POJ 3155 Hard Life(最小割-最大密集子图)

题目链接:http://poj.org/problem?id=3155

题意：给定一个n个点m条边的无向图。输出最大密集子图中的顶点个数和各个顶点编号。

思路：二分答案g，原图中的边(u,v)连边<u,v,1>和<v,u,1>。s和每个点连边<s,i,m>,每个点和汇点连边<i,t,m+2*g-d[i]>。d[i]为每个点的度。

#include <iostream>

#include <stdio.h>

#include <string.h>

#include <algorithm>

#include <cmath>

#include <vector>

#include <queue>

#include <set>

#include <stack>

#include <string>

#include <map>





#define max(x,y) ((x)>(y)?(x):(y))

#define min(x,y) ((x)<(y)?(x):(y))

#define abs(x) ((x)>=0?(x):-(x))

#define i64 long long

#define u32 unsigned int

#define u64 unsigned long long

#define clr(x,y) memset(x,y,sizeof(x))

#define CLR(x) x.clear()

#define ph(x) push(x)

#define pb(x) push_back(x)

#define Len(x) x.length()

#define SZ(x) x.size()

#define PI acos(-1.0)

#define sqr(x) ((x)*(x))

#define MP(x,y) make_pair(x,y)

#define EPS 1e-9



#define FOR0(i,x) for(i=0;i<x;i++)

#define FOR1(i,x) for(i=1;i<=x;i++)

#define FOR(i,a,b) for(i=a;i<=b;i++)

#define FORL0(i,a) for(i=a;i>=0;i--)

#define FORL1(i,a) for(i=a;i>=1;i--)

#define FORL(i,a,b)for(i=a;i>=b;i--)

using namespace std;





void RD(int &x){scanf("%d",&x);}

void RD(u32 &x){scanf("%u",&x);}

void RD(double &x){scanf("%lf",&x);}

void RD(int &x,int &y){scanf("%d%d",&x,&y);}

void RD(u32 &x,u32 &y){scanf("%u%u",&x,&y);}

void RD(double &x,double &y){scanf("%lf%lf",&x,&y);}

void RD(int &x,int &y,int &z){scanf("%d%d%d",&x,&y,&z);}

void RD(int &x,int &y,int &z,int &t){scanf("%d%d%d%d",&x,&y,&z,&t);}

void RD(u32 &x,u32 &y,u32 &z){scanf("%u%u%u",&x,&y,&z);}

void RD(double &x,double &y,double &z){scanf("%lf%lf%lf",&x,&y,&z);}

void RD(char &x){x=getchar();}

void RD(char *s){scanf("%s",s);}

void RD(string &s){cin>>s;}





void PR(int x) {printf("%d\n",x);}

void PR(int x,int y) {printf("%d %d\n",x,y);}

void PR(i64 x) {printf("%lld\n",x);}

void PR(u32 x) {printf("%u\n",x);}

void PR(double x) {printf("%.5lf\n",x);}

void PR(char x) {printf("%c\n",x);}

void PR(char *x) {printf("%s\n",x);}

void PR(string x) {cout<<x<<endl;}





const int INF=1000000000;

const int N=100005;









struct Edge

{

	int u,v;

	double cap,flow;

	int next;

};



Edge edges[30000];

int head[105],e,visit[105];

int n,m,s,t;

int a[1005],b[1005],d[105];

int num[105],h[105],curedge[105],pre[105];

int ans[105];





void add(int u,int v,double cap)

{

	edges[e].u=u;

	edges[e].v=v;

	edges[e].cap=cap;

	edges[e].flow=0.0;

	edges[e].next=head[u];

	head[u]=e++;

}



void Add(int u,int v,double cap)

{

	add(u,v,cap);

	add(v,u,0.0);

}



void init(double mid)

{

	int i;

	clr(head,-1); e=0;

	FOR1(i,m)

	{

		Add(a[i],b[i],1.0);

		Add(b[i],a[i],1.0);

	}

	FOR1(i,n)

	{

		Add(s,i,1.0*m);

		Add(i,t,m+2*mid-d[i]);

	}

}







double Maxflow(int s,int t)

{

	double maxflow=0,d;

	int i,k,x,u;



	memset(num,0,sizeof(num));

	memset(h,0,sizeof(h));

	for(i=0;i<=t;i++) curedge[i]=head[i];

	num[n]=n;u=s;

	while(h[s]<n)

	{

		if(u==t)

		{

			for(d=INF+1,i=s;i!=t;i=edges[curedge[i]].v)if(d>edges[curedge[i]].cap)

				k=i,d=edges[curedge[i]].cap;

			for(i=s;i!=t;i=edges[curedge[i]].v)

			{

				x=curedge[i];

				edges[x].cap-=d;

				edges[x].flow+=d;

				edges[x^1].cap+=d;

				edges[x^1].flow-=d;

			}

			maxflow+=d;u=k;

		}

		for(i=curedge[u];i!=-1;i=edges[i].next)if(edges[i].cap>0&&h[u]==h[edges[i].v]+1)

			break;

		if(i!=-1)

		{

			curedge[u]=i;

			pre[edges[i].v]=u;

			u=edges[i].v;

		}

		else

		{

			if(0==--num[h[u]]) break;

			curedge[u]=head[u];

			for(x=n,i=head[u];i!=-1;i=edges[i].next) if(edges[i].cap>0)

				x=min(x,h[edges[i].v]);

			h[u]=x+1;num[h[u]]++;

			if(u!=s) u=pre[u];

		}

	}

	return maxflow;

}



void DFS(int u)

{

	int i;

	visit[u]=1;

	if(u!=s) ans[++ans[0]]=u;

	for(i=head[u];i!=-1;i=edges[i].next)

	{

	    if(edges[i].cap>1e-8&&!visit[edges[i].v])

		{

		    DFS(edges[i].v);

		}

	}

}





double calMaxDensity(int s,int t)

{

	double low,high,mid,flow;



	low=0.0;high=1.0*m;

	while(high-low>=1.0/n/n)

	{

		mid=(low+high)/2;

		init(mid);

		flow=Maxflow(s,t);

		flow=(1.0*m*n-flow)/2;

		if(flow>1e-8) low=mid;

		else high=mid;

	}

	init(low); Maxflow(s,t);clr(visit,0);

	ans[0]=0;DFS(s); sort(ans+1,ans+ans[0]+1);

	return low;

}





int main()

{

	while(scanf("%d%d",&n,&m)!=EOF)

	{

	    int i;

	    clr(d,0);

	    FOR1(i,m)

	    {

	        RD(a[i],b[i]);

	        d[a[i]]++;

	        d[b[i]]++;

        }

        if(!m)

        {

            puts("1"); puts("1");

            continue;

        }

        s=0;t=n+1;

        calMaxDensity(s,t);

        PR(ans[0]);

        FOR1(i,ans[0]) PR(ans[i]);

	}

	return 0;

}