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=0;

struct node{
    int id,num;
    long long lazy,val,sum;
    node *left,*right,*father;
    node(int id_=0,long long val_=0,int num_=0,long long lazy_=0,long long sum_=0,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=1;
    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 = 0;
    }
}

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,1,0,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 0;
}

int main()
{
    int n;
    rt=NULL;
    scanf("%d",&n);
    insert(1<<30,0,rt,NULL); insert(-1<<30,0,rt,NULL);
    for (int i=1;i<=n;i++)
    {    
        char s[3]; int x,y,z;
        scanf("%s%d%d",s,&x,&y);
        if (s[0]=='I') insert(x,y,rt,NULL); 
        if (s[0]=='D') del(x,y);
        if (s[0]=='M')
        {
            scanf("%d",&z);
            add(x,y,z);
        }
        if (s[0]=='Q') cout<<query(x,y)<<endl;
    }
}