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732. My Calendar III

Description

A k-booking happens when k events have some non-empty intersection (i.e., there is some time that is common to all k events.)

You are given some events [startTime, endTime), after each given event, return an integer k representing the maximum k-booking between all the previous events.

Implement the MyCalendarThree class:

  • MyCalendarThree() Initializes the object.
  • int book(int startTime, int endTime) Returns an integer k representing the largest integer such that there exists a k-booking in the calendar.

 

Example 1:

Input
["MyCalendarThree", "book", "book", "book", "book", "book", "book"]
[[], [10, 20], [50, 60], [10, 40], [5, 15], [5, 10], [25, 55]]
Output
[null, 1, 1, 2, 3, 3, 3]

Explanation
MyCalendarThree myCalendarThree = new MyCalendarThree();
myCalendarThree.book(10, 20); // return 1
myCalendarThree.book(50, 60); // return 1
myCalendarThree.book(10, 40); // return 2
myCalendarThree.book(5, 15); // return 3
myCalendarThree.book(5, 10); // return 3
myCalendarThree.book(25, 55); // return 3

 

Constraints:

  • 0 <= startTime < endTime <= 109
  • At most 400 calls will be made to book.

Solutions

Solution 1

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class Node:
    def __init__(self, l, r):
        self.left = None
        self.right = None
        self.l = l
        self.r = r
        self.mid = (l + r) >> 1
        self.v = 0
        self.add = 0


class SegmentTree:
    def __init__(self):
        self.root = Node(1, int(1e9 + 1))

    def modify(self, l, r, v, node=None):
        if l > r:
            return
        if node is None:
            node = self.root
        if node.l >= l and node.r <= r:
            node.v += v
            node.add += v
            return
        self.pushdown(node)
        if l <= node.mid:
            self.modify(l, r, v, node.left)
        if r > node.mid:
            self.modify(l, r, v, node.right)
        self.pushup(node)

    def query(self, l, r, node=None):
        if l > r:
            return 0
        if node is None:
            node = self.root
        if node.l >= l and node.r <= r:
            return node.v
        self.pushdown(node)
        v = 0
        if l <= node.mid:
            v = max(v, self.query(l, r, node.left))
        if r > node.mid:
            v = max(v, self.query(l, r, node.right))
        return v

    def pushup(self, node):
        node.v = max(node.left.v, node.right.v)

    def pushdown(self, node):
        if node.left is None:
            node.left = Node(node.l, node.mid)
        if node.right is None:
            node.right = Node(node.mid + 1, node.r)
        if node.add:
            node.left.v += node.add
            node.right.v += node.add
            node.left.add += node.add
            node.right.add += node.add
            node.add = 0


class MyCalendarThree:
    def __init__(self):
        self.tree = SegmentTree()

    def book(self, start: int, end: int) -> int:
        self.tree.modify(start + 1, end, 1)
        return self.tree.query(1, int(1e9 + 1))


# Your MyCalendarThree object will be instantiated and called as such:
# obj = MyCalendarThree()
# param_1 = obj.book(start,end)

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class Node {
    Node left;
    Node right;
    int l;
    int r;
    int mid;
    int v;
    int add;
    public Node(int l, int r) {
        this.l = l;
        this.r = r;
        this.mid =