NOI模拟 奥义商店【分块+概率dp】

题目描述：

解题思路：

#include<bits/stdc++.h>
#define ll long long
using namespace std;
int getint()
{
    int i=0,f=1;char c;
    for(c=getchar();(c!='-')&&(c<'0'||c>'9');c=getchar());
    if(c=='-')c=getchar(),f=-1;
    for(;c>='0'&&c<='9';c=getchar())i=(i<<3)+(i<<1)+c-'0';
    return i*f;
}
const int N=100005,S=300;
int n,m,a[N],sum[S][S];
double p[S];
int query1()
{
    int res=0,k=getint(),d=getint();getint();
    if(d<S)return sum[d][k%d];
    else
    {
        for(int i=k;i>=1;i-=d)res+=a[i];
        for(int i=k+d;i<=n;i+=d)res+=a[i];
    }
    return res;
}
double query2(int t)
{
    int k=getint(),d=getint(),c=N;
    for(int i=1;i<=t;i++)c=min(c,getint());
    p[0]=1;int L=min(100,c);
    for(int i=1;i<=L;i++)p[i]=p[i-1]*(c-i+1)/(n-i);
    double res=0;
    for(int i=0;i<=L&&k-i*d>=1;i++)res+=a[k-i*d]*p[i];
    for(int i=1;i<=L&&k+i*d<=n;i++)res+=a[k+i*d]*p[i];
    return res;
}
int main()
{
    freopen("lzz.in","r",stdin);
    freopen("lzz.out","w",stdout);
    n=getint(),m=getint();
    for(int i=1;i<=n;i++)
    {
        a[i]=getint();
        for(int j=1;j<S;j++)sum[j][i%j]+=a[i];
    }
    while(m--)
    {
        int op=getint();
        if(op==1)
        {
            int i=getint(),x=getint();
            for(int j=1;j<S;j++)sum[j][i%j]+=x-a[i];
            a[i]=x;
        }
        else
        {
            int t=getint();
            if(t==1)printf("%0.4lf\n",(double)query1());
            else printf("%0.4lf\n",query2(t));
        }
    }
    return 0;
}