概率DP合集
http://www.bnuoj.com/v3/contest_show.php?cid=7521#problem/D
根据kuangbin的概率DP集合刷的 Orz 感谢kuangbin巨巨
http://www.cnblogs.com/kuangbin/archive/2012/10/02/2710606.html
上边的blog已经总结的很好了…
剩下的题有些东西没学以后再补…
B.POJ 2096 Collecting Bugs
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
#include<math.h>
#include<queue>
#include<stack>
#include<string>
#include<vector>
#include<map>
#include<set>
using namespace std;
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define sfor(i,a,h) for(i=h[a];i!=-1;i=e[i].next)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
#define cheak(i) printf("%d ",i)
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define inf 0x3f3f3f3f
#define lowbit(x) (x&(-x))
typedef long long LL;
#define maxn 1005
#define f(x) (x*1.0)
#define maxm maxn*maxn
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
double dp[maxn][maxn];
int main()
{
int i,j,n,s;
scanf("%d%d",&n,&s);
dp[n][s]=0;
lfor(i,n,0)
{
lfor(j,s,0)
{
if(i==n&&j==s) continue;
double x=n*s*1.0,y=i*j*1.0;
//dp[i][j]=(1+dp[i+1][j]*(n-i)*j/x+dp[i][j+1]*i*(s-j)/x+dp[i+1][j+1]*(n-i)*(s-j)/x)/(1-i*j/x);
dp[i][j]=(1+dp[i+1][j]*(1.0-f(i)/f(n))*(f(j)/f(s))+dp[i][j+1]*(1.0-f(j)/f(s))*(f(i)/f(n))+dp[i+1][j+1]*(1.0-f(i)/f(n))*(1.0-f(j)/f(s)))/(1.0-y/x);
}
}
printf("%.4f\n",dp[0][0]);
return 0;
} C. ZOJ 3329 One Person Game
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 1005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
double dp[maxn],p[maxn],A[maxn],B[maxn];
int main()
{
int T,n,k1,k2,k3,a,b,c,i,j,k;
scanf("%d",&T);
while(T--)
{
scanf("%d%d%d%d%d%d%d",&n,&k1,&k2,&k3,&a,&b,&c);
mem(dp,0);mem(p,0);
double x=1.0/(1.0*k1*k2*k3);
rfor(i,1,k1)
rfor(j,1,k2)
rfor(k,1,k3)
if(i!=a||j!=b||k!=c)
p[i+j+k]+=x;
mem(A,0);mem(B,0);
lfor(i,n,0)
{
rfor(j,3,k1+k2+k3)
{
A[i]+=p[j]*A[i+j];
B[i]+=p[j]*B[i+j];
}
A[i]+=x;
B[i]++;
}
printf("%.15lf\n",B[0]/(1-A[0]));
}
return 0;
}D. HDU 4405 Aeroplane chess
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 100005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
double dp[maxn];
int fly[maxn];
int main()
{
int n,m,i,j,x,y;
while(~scanf("%d%d",&n,&m))
{
if(n==0&&m==0) break;
mem(fly,-1);mem(dp,0);
rfor(i,1,m)
{
scanf("%d%d",&x,&y);
fly[x]=max(fly[x],y);
}
double x=1.0/6.0;
lfor(i,n-1,0)
{
if(fly[i]==-1)
rfor(j,1,6)
{
dp[i]+=dp[i+j]*x;
}
else dp[i]=dp[fly[i]];
if(fly[i]==-1) dp[i]++;
}
printf("%.4f\n",dp[0]);
}
return 0;
}E. HDU 4089 Activation
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 2005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
/*
1 激活失败 留在队列中等待下一次激活（概率为p1)
2 失去连接 出队列 然后排在队列的最后（概率为p2）
3 激活成功 离开队列（概率为p3）
4 服务器瘫痪 服务器停止激活 所有人都无法激活了
*/
/*
if(j==1)
dp[i][1]=dp[i][1]*p1+dp[i][i]*p2+p4;
else if(j<=k)
dp[i][j]=dp[i][j]*p1+dp[i][j-1]*p2+dp[i-1][j-1]*p3+p4;
else
dp[i][j]=dp[i][j]*p1+dp[i][j-1]*p2+dp[i-1][j-1]*p3;
*/
/*
dp[i][j] i 个人 排在 j 1<=j<=i
a=p2/(1-p1) b=p3/(1-p1) c=p4/(1-p1)
if(j==1)
dp[i][1]=a*dp[i][i]+c;
else if(j<=k)
dp[i][j]=a*dp[i][j-1]+b*dp[i-1][j-1]+c;
