BZOJ 4318(OSU!-立方的期望)

已知一个01数列，第i位为0的概率为 ai ,求这段01序列‘连续1’的立方和的期望

dp
令f(x)表示前x个的立方和的期望
f(x+1)=(1−ai)fx+aiE(fx+(li−1+1)3−l3i−1)=fx+E(3l2+3l+1)ai

#include <iostream>
#include <cmath>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <string>
#include <vector>
#include <map>
#include <functional>
#include <cstdlib>
#include <queue>
#include <stack>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=Pre[x];p;p=Next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=Next[p]) 
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (100000007)
#define pb push_back
#define mp make_pair 
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
typedef long long ll;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int read()
{
    int x=0,f=1; char ch=getchar();
    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
    return x*f;
} 
#define MAXN (100000+10)
double a[MAXN];
double f[MAXN],l[MAXN],l2[MAXN],ans[MAXN];
int main() {
    int n=read();
    f[0]=l[0]=l2[0]=ans[0]=0;
    For(i,n) {
        cin>>a[i];
        l[i]=(l[i-1]+1)*a[i];
        l2[i]=(l2[i-1]+2*l[i-1]+1)*a[i];
        ans[i]=ans[i-1]+a[i]*(3*l2[i-1]+3*l[i-1]+1);
    }
    printf("%.1lf\n",ans[n]);
    return 0;
}