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731. 我的日程安排表 II

题目描述

实现一个 MyCalendar 类来存放你的日程安排。如果要添加的时间内不会导致三重预订时，则可以存储这个新的日程安排。

MyCalendar 有一个 book(int start, int end)方法。它意味着在 start 到 end 时间内增加一个日程安排，注意，这里的时间是半开区间，即 [start, end), 实数 x 的范围为，  start <= x < end。

当三个日程安排有一些时间上的交叉时（例如三个日程安排都在同一时间内），就会产生三重预订。

每次调用 MyCalendar.book方法时，如果可以将日程安排成功添加到日历中而不会导致三重预订，返回 true。否则，返回 false 并且不要将该日程安排添加到日历中。

请按照以下步骤调用MyCalendar 类: MyCalendar cal = new MyCalendar(); MyCalendar.book(start, end)

 

示例：

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
解释： 
前两个日程安排可以添加至日历中。 第三个日程安排会导致双重预订，但可以添加至日历中。
第四个日程安排活动（5,15）不能添加至日历中，因为它会导致三重预订。
第五个日程安排（5,10）可以添加至日历中，因为它未使用已经双重预订的时间10。
第六个日程安排（25,55）可以添加至日历中，因为时间 [25,40] 将和第三个日程安排双重预订；
时间 [40,50] 将单独预订，时间 [50,55）将和第二个日程安排双重预订。

 

提示：

  • 每个测试用例，调用 MyCalendar.book 函数最多不超过 1000次。
  • 调用函数 MyCalendar.book(start, end)时， start 和 end 的取值范围为 [0, 10^9]。

解法

方法一：差分

利用有序哈希表实现。

时间复杂度 $O(n^2)$，其中 $n$ 表示日程安排的数量。

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from sortedcontainers import SortedDict


class MyCalendarTwo:
    def __init__(self):
        self.sd = SortedDict()

    def book(self, start: int, end: int) -> bool:
        self.sd[start] = self.sd.get(start, 0) + 1
        self.sd[end] = self.sd.get(end, 0) - 1
        s = 0
        for v in self.sd.values():
            s += v
            if s > 2:
                self.sd[start] -= 1
                self.sd[end] += 1
                return False
        return True


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

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class MyCalendarTwo {
    private Map<Integer, Integer> tm = new TreeMap<>();

    public MyCalendarTwo() {
    }

    public boolean book(int start, int end) {
        tm.put(start, tm.getOrDefault(start, 0) + 1);
        tm.put(end, tm.getOrDefault(end, 0) - 1);
        int s = 0;
        for (int v : tm.values()) {
            s += v;
            if (s > 2) {
                tm.put(start, tm.get(start) - 1);
                tm.put(end, tm.get(end) + 1);
                return false;
            }
        }
        return true;
    }
}

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

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class MyCalendarTwo {
public:
    map<int, int> m;

    MyCalendarTwo() {
    }

    bool book(int start, int end) {
        ++m[start];
        --m[end];
        int s = 0;
        for (auto& [_, v] : m) {
            s += v;
            if (s > 2) {
                --m[start];
                ++m[end];
                return false;
            }
        }
        return true;
    }
};

/**
 * Your MyCalendarTwo object will be instantiated and called as such:
 * MyCalendarTwo* obj = new MyCalendarTwo();
 * bool param_1 = obj->book(start,end);
 */

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type MyCalendarTwo struct {
    *redblacktree.Tree
}

func Constructor() MyCalendarTwo {
    return MyCalendarTwo{redblacktree.NewWithIntComparator()}
}

func (this *MyCalendarTwo) Book(start int, end int) bool {
    add := func(key, val int) {
        if v, ok := this.Get(key); ok {
            this.Put(key, v.(int)+val)
        } else {
            this.Put(key, val)
        }
    }
    add(start, 1)
    add(end, -1)
    s := 0
    it := this.Iterator()
    for it.Next() {
        s += it.Value().(int)
        if s > 2 {
            add(start, -1)
            add(end, 1)
            return false
        }
    }
    return true
}