else
dp[i][j]=a*dp[i][j-1]+b*dp[i-1][j-1];
*/
//dp[i][j]=sigma(dp[i][j]*a|1<=j<=i)+sigma(b*dp[i-1][j-1]+c)+j<=k?c:0;
int n,m,k;
double p1,p2,p3,p4,a,b,c;
double dp[maxn][maxn],A[maxn];
int main()
{
int i,j;
while(~scanf("%d%d%d%lf%lf%lf%lf",&n,&m,&k,&p1,&p2,&p3,&p4))
{
if(p4<(1e-10))
{
printf("0.00000\n");
continue;
}
a=p2/(1.0-p1),b=p3/(1.0-p1),c=p4/(1.0-p1);
//printf("%lf %lf %lf\n",a,b,c);
dp[1][1]=(p4)/(1-p1-p2);
rfor(i,2,n)
{
rfor(j,2,(i<=k?i:k))
A[j]=b*dp[i-1][j-1]+c;
rfor(j,k+1,i)
A[j]=b*dp[i-1][j-1];
double p=1,tmp=0;
lfor(j,i,2)
{
tmp+=p*A[j];
p*=a;
}
dp[i][i]=(tmp+c*p)/(1.0-p*a);
dp[i][1]=a*dp[i][i]+c;
rfor(j,2,i-1)
dp[i][j]=a*dp[i][j-1]+A[j];
}
printf("%.5f\n",dp[n][m]);
}
return 0;
}F. HDU 4035 Maze
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 10005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
vector<int>vec[maxn];
struct node
{
double die,out;
}A[maxn];
double dp[maxn],a[maxn],b[maxn],c[maxn];
int dfs(int u,int fa)
{
int Size=vec[u].size(),i;
a[u]=A[u].die;
b[u]=(1-A[u].die-A[u].out)/Size;
c[u]=1-A[u].die-A[u].out;
double tmp=0;
rfor(i,0,Size-1)
{
int v=vec[u][i];
if(v!=fa)
{
if(!dfs(v,u)) return 0;
a[u]+=(1-A[u].die-A[u].out)/f(Size)*a[v];
c[u]+=(1-A[u].die-A[u].out)/f(Size)*c[v];
tmp+=(1-A[u].die-A[u].out)/f(Size)*b[v];
}
}
if(fabs(tmp-1)<1e-9) return 0;
a[u]/=1-tmp;
b[u]/=1-tmp;
c[u]/=1-tmp;
return 1;
}
int main()
{
int o=0,T,i,n,u,v;
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
rfor(i,1,n) vec[i].clear();
rfor(i,1,n-1)
{
scanf("%d%d",&u,&v);
vec[u].push_back(v);
vec[v].push_back(u);
}
rfor(i,1,n)
{
scanf("%d %d",&u,&v);
A[i].die=f(u)/100.0;
A[i].out=f(v)/100.0;
}
printf("Case %d: ",++o);
if(dfs(1,0)&&fabs(1-a[1])>1e-9)
printf("%.6lf\n",c[1]/(1-a[1]));
else printf("impossible\n");
}
return 0;
}G. HDU 3853 LOOPS
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 1005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
double A[maxn][maxn],B[maxn][maxn],C[maxn][maxn];
double dp[maxn][maxn];
//不动 向右 向下
int main()
{
int i,j,n,m;
while(~scanf("%d%d",&n,&m))
{
rfor(i,1,n)
{
rfor(j,1,m)
{
scanf("%lf%lf%lf",&A[i][j],&B[i][j],&C[i][j]);
}
}
mem(dp,0);
dp[n][m]=0;
lfor(i,n,1)
{
lfor(j,m,1)
{
if(i==n&&j==m) continue;
if(A[i][j]==1.0) continue;
dp[i][j]=(dp[i+1][j]*C[i][j]+dp[i][j+1]*B[i][j]+2)/(1.0-A[i][j]);
}
}
printf("%.3f\n",dp[1][1]);
}
return 0;
} H POJ 2151 Check the difficulty of problems
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 1005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
// M道题 T个队
// i队解决j道题的概率
// 问冠军至少N道题&&每队AC一题概率==每队至少AC一道-每队AC都在1~N-1
//每队AC概率==(1-每道题都不AC)的乘积
// 每队AC一题的概率==(1-(1-p[i][j]))的乘积
double A[maxn][35],dp[maxn][35][35],p[maxn][35];
int main()
{
int i,j,k,m,t,n;
while(~scanf("%d%d%d",&m,&t,&n))
{
if(m==0&&t==0&&n==0) break;
rfor(i,1,t)
{
rfor(j,1,m)
scanf("%lf",&A[i][j]);
}
rfor(i,1,t)//第i个队
{
dp[i][0][0]=1.0;
double x=1;
rfor(j,1,m)//前j道题
{
x*=(1-A[i][j]);
dp[i][j][0]=x;
rfor(k,1,n)//解出k道题
