loj2512 [BJOI2018]链上二次求和

传送门

分析

咕咕咕

代码

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cctype>
#include<cmath>
#include<cstdlib>
#include<queue>
#include<ctime>
#include<vector>
#include<set>
#include<map>
#include<stack>
using namespace std;
#define int long long
const int mod = 1e9+;
const int t = 5e8+;
int n,m,p[],pp[],d[],Ans,f1[],f2[];
int cola[],colb[],colc[];
inline void build(int le,int ri,int wh){
    if(le==ri){
      d[wh]=pp[le]*%mod;
      return;
    }
    int mid=(le+ri)>>;
    build(le,mid,wh<<);
    build(mid+,ri,wh<<|);
    d[wh]=(d[wh<<]+d[wh<<|])%mod;
}
inline int S(int le,int ri,int a,int b,int c){
    int res=c*(ri-le+)%mod+b*((f1[ri]-(le?f1[le-]:)+mod)%mod)%mod
              +a*((f2[ri]-(le?f2[le-]:)+mod)%mod)%mod;
    return res%mod;
}
inline void pd(int wh,int le,int mid,int ri){
    int a=cola[wh],b=colb[wh],c=colc[wh];
    if(!a&&!b&&!c)return;
    cola[wh<<]+=a,colb[wh<<]+=b,colc[wh<<]+=c;
    cola[wh<<]%=mod,colb[wh<<]%=mod,colc[wh<<]%=mod;
    d[wh<<]+=S(le,mid,a,b,c);
    d[wh<<]%=mod;
    cola[wh<<|]+=a,colb[wh<<|]+=b,colc[wh<<|]+=c;
    cola[wh<<|]%=mod,colb[wh<<|]%=mod,colc[wh<<|]%=mod;
    d[wh<<|]+=S(mid+,ri,a,b,c);
    d[wh<<|]%=mod;
    cola[wh]=colb[wh]=colc[wh]=;
}
inline void update(int le,int ri,int wh,int x,int y,int a,int b,int c){
    if(le>=x&&ri<=y){
      cola[wh]+=a,colb[wh]+=b,colc[wh]+=c;
      cola[wh]%=mod,colb[wh]%=mod,colc[wh]%=mod;
      d[wh]+=S(le,ri,a,b,c);
      d[wh]%=mod;
      return;
    }
    int mid=(le+ri)>>;
    pd(wh,le,mid,ri);
    if(mid>=x)update(le,mid,wh<<,x,y,a,b,c);
    if(mid<y)update(mid+,ri,wh<<|,x,y,a,b,c);
    d[wh]=(d[wh<<]+d[wh<<|])%mod;
}
inline int q(int le,int ri,int wh,int x,int y){
    if(le>=x&&ri<=y)return d[wh];
    int mid=(le+ri)>>,ans=;
    pd(wh,le,mid,ri);
    if(mid>=x)ans=(ans+q(le,mid,wh<<,x,y))%mod;
    if(mid<y)ans=(ans+q(mid+,ri,wh<<|,x,y))%mod;
    d[wh]=(d[wh<<]+d[wh<<|])%mod;
    return ans;
}
signed main(){
    int i,j,k;
    scanf("%lld%lld",&n,&m);
    for(i=;i<=n;i++)scanf("%lld",&p[i]),p[i]=(p[i]+p[i-])%mod;
    for(i=;i<=n;i++)pp[i]=(pp[i-]+p[i])%mod;
    for(i=;i<=n;i++)f1[i]=(f1[i-]+i)%mod,f2[i]=(f2[i-]+i*i)%mod;
    build(,n,);
    for(i=;i<=m;i++){
      scanf("%lld",&k);
      int le,ri,len,D;
      if(k==){
          scanf("%lld%lld%lld",&le,&ri,&D);
          if(le>ri)swap(le,ri);
          len=ri-le+;
          int a=D,b=(-*le%mod+mod)%mod*D%mod;
        int c=(le*le%mod-*le%mod++mod)%mod*D%mod;
          update(,n,,le,ri,a,b,c);
          if(ri==n)continue;
          a=,b=*len*D%mod,c=(len*(len+-*ri)%mod+mod)%mod*D%mod;
        update(,n,,ri+,n,a,b,c);
      }else {
          scanf("%lld%lld",&le,&ri);
          len=ri-le+;
          Ans=len*q(,n,,n,n)%mod;
          Ans=(Ans-q(,n,,le-,ri-)+mod)%mod;
        Ans=(Ans-q(,n,,n-ri,n-le)+mod)%mod;
          printf("%lld\n",Ans*t%mod);
      }
    }
    return ;
}