g0701_0800.s0732_my_calendar_iii.MyCalendarThree Maven / Gradle / Ivy

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package g0701_0800.s0732_my_calendar_iii;

// #Hard #Binary_Search #Design #Ordered_Set #Segment_Tree
// #2022_03_25_Time_40_ms_(95.37%)_Space_61.9_MB_(11.11%)

/**
 * 732 - My Calendar III\.
 *
 * Hard
 *
 * 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 `[start, end)`, 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 start, int end)` 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, The first event can be booked and is disjoint, so the maximum k-booking is a 1-booking. 
 *     myCalendarThree.book(50, 60); // return 1, The second event can be booked and is disjoint, so the maximum k-booking is a 1-booking. 
 *     myCalendarThree.book(10, 40); // return 2, The third event [10, 40) intersects the first event, and the maximum k-booking is a 2-booking. 
 *     myCalendarThree.book(5, 15); // return 3, The remaining events cause the maximum K-booking to be only a 3-booking. 
 *     myCalendarThree.book(5, 10); // return 3 
 *     myCalendarThree.book(25, 55); // return 3
 *
 * **Constraints:**
 *
 * *   0 <= start < end <= 10⁹
 * *   At most `400` calls will be made to `book`.
**/
public class MyCalendarThree {
    private final Node root;

    public MyCalendarThree() {
        root = new Node(0, 1000000000, 0);
    }

    public int book(int start, int end) {
        updateTree(root, start, end - 1);
        return root.val;
    }

    private void updateTree(Node root, int start, int end) {
        if (root == null) {
            return;
        }
        if (root.low >= start && root.high <= end) {
            root.val++;
            if (root.left != null) {
                updateTree(root.left, start, end);
            }
            if (root.right != null) {
                updateTree(root.right, start, end);
            }
            return;
        }

        int mid = (root.low + root.high) / 2;
        if (root.left == null) {
            root.left = new Node(root.low, mid, root.val);
        }

        if (root.right == null) {
            root.right = new Node(mid + 1, root.high, root.val);
        }

        if (start <= mid) {
            updateTree(root.left, start, end);
        }

        if (end > mid) {
            updateTree(root.right, start, end);
        }

        root.val = Math.max(root.left.val, root.right.val);
    }

    static class Node {
        int low;
        int high;
        int val;
        Node left;
        Node right;

        public Node(int low, int high, int val) {
            this.low = low;
            this.high = high;
            this.val = val;
        }
    }
}

/*
 * Your MyCalendarThree object will be instantiated and called as such:
 * MyCalendarThree obj = new MyCalendarThree();
 * int param_1 = obj.book(start,end);
 */