3188: [Coci 2011]Upit splay

splay，对于区间加等差数列的操作，我们可以发现等差数列的首项和公差是可以分开考虑并且可叠加的。那么就打标记就好了。

#include<iostream>
#include<cstdio>
using namespace std;

const int N=200005;
int n,Q,t1,t2,tot,root;
int fa[N],tree[N][2];
long long size[N],sum[N],tag[N][4],val[N];

inline long long read()
{
    long long a=0,f=1; char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1; c=getchar();}
    while (c>='0'&&c<='9') {a=a*10+c-'0'; c=getchar();}
    return a*f;
}

inline void modify(int k,long long x)
{
    tag[k][0]=1; tag[k][1]=x; 
    tag[k][2]=0; tag[k][3]=0;
    sum[k]=size[k]*x; val[k]=x;
}

inline void update(int k,long long y,long long z)
{
    tag[k][2]+=y; tag[k][3]+=z;
    val[k]+=y+size[tree[k][0]]*z;
    sum[k]+=size[k]*y+size[k]*(size[k]-1)/2ll*z;
}

inline void pushup(int k)
{
    sum[k]=sum[tree[k][0]]+sum[tree[k][1]]+val[k];
    size[k]=size[tree[k][0]]+size[tree[k][1]]+1;
}

inline void pushdown(int k)
{
    if (tag[k][0])
    {
        modify(tree[k][0],tag[k][1]);
        modify(tree[k][1],tag[k][1]);
        tag[k][0]=0;
    }
    if (tag[k][2]||tag[k][3])
    {
        update(tree[k][0],tag[k][2],tag[k][3]);
        update(tree[k][1],tag[k][2]+tag[k][3]*(size[tree[k][0]]+1),tag[k][3]);
        tag[k][2]=tag[k][3]=0;
    }
}

inline void rotate(int x,int &k)
{
    int y=fa[x],z=fa[y],l=tree[y][1]==x,r=l^1;
    if (y==k) k=x; else tree[z][tree[z][1]==y]=x;
    fa[x]=z; fa[y]=x; fa[tree[x][r]]=y;
    tree[y][l]=tree[x][r]; tree[x][r]=y;
    pushup(y); pushup(x);
}

inline void splay(int x,int &k)
{
    while (x!=k)
    {       
        int y=fa[x],z=fa[y];
        if (y!=k)
        {
            if (tree[y][0]==x^tree[z][0]==y) rotate(x,k); else rotate(y,k);
        }
        rotate(x,k);
    }
}

int find(int k,int x)
{
    pushdown(k);
    if (size[tree[k][0]]+1==x) return k;
    else if (size[tree[k][0]]+1>x) return find(tree[k][0],x);
    else return find(tree[k][1],x-size[tree[k][0]]-1);
}

inline void split(int x,int y)
{
    t1=find(root,x); t2=find(root,y);
    splay(t1,root); splay(t2,tree[t1][1]);
}

void build(int l,int r,int f)
{
    if (l>r) return;
    int mid=l+r>>1;
    fa[mid]=f; tree[f][mid>f]=mid;
    if (l==r) {sum[mid]=val[mid]; size[mid]=1; return;}
    build(l,mid-1,mid); build(mid+1,r,mid);
    pushup(mid);
}

int main()
{
//  freopen("txt.in","r",stdin);
//  freopen("my.out","w",stdout);

    n=read(); Q=read();
    for (int i=2;i<=n+1;i++) val[i]=read();
    root=(n+3)>>1; tot=n+2;
    build(1,n+2,0);
    while (Q--)
    {
        int opt=read();
        long long z;
        if (opt==3)
        {
            int x=read();
            split(x,x+1);
            tree[t2][0]=++tot;
            fa[tot]=t2;
            val[tot]=sum[tot]=read();
            size[tot]=1;
        }
        else
        {
            int x=read(),y=read();
            split(x,y+2);
            if (opt==1) modify(tree[t2][0],read());
            else if (opt==4) printf("%lld\n",sum[tree[t2][0]]);
            else z=read(),update(tree[t2][0],z,z);
        }
        pushup(t2); pushup(t1);
    }
    return 0;
}