Tyvj 1729 文艺平衡树(Splay)

题目

Description

您需要写一种数据结构（可参考题目标题），来维护一个有序数列，其中需要提供以下操作：

翻转一个区间，例如原有序序列是5 4 3 2 1，翻转区间是[2,4]的话，结果是5 2 3 4 1

Input

第一行为n,m n表示初始序列有n个数，这个序列依次是(1,2……n-1,n) m表示翻转操作次数

接下来m行每行两个数[l,r] 数据保证 1<=l<=r<=n

Output

输出一行n个数字，表示原始序列经过m次变换后的结果

Sample Input

5 3
1 3
1 3
1 4

Sample Output

4 3 2 1 5

HINT

N,M<=100000

题解

这题我目前知道两种做法:

1. Splay
2. FHQ Treap

由于暂时没写出FHQ Treap的代码(也不太实用)， 以后再补

伸展树 Splay

初始化 init

首先按原序列构建树，此外向树中插入0和n+1，并将其size定为0，方便后面操作

反转区间 reverse

1. 从根结点开始，向下找到对应下标为l-1和r+1的结点，每访问一个结点下传旋转标记
2. 将l-1对应的结点splay到根，此时保证r+1在其右子树
3. 将r+1对应的结点splay到根的右儿子处，此时保证需要操作的区间为r+1对应结点的左子树
4. 对r+1对应结点的左子树进行标记，若已标记则消除标记

得到操作后序列 c_list

将树中序遍历(忽略0和n+1)的结果保存在一个vector中返回

详情见代码

代码 code

#include<cstdio>
#include<vector>
using namespace std;
int f(-1);
inline char GetCharacter() {
	static char buf[2000000], *p1 = buf, *p2 = buf;
	return (p1 == p2) &&
	       (p2 = (p1 = buf) + fread(buf, 1, 2000000, stdin), p1 == p2) ? 
	       EOF : *p1++;
}
#define IS_DIGIT(c) (c >= '0' && c <= '9')
inline void Read(int &x) {
	f = 1, x = 0;
	static char c = GetCharacter();
	while (!IS_DIGIT(c)) {
		if (c == '-') f = -1;
		c = GetCharacter();
	}
	while (IS_DIGIT(c)) x = x * 10 + c - '0', c = GetCharacter();
	x *= f;
}
#undef IS_DIGIT
class splay_tree {
  private:
    struct node {
      int value,delta,size;
      node *left, *right, *father;
      node(const int v = 0) {
        value = v, delta = 0, size = 1;
        left = right = father = NULL;
      }
    };
    node *root;
    int Left, Right;
    node *left_node, *right_node;
    vector<int> List;
    inline void update(register node *x) {
      if (x) x->size = (x->value < Left || x->value > Right ? 0 : 1) + 
             (x->left ? x->left->size : 0) + 
             (x->right ? x->right->size : 0);
    }
#define SIZE(x) (x ? x->size : 0)
    inline void push_down(register node *x) {
      if (x) {
        if (x->delta) {
          swap(x->left, x->right);
          if (x->left) x->left->delta ^= 1;
          if (x->right) x->right->delta ^= 1;
          x->delta = 0;
        }
      }
    }
    inline void left_rotate(register node *x) {
      register node *y = x->father;
      y->right = x->left;
      if (x->left) x->left->father = y;
      x->father = y->father;
      if (y->father) {
        if (y == y->father->left) y->father->left = x;
        else y->father->right = x;
      }
      x->left = y;
      y->father = x;
      update(y);
      update(x);
    }
    inline void right_rotate(register node *x) {
      register node *y = x->father;
      y->left = x->right;
      if (x->right) x->right->father = y;
      x->father = y->father;
      if (y->father) {
        if (y == y->father->right) y->father->right = x;
        else y->father->left = x;
      }
      x->right = y;
      y->father = x;
      update(y);
      update(x);
    }
    inline void splay(register node *x,const node *target=NULL) {
      register node *y;
      while (x->father != target) {
        y = x->father;
        if (x == y->left) {
          if (y->father != target && y == y->father->left) right_rotate(y);
          right_rotate(x);
        } else {
          if (y->father != target && y == y->father->right) left_rotate(y);
          left_rotate(x);
        }
      }
      if (!target) root = x;
    }
    inline node *find(register int index) {  
      register node *x = root;
      while(1) {
        if (!x) break;
        push_down(x);
        if (x->value < Left) {
          x = x->right;
        } else if (x->value > Right) x = x->left;
        else if (SIZE(x->left) == index - 1) break;
        else if (SIZE(x->left) >= index) x = x->left;
        else index -= SIZE(x->left) + 1, x = x->right;
      }
      return x;
    }
    inline void Order(register node *x) {
      if (!x) return;
      push_down(x);
      Order(x->left);
      if (x->value >= Left && x->value <= Right) List.push_back(x->value);
      Order(x->right);
    }
  public:
    splay_tree() {
      root = NULL;
    }
    inline void insert(const int &key) {
      register node *x = root, *y = NULL;
      while(1) {
        if (!x) break;
        y = x;
        if (x->value < key) x = x->right;
        else if (x->value > key) x = x->left;
      }
      x = new node(key);
      x->father = y;
      if (y) {
        if (x->value > y->value) y->right = x;
        else y->left = x;
      }
      if (!y) root = x;
      update(y);
      splay(x);
    }
    inline void init(const int &l,const int &r) {
      register node *x = new node(l - 1), *y = new node(r + 1);
      Left = l, Right = r;
      x->size = y->size = 0;
      x->right = y, y->father = x;
      root = x;
      left_node = x, right_node = y;
      for (register int i(l); i <= r; ++i) {
        insert(i);
      }
    }
    inline void reverse(const int &l, const int &r) {
      register node *x(l == Left ? left_node : find(l - 1)), 
                    *y(r == Right ? right_node : find(r + 1));
      splay(x), splay(y, x);
      if (y->left) y->left->delta ^= 1;
    }
    inline vector<int> c_list() {
      List.clear();
      Order(root->left);
      if (root->value >= Left && root->value <= Right) 
        List.push_back(root->value);
      Order(root->right);
      return List;
    }
};
splay_tree tree;
int n, m, l, r;
int main(int argc,char **argv) {
  Read(n), Read(m);
  tree.init(1, n);
  while (m--) {
    Read(l), Read(r);
    tree.reverse(l, r);
  }
  register vector<int> output_list = tree.c_list();
  for(register int i(0), list_size(output_list.size()); i < list_size; ++i) {
    printf("%d ", output_list[i]);
  }
  return 0;
}