poj1737

Connected Graph

POJ - 1737

An undirected graph is a set V of vertices and a set of E∈{V*V} edges.An undirected graph is connected if and only if for every pair (u,v) of vertices,u is reachable from v. 
You are to write a program that tries to calculate the number of different connected undirected graph with n vertices. 
For example,there are 4 different connected undirected graphs with 3 vertices. 

Input

The input contains several test cases. Each test case contains an integer n, denoting the number of vertices. You may assume that 1<=n<=50. The last test case is followed by one zero.

Output

For each test case output the answer on a single line.

Sample Input

1
2
3
4
0

Sample Output

1
1
4
38

题意：求n个点的联通图个数

sol：就是所有图-不连通的个数，令P[i]表示i个点的图的所有情况，那么P[i]=2i*(i-1)/2，Ans[i]表示答案
枚举j∑(1,i-1)表示节点1所在的联通块大小，Ans[i]=P[i]-Ans[j]*C(i-1,j-1)*P[i-j]

#include <string>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef int ll;
inline ll read()
{
    ll s=; bool f=; char ch=' ';
    while(!isdigit(ch)) {f|=(ch=='-'); ch=getchar();}
    while(isdigit(ch)) {s=(s<<)+(s<<)+(ch^); ch=getchar();}
    return (f)?(-s):(s);
}
#define R(x) x=read()
inline void write(ll x)
{
    if(x<) {putchar('-'); x=-x;}
    if(x<) {putchar(x+''); return;}
    write(x/); putchar((x%)+'');
}
#define W(x) write(x),putchar(' ')
#define Wl(x) write(x),putchar('\n')
const int power=,Base=;
struct Int
{
    int a[];
    Int() {memset(a,,sizeof a);}
    Int(int x)
    {
        memset(a,,sizeof a);
//        cout<<"x="<<x<<endl;
        while(x>)
        {
            a[++a[]]=x%Base; x/=Base;
        }
    }
    inline void print()
    {
        int i;
        write(a[a[]]);
        for(i=a[]-;i>=;i--)
        {
            if(a[i]<) putchar('');
            if(a[i]<) putchar('');
            if(a[i]<) putchar('');
            write(a[i]);
        }
    }
}Bin[],C[][],Ans[];
#define P(x) x.print(),putchar(' ')
#define Pl(x) x.print(),putchar('\n')
inline Int operator+(Int p,Int q)
{
    int i; Int res=p; res.a[]=max(p.a[],q.a[]);
    for(i=;i<=q.a[];i++)
    {
        res.a[i]+=q.a[i];
        res.a[i+]+=res.a[i]/Base;
        res.a[i]%=Base;
    }
    while(res.a[res.a[]+]) res.a[]++;
    return res;
}
inline Int operator-(Int p,Int q)
{
    int i; Int res=p;
    for(i=;i<=q.a[];i++)
    {
        res.a[i]-=q.a[i];
        if(res.a[i]<)
        {
            res.a[i+]--; res.a[i]+=Base;
        }
    }
    while(!res.a[res.a[]]) res.a[]--;
    return res;
}
inline Int operator*(Int p,int q)
{
    int i; Int res=p;
    for(i=;i<=res.a[];i++) res.a[i]*=q;
    for(i=;i<=res.a[];i++)
    {
        res.a[i+]+=res.a[i]/Base; res.a[i]%=Base;
    }
    while(res.a[res.a[]+])
    {
        res.a[]++; res.a[res.a[]+]+=res.a[res.a[]]/Base; res.a[res.a[]]%=Base;
    }
    return res;
}
inline Int operator*(Int p,Int q)
{
    int i,j; Int res; res.a[]=p.a[]+q.a[];
    for(i=;i<=p.a[];i++) for(j=;j<=q.a[];j++)
    {
        res.a[i+j-]+=p.a[i]*q.a[j];
        res.a[i+j]+=res.a[i+j-]/Base;
        res.a[i+j-]%=Base;
    }
    while(!res.a[res.a[]]) res.a[]--;
    return res;
}
int main()
{
//    freopen("data.in","r",stdin);
    int i,j,n;
    Bin[]=Int(); for(i=;i<=;i++) Bin[i]=Bin[i-]*;
//    for(i=1;i<=32;i++) Pl(Bin[i]);
    C[][]=Int();
    for(i=;i<=;i++)
    {
        C[i][]=Int();
        for(j=;j<=i;j++) C[i][j]=C[i-][j]+C[i-][j-];
    }
//    for(i=0;i<=4;i++)
//    {
//        for(j=0;j<=i;j++) P(C[i][j]);
//        puts("");
//    }
    Ans[]=Int();
    for(i=;i<=;i++)
    {
        Ans[i]=Bin[i*(i-)/];
        for(j=;j<i;j++)
        {
            Ans[i]=Ans[i]-Ans[j]*C[i-][j-]*Bin[(i-j)*((i-j)-)/];
        }
    }
    for(;;)
    {
        R(n); if(n==) break; Pl(Ans[n]);
    }
    return ;
}
/*
input
1
2
3
4
0
output
1
1
4
38
*/