such that there exists a K-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 most 400.
In calls to MyCalendarThree.book(start, end), start and end are integers in the range [0, 10^9].

用BST做这题较简单，就是用TreeMap存储起始点和结束点。再遍历一遍。但是时间复杂度太高，每次book时间复杂度O(n*log n)。

参考了别人的思路，用线段树，每次调用book方法相当于线段树的update操作。因为以前的线段树实现都是用一段给定较小范围的数据上操作。这题的数据范围是10^9所以,用节点版本的线段树，不需要为每一个数建立节点。有时只需要为一段建立节点就行了。

以下是基于节点存区间信息的思想写的线段树，并没有参考评论区的写法。这里的build方法类似线段树的update操作，每次book时间复杂度O(log len)。len为线段树区间范围。

class MyCalendarThree {
    class TreeNode{
        int val=0;//区间最大
        TreeNode left;
        TreeNode right;
        TreeNode(int val){
            this.val=val;
        }
    }
    TreeNode root;
    public MyCalendarThree() {
        root=new TreeNode(0);
    }
    
    public int book(int start, int end) {
        return build(start,end-1,root,0,1000000000);
    }
    int build(int s,int e,TreeNode node,int l,int r){//l,r代表范围
        if(s==l&&e==r&&node.left==null&&node.right==null){//后面的暂时不用
            node.val++;
            return node.val;
        }
        if(node.left==null){
            node.left=new TreeNode(node.val);
            node.right=new TreeNode(node.val);
        }
        int m=(l+r)/2;
        if(m>=e){
            node.val=Math.max(node.val,build(s,e,node.left,l,m));
        }else if(m<s){
            node.val=Math.max(node.val,build(s,e,node.right,m+1,r));
        }else{
            int v=Math.max(build(s,m,node.left,l,m),build(m+1,e,node.right,m+1,r));
            node.val=Math.max(node.val,v);
        }
        return node.val;
    }
}

参考：https://blog.youkuaiyun.com/guo15331092/article/details/78883265

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代码样本中看到一种更精彩的方法，BST存区间的信息，随着插入区间，不断的更新区间的大小。。。有点像线段树。