/**
 * Your MyCalendarTwo object will be instantiated and called as such:
 * obj := Constructor();
 * param_1 := obj.Book(start,end);
 */

方法二：线段树

线段树将整个区间分割为多个不连续的子区间，子区间的数量不超过 $log(width)$。更新某个元素的值，只需要更新 $log(width)$ 个区间，并且这些区间都包含在一个包含该元素的大区间内。区间修改时，需要使用懒标记保证效率。

  • 线段树的每个节点代表一个区间；
  • 线段树具有唯一的根节点，代表的区间是整个统计范围，如 $[1,N]$；
  • 线段树的每个叶子节点代表一个长度为 $1$ 的元区间 $[x, x]$；
  • 对于每个内部节点 $[l,r]$，它的左儿子是 $[l,mid]$，右儿子是 $[mid+1,r]$, 其中 $mid = ⌊(l+r)/2⌋$ (即向下取整)。

对于本题，线段树节点维护的信息有：

  1. 区间范围内被预定的次数的最大值 $v$
  2. 懒标记 $add$

由于时间范围为 $10^9$，非常大，因此我们采用动态开点。

时间复杂度 $O(nlogn)$，其中 $n$ 表示日程安排的数量。

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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 MyCalendarTwo:
    def __init__(self):
        self.tree = SegmentTree()

    def book(self, start: int, end: int) -> bool:
        if self.tree.query(start + 1, end) >= 2:
            return False
        self.tree.modify(start + 1, end, 1)
        return True


# Your MyCalendarTwo object will be instantiated and called as such:
# obj = MyCalendarTwo()
# 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 = (l + r) >> 1;
    }
}

class SegmentTree {
    private Node root = new Node(1, (int) 1e9 + 1);

    public SegmentTree() {
    }

    public void modify(int l, int r, int v) {
        modify(l, r, v, root);
    }

    public void modify(int l, int r, int v, Node node) {
        if (l > r) {
            return;
        }
        if (node.l >= l && node.r <= r) {
            node.v += v;
            node.add += v;
            return;
        }
        pushdown(node);
        if (l <= node.mid) {
            modify(l, r, v, node.left);
        }
        if (r > node.mid) {
            modify(l, r, v, node.right);
        }
        pushup(node);
    }

    public int query(int l, int r) {
        return query(l, r, root);
    }

    public int query(int l, int r, Node node) {
        if (l > r) {
            return 0;
        }
        if (node.l >= l && node.r <= r) {
            return node.v;
        }
        pushdown(node);
        int v = 0;
        if (l <= node.mid) {
            v = Math.max(v, query(l, r, node.left));
        }
        if (r > node.mid) {
            v = Math.max(v, query(l, r, node.right));
        }
        return v;
    }

    public void pushup(Node node) {
        node.v = Math.max(node.left.v, node.right.v);
    }

    public void pushdown(Node node) {
        if (node.left == null) {
            node.left = new Node(node.l, node.mid);
        }
        if (node.right == null) {
            node.right = new Node(node.mid + 1, node.r);
        }
        if (node.add != 0) {
            Node left = node.left, right = node.right;
            left.add += node.add;
            right.add += node.add;
            left.v += node.add;
            right.v += node.add;
            node.add = 0;
        }
    }
}

class MyCalendarTwo {
    private SegmentTree tree = new SegmentTree();

    public MyCalendarTwo() {
    }

    public boolean book(int start, int end) {
        if (tree.query(start + 1, end) >= 2) {
            return false;
        }
        tree.modify(start + 1, end, 1);
        return true;
    }
}

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

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class Node {
public:
    Node* left;
    Node* right;
    int l;
    int r;
    int mid;
    int v;
    int add;

