BZOJ 4318(OSU!-立方的期望)

来源：互联网发布：移动宽带网络设置编辑：程序博客网时间：2024/04/30 02:42

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;}

0 0