LC.P732[我的日程安排表III]

方法一：差分数组

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class MyCalendarThree {

    private TreeMap<Integer, Integer> cnt;

    public MyCalendarThree() {
        cnt = new TreeMap<Integer, Integer>();
    }
    
    public int book(int start, int end) {
        int ans = 0;
        int maxBook = 0;
        cnt.put(start, cnt.getOrDefault(start, 0) + 1);
        cnt.put(end, cnt.getOrDefault(end, 0) - 1);
        for (Map.Entry<Integer, Integer> entry : cnt.entrySet()) {
            int freq = entry.getValue();
            maxBook += freq;
            ans = Math.max(maxBook, ans);
        }
        return ans;
    }
}

/**
 * Your MyCalendarThree object will be instantiated and called as such:
 * MyCalendarThree obj = new MyCalendarThree();
 * int param_1 = obj.book(start,end);
 */
  • 时间复杂度：$O(n^2)$
  • 空间复杂度：$O(n)$

方法二：线段树

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class MyCalendarThree {

    public MyCalendarThree() {

    }
    
    public int book(int start, int end) {
        // 只用到了 update
        update(root, 0, N, start, end - 1, 1);
        // 最大值即为根节点的值
        return root.val;
    }

    private static class Node {
        // 左右孩子节点
        Node left, right;
        // 当前节点值，以及懒惰标记的值
        int val, add;
    }
    
    private int N = (int) 1e9;
    private Node root = new Node();

    public void update(Node node, int start, int end, int l, int r, int val) {
        if (l <= start && end <= r) {
            node.val += val;
            node.add += val;
            return;
        }
        pushDown(node);
        int mid = (start + end) >> 1;
        if (l <= mid) update(node.left, start, mid, l, r, val);
        if (r > mid) update(node.right, mid + 1, end, l, r, val);
        pushUp(node);
    }
    public int query(Node node, int start, int end, int l, int r) {
        if (l <= start && end <= r) return node.val;
        pushDown(node);
        int mid = (start + end) >> 1, ans = 0;
        if (l <= mid) ans = query(node.left, start, mid, l, r);
        if (r > mid) ans = Math.max(ans, query(node.right, mid + 1, end, l, r));
        return ans;
    }
    private void pushUp(Node node) {
        // 每个节点存的是当前区间的最大值
        node.val = Math.max(node.left.val, node.right.val);
    }
    private void pushDown(Node node) {
        if (node.left == null) node.left = new Node();
        if (node.right == null) node.right = new Node();
        if (node.add == 0) return ;
        node.left.val += node.add;
        node.right.val += node.add;
        node.left.add += node.add;
        node.right.add += node.add;
        node.add = 0;
    }
}

/**
 * Your MyCalendarThree object will be instantiated and called as such:
 * MyCalendarThree obj = new MyCalendarThree();
 * int param_1 = obj.book(startTime,endTime);
 */
  • 时间复杂度：$O(logn)$
  • 空间复杂度：$O(mlogn)$，其中$m$为查询次数