dp[i][j][k]=dp[i][j-1][k-1]*A[i][j]+dp[i][j-1][k]*(1-A[i][j]);
}
}
/*rfor(i,1,t)
{
rfor(j,1,m)
printf("%lf ",dp[i][m][j]);
printf("\n");
}printf("\n");*/
double p1=1;
rfor(i,1,t)
{
double x=1;
rfor(j,1,m)
x*=(1-A[i][j]);
p1*=(1.0-x);
}
double p2=1;
rfor(i,1,t)
{
double x=0;
rfor(j,1,n-1)
x+=dp[i][m][j];
p2*=x;
}
printf("%.3lf\n",p1-p2);
}
return 0;
}I. Codeforces 148D Bag of mice
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 1005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
double dp[maxn][maxn];
int main()
{
int w,b,i,j;
while(~scanf("%d%d",&w,&b))
{
mem(dp,0);
rfor(i,1,w) dp[i][0]=1;
rfor(i,1,b) dp[0][i]=0;
rfor(i,1,w)
{
rfor(j,1,b)
{
dp[i][j]+=f(i)/f(i+j);
if(j>=3)
dp[i][j]+=f(j)/f(i+j)*f(j-1)/f(i+j-1)*f(j-2)/f(i+j-2)*dp[i][j-3];
if(i>=2)
dp[i][j]+=f(j)/f(i+j)*f(j-1)/f(i+j-1)*f(i)/f(i+j-2)*dp[i-1][j-2];
}
}
printf("%.9f\n",dp[w][b]);
}
return 0;
} J .POJ 3071 Football
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 505
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
double A[maxn][maxn],dp[8][maxn];
int main()
{
int i,j,k,n;
while(~scanf("%d",&n)&&n!=-1)
{
int m=1<<n;
rfor(i,1,m)
{
rfor(j,1,m)
{
scanf("%lf",&A[i][j]);
}
}
mem(dp,0);
rfor(i,1,m)
if(i%2) dp[1][i]=A[i][i+1];
else dp[1][i]=A[i][i-1];
rfor(i,2,n)
{
rfor(j,1,m)
{
int t=1<<i,pos=1;
while(j>=t+pos) pos+=t;
if(j<pos+t/2) pos+=t/2;//printf("%d %d %d\n",i,t,pos);
rfor(k,pos,pos+t/2-1)
dp[i][j]+=dp[i-1][k]*A[j][k]*dp[i-1][j];
}
}
//rfor(i,1,m) printf("%lf ",dp[n][i]);printf("\n");
int flag=1;
rfor(i,2,m)
if(dp[n][flag]<dp[n][i]) flag=i;
printf("%d\n",flag);
}
return 0;
}K. SGU 495 Kids and Prizes
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 100005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
//n-n*((n-1)/n)^m
int main()
{
double n,m;
while(~scanf("%lf%lf",&n,&m))
{
double ans;
ans=n-n*pow((n-1)/n,m);
printf("%.9lf\n",ans);
}
return 0;
}M. ZOJ 3640 Help Me Escape
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<math.h>
#include<string>
#include<vector>
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
#define maxn 20005
#define f(x) (x*1.0)
#define inf 0x3f3f3f3f
#define maxm maxn*maxn
#define min(a,b) (a>b?b:a)
#define max(a,b) (a>b?a:b)
#define lowbit(x) (x&(-x))
#define cheak(i) printf("%d ",i)
#define lson(x) (splay[x].son[0])
#define rson(x) (splay[x].son[1])
#define rfor(i,a,b) for(i=a;i<=b;++i)
#define lfor(i,a,b) for(i=a;i>=b;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#define mec(a,b) memcpy(a,b,sizeof(b))
const double tt=(1.0+sqrt(5.0))/2.0;
double dp[maxn];
int A[105];
int main()
{
int i,j,n,f;
while(~scanf("%d%d",&n,&f))
{
double x=f(1)/f(n);
rfor(i,1,n) scanf("%d",&A[i]);
sort(A+1,A+n+1);
mem(dp,0);
double t=0;
rfor(i,1,n)
{
int tmp=tt*A[i]*A[i];
t+=(double)tmp*x;
}
rfor(i,A[n]+1,A[n]*2) dp[i]=t;
lfor(i,A[n],f)
{
rfor(j,1,n)
{
if(i>A[j])
{
int tmp=tt*A[j]*A[j];
t=tmp*x;
dp[i]+=t;
}
else dp[i]+=(1+dp[i+A[j]])*x;
}
}
printf("%.3lf\n",dp[f]);
}
return 0;
}