# "Codeforces 261B" Maxim and Restaurant (DP, expected)

Source: Internet
Author: User

The first solution is $o (n^3*p)$:
F[i][j][k] indicates that the first I person into J individual length of K has several schemes (arranged fixed to 123). N).
$f [i][j][k]=f[i-1][j][k]+f[i-1][j-1][k-a[i]]$
The outermost enumeration T represents the person being stuck. I=t not add f[i-1][j-1][k-a[i]].
$ans ={{(\sum f[n][j][k]*j*j!* (N-1-J)!) + (\sum f[n][n][k]*n)}}/(n!)$

< Span class= "Mjx-char mjxc-tex-main-r" >< Span class= "Mjx-char mjxc-tex-math-i" > < Span class= "MJX_ASSISTIVE_MATHML" >
to see this

#include <cstdio> #include <cstring> #define N 55int n,p,a[n];d ouble f[n][n][n],ans,c[n]= {1};int main () {    scanf ("%d", &n);    for (int i=1; i<=n; i++) {        scanf ("%d", &a[i]);        c[i]=c[i-1]*i;    }    scanf ("%d", &p);    for (int t=0; t<=n; t++) {        memset (f,0,sizeof f);        F[0][0][0]=1;        for (int i=1, i<=n; i++) for            (int j=0; j<=i; j + +) for                (int k=0; k<=p; k++) {                    f[i][j][k]=f[i-1][j][k ];                    if (J>=1&&t!=i&&k>=a[i]) f[i][j][k]+=f[i-1][j-1][k-a[i]];                }        for (int j=1; j<n; j + +) for            (int k=1; k<=p; k++) if (a[t]+k>p)                ans+=c[j]*c[n-1-j]/c[n]*f[n][j][k]*j;        for (int k=1; k<=p; k++) ans+=f[n][n][k]*n;    }    printf ("%lf", ans);}

can also be more efficient, $O (N^2*P)$
Reference

F[i][j][k] represents the first I person at least into J personal This J person's length and for K has several schemes (ranked as 123). N).
So $ans= (\sum f[n][j][k]*j!* (n-j)!/(n!)$

I didn't quite understand why at least J was such a push, asked the next teammate, said because there is no card behind, so it is possible to enter more people.
In fact, the first method of F is also at least J person, and then add ans in the back when the third j+1 person.

And you can use a scrolling array to optimize to a 2-D array.

#include <cstdio> #define N 51int n,a[n],p;double fac[n]= {1},f[n][n],tol,ans;int main () {    scanf ("%d", &n) ;    for (int i=1; i<=n; i++)    {        scanf ("%d", a+i);        Fac[i]=fac[i-1]*i;        Tol+=a[i];    }    scanf ("%d", &p);    if (tol<=p)    {        printf ("%d", n);        return 0;    }    F[0][0]=1;    for (int i=1, i<=n; i++) for        (int. j=n-1; j>=0; j--) for            (int k=0; k+a[i]<=p; k++)                f[j+1][k+a[i]]+= F[J][K];    for (int j=1; j<=n; j + +) for        (int k=0; k<=p; k++)            ans+=f[j][k]*fac[j]*fac[n-j];    Ans/=fac[n];    printf ("%lf", ans);}

"Codeforces 261B" Maxim and Restaurant (DP, expected)

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