    Node(int l, int r) {
        this->l = l;
        this->r = r;
        this->mid = (l + r) >> 1;
        this->left = this->right = nullptr;
        v = add = 0;
    }
};

class SegmentTree {
private:
    Node* root;

public:
    SegmentTree() {
        root = new Node(1, 1e9 + 1);
    }

    void modify(int l, int r, int v) {
        modify(l, r, v, root);
    }

    void modify(int l, int r, int v, Node* node) {
        if (l > r) return;
        if (node->l >= l && node->r <= r) {
            node->v += v;
            node->add += v;
            return;
        }
        pushdown(node);
        if (l <= node->mid) modify(l, r, v, node->left);
        if (r > node->mid) modify(l, r, v, node->right);
        pushup(node);
    }

    int query(int l, int r) {
        return query(l, r, root);
    }

    int query(int l, int r, Node* node) {
        if (l > r) return 0;
        if (node->l >= l && node->r <= r) return node->v;
        pushdown(node);
        int v = 0;
        if (l <= node->mid) v = max(v, query(l, r, node->left));
        if (r > node->mid) v = max(v, query(l, r, node->right));
        return v;
    }

    void pushup(Node* node) {
        node->v = max(node->left->v, node->right->v);
    }

    void pushdown(Node* node) {
        if (!node->left) node->left = new Node(node->l, node->mid);
        if (!node->right) node->right = new Node(node->mid + 1, node->r);
        if (node->add) {
            Node* left = node->left;
            Node* right = node->right;
            left->v += node->add;
            right->v += node->add;
            left->add += node->add;
            right->add += node->add;
            node->add = 0;
        }
    }
};

class MyCalendarTwo {
public:
    SegmentTree* tree = new SegmentTree();

    MyCalendarTwo() {
    }

    bool book(int start, int end) {
        if (tree->query(start + 1, end) >= 2) return false;
        tree->modify(start + 1, end, 1);
        return true;
    }
};

/**
 * Your MyCalendarTwo object will be instantiated and called as such:
 * MyCalendarTwo* obj = new MyCalendarTwo();
 * bool param_1 = obj->book(start,end);
 */

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type node struct {
    left      *node
    right     *node
    l, mid, r int
    v, add    int
}

func newNode(l, r int) *node {
    return &node{
        l:   l,
        r:   r,
        mid: int(uint(l+r) >> 1),
    }
}

type segmentTree struct {
    root *node
}

func newSegmentTree() *segmentTree {
    return &segmentTree{
        root: newNode(1, 1e9+1),
    }
}

func (t *segmentTree) modify(l, r, v int, n *node) {
    if l > r {
        return
    }
    if n.l >= l && n.r <= r {
        n.v += v
        n.add += v
        return
    }
    t.pushdown(n)
    if l <= n.mid {
        t.modify(l, r, v, n.left)
    }
    if r > n.mid {
        t.modify(l, r, v, n.right)
    }
    t.pushup(n)
}

func (t *segmentTree) query(l, r int, n *node) int {
    if l > r {
        return 0
    }
    if n.l >= l && n.r <= r {
        return n.v
    }
    t.pushdown(n)
    v := 0
    if l <= n.mid {
        v = max(v, t.query(l, r, n.left))
    }
    if r > n.mid {
        v = max(v, t.query(l, r, n.right))
    }
    return v
}

func (t *segmentTree) pushup(n *node) {
    n.v = max(n.left.v, n.right.v)
}

func (t *segmentTree) pushdown(n *node) {
    if n.left == nil {
        n.left = newNode(n.l, n.mid)
    }
    if n.right == nil {
        n.right = newNode(n.mid+1, n.r)
    }
    if n.add != 0 {
        n.left.add += n.add
        n.right.add += n.add
        n.left.v += n.add
        n.right.v += n.add
        n.add = 0
    }
}

type MyCalendarTwo struct {
    tree *segmentTree
}

func Constructor() MyCalendarTwo {
    return MyCalendarTwo{newSegmentTree()}
}

func (this *MyCalendarTwo) Book(start int, end int) bool {
    if this.tree.query(start+1, end, this.tree.root) >= 2 {
        return false
    }
    this.tree.modify(start+1, end, 1, this.tree.root)
    return true
}

/**
 * Your MyCalendarTwo object will be instantiated and called as such:
 * obj := Constructor();
 * param_1 := obj.Book(start,end);
 */

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