POJ 3155Hard Life(最大密度子图)

论文出处：最小割模型在信息学竞赛终的应用

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;

const double eps = 1e-9;
const int inf = 0x3f3f3f3f;
const int maxn = 100 + 5;
const int maxe = 1000 + 5;
struct edge{
    int to, next;
    double w;
} ed[maxe*10];
int head[maxn], tot;
int n, m, ans;
int sp, tp, degree[maxn], d[maxn];
struct E{
    int u, v;
}p[maxe];
bool vis[maxn];
inline void init(){
    memset( head, -1, sizeof(head) );
    tot = 1;
}

inline void add( int u, int v, double w ){
    ed[++tot].to = v; ed[tot].w = w; ed[tot].next = head[u]; head[u] = tot;
    ed[++tot].to = u; ed[tot].w = 0; ed[tot].next = head[v]; head[v] = tot;
}

inline bool bfs(){
    memset( d, 0, sizeof(d) );
    queue<int> q;
    d[sp] = 1;
    q.push(sp);
    while( q.size() ){
        int x = q.front();
        q.pop();
        for( int i=head[x]; ~i; i=ed[i].next ){
            int y = ed[i].to;
            if( ed[i].w>=eps && !d[y] ){
                d[y] = d[x] + 1;
                q.push(y);
                if( y==tp ) return 1;
            }
        }
    }
    return 0;
}

inline double dfs( int x, double flow ){
    if( x==tp ) return flow;
    double res = flow, k;
    for( int i=head[x]; ~i&&res>=eps; i=ed[i].next ){
        int y = ed[i].to;
        if( ed[i].w>=eps && d[y]==d[x]+1 ){
            k = dfs( y, min(res, ed[i].w) );
            if( k<eps ) d[y] = 0;
            ed[i].w -= k;
            ed[i^1].w += k;
            res -= k;
        }
    }
    return flow-res;
}


inline double check( double g ){
    init();
    for( int i=0; i<m; i++ ){
        add( p[i].u, p[i].v, 1 );
        add( p[i].v, p[i].u, 1 );
    }
    double U = m;
    for( int i=1; i<=n; i++ ){
        add( sp, i, U );
        add( i, tp, U+2*g-degree[i] );
    }
    double maxflow=0, flow;
    while( bfs() ){
        while( (flow=dfs(sp, inf))>=eps ) maxflow += flow;
    }
    return (U*n-maxflow)*0.5;
}

inline void find_cut( int x ){
    for( int i=head[x]; ~i; i=ed[i].next ){
        int y = ed[i].to;
        if( ed[i].w>=eps && !vis[y] ){
            vis[y] = 1;
            ans ++;
            find_cut(y);
        }
    }
}

int main(){
    // freopen("in.txt", "r", stdin);
    while(~scanf("%d%d", &n, &m)){
        if( !m ){
            puts("1\n1");
            continue;
        }
        memset( degree, 0, sizeof(degree) );
        memset( vis, 0, sizeof(vis) );
        sp = 0; tp = n+1;
        for( int i=0; i<m; i++ ){
            scanf("%d%d", &p[i].u, &p[i].v);
            degree[p[i].u] ++;
            degree[p[i].v] ++;
        }
        double l = 0, r = m;
        double tmp = 1.0/n/n;               //这里需要设定一个上界啊，不然WA，具体证明请看论文
        while( r-l>=tmp ){
            double mid = (l+r)*0.5;
            if( check(mid)<eps ) r = mid;
            else l = mid;
        }
        check(l);                       //保证精度
        vis[sp] = 1;
        find_cut(sp);
        printf("%d\n", ans);
        for( int i=1; i<=n; i++ ) if(vis[i]) printf("%d\n", i);
    }

    return 0;
}