Hihocoder 1333 （splay）

Problem 平衡树 splay2

题目大意

　　维护一个序列，支持四种操作：

　　操作1：添加一个数，编号为x，权值为y。

　　操作2：删除编号在区间【x,y】内的数。

　　操作3：将编号在区间【x,y】内的数的权值增加为z。

　　操作4：询问编号在区间【x,y]内的数的权值和。

解题分析

　　由于增加了区间加和区间查询，所以要给每个增加一个lazy标记。

　　在每次搜索树的时候要对每个经过的节点进行一次pushdown，当树的形态或树的结点信息改变时要进行一次pushup。

参考程序

 #include <bits/stdc++.h>
 using namespace std;

 int tag=;

 struct node{
     int id,num;
     long long lazy,val,sum;
     node *left,*right,*father;
     node(int id_=,long long val_=,int num_=,long long lazy_=,long long sum_=,node* father_=NULL,node* left_=NULL,node* right_=NULL)
     {
         id=id_; val=val_; num=num_; lazy=lazy_; sum=sum_;
         father=father_; left=left_; right=right_;
     }
 }*rt,*t1,*t2;

 void search(node *now)
 {
     cout<<now->id; cout<<" val= "<<now->val<<" sum= "<<now->sum<<" num= "<<now->num<<" lazy= "<<now->lazy;
     if (now->left) cout<<" lson: "<<now->left->id;
     if (now->right) cout<<" rson: "<<now->right->id;
     cout<<endl;
     if (now->left) search(now->left);
     if (now->right) search(now->right);
 }

 void pushup(node* x)
 {
     x->sum=x->val; x->num=;
     if (x->left)  x->sum+=x->left->sum,x->num+=x->left->num;
     if (x->right) x->sum+=x->right->sum,x->num+=x->right->num;
 }

 void pushdown(node* x)
 {
     if (x->lazy)
     {
         node *l = x->left,*r = x->right;
         if (l)
         {
             l->lazy += x->lazy;
             l->val += x->lazy;
             l->sum += x->lazy * l->num;
         }
         if (r)
         {
             r->lazy += x->lazy;
             r->val += x->lazy;
             r->sum += x->lazy * r->num;
         }
         x->lazy = ;
     }
 }

 void right(node* x,node* &rt)
 {
     node *y=x->father,*z=y->father;
     if (y==rt) rt=x;
     else if (z->left==y) z->left=x; else z->right=x; //需要判断是左右孩子
     x->father=z; y->father=x; if (x->right) x->right->father=y;  //防止对空指针进行操作
     y->left=x->right; x->right=y;
     pushup(y); pushup(x);
 }

 void left(node* x,node* &rt)
 {
     node *y=x->father,*z=y->father;
     if (y==rt) rt=x;
     else if (z->left==y) z->left=x; else z->right=x;
     x->father=z; y->father=x; if (x->left) x->left->father=y;
     y->right=x->left; x->left=y;
     pushup(y); pushup(x);
 }

 void splay(node* x,node* &rt)
 {
     while (x!=rt)
     {
         node *y=x->father, *z=y->father;
         if (y==rt)
         {
             if (x==y->left) right(x,rt);
             else left(x,rt);
         }
         else
         {
             if (y==z->left)
                 if (x==y->left) { right(y,rt); right(x,rt); }
                 else { left(x,rt); right(x,rt); }
             else
                 if (x==y->right) { left(y,rt); left(x,rt); }
                 else { right(x,rt); left(x,rt); }
         }
     }
 }

 void insert(int id,int val,node* &now,node *last)
 {
     if (now==NULL)
     {
         now=new node(id,val,,,val,last);
         splay(now,rt);
         return;
     }
     pushdown(now);
     if (id < now->id) insert(id,val,now->left,now); else  insert(id,val,now->right,now);
     //else还是要加的 返回的时候树的形态已经改变了
 }

 void find_1(int id,node *x)
 {
     if (x==NULL) return;
     pushdown(x);
     if (x->id>=id) find_1(id,x->left);
     else {t1=x; find_1(id,x->right);}
 }

 void find_2(int id,node *x)
 {
     if (x==NULL) return;
     pushdown(x);
     if (x->id<=id) find_2(id,x->right);
     else {t2=x; find_2(id,x->left);}
 }

 void del(int l,int r)
 {
     t1=t2=NULL;
     find_1(l,rt); splay(t1,rt);
     find_2(r,rt->right); splay(t2,rt->right);
     rt->right->left=NULL;
     pushup(rt->right); pushup(rt);
 }

 void add(int l,int r,int val)
 {
     t1=t2=NULL;
     find_1(l,rt); splay(t1,rt);
     find_2(r,rt->right); splay(t2,rt->right);
     if (rt->right->left)
     {
         rt->right->left->lazy += val;
         rt->right->left->sum += 1ll* val * rt->right->left->num;
         rt->right->left->val += val;
      }
      pushup(rt->right); pushup(rt);
 }

 long long query(int l,int r)
 {
     t1=t2=NULL;
     find_1(l,rt); splay(t1,rt);
     find_2(r,rt->right); splay(t2,rt->right);
     if (rt->right->left)
         return rt->right->left->sum;
     else return ;
 }

 int main()
 {
     int n;
     rt=NULL;
     scanf("%d",&n);
     insert(<<,,rt,NULL); insert(-<<,,rt,NULL);
     for (int i=;i<=n;i++)
     {
         char s[]; int x,y,z;
         scanf("%s%d%d",s,&x,&y);
         if (s[]=='I') insert(x,y,rt,NULL);
         if (s[]=='D') del(x,y);
         if (s[]=='M')
         {
             scanf("%d",&z);
             add(x,y,z);
         }
         if (s[]=='Q') cout<<query(x,y)<<endl;
     }
 }