poj3155【分數規劃】

我是薩比

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

int n,m;
int ans[110];
int hehe;

int U[1010],V[1010],d[1010];
bool vis[110];

struct edge {
	int v,next;
	double f;
}e[3010];
int cnt,head[110];

int gap[110],h[110];

int read_int () {
	char c = getchar();
	int re = 0;
	for(;c > '9' || c < '0';c = getchar());
	for(;c >= '0' && c <= '9';c = getchar())
		re = re * 10 + c - '0';
	return re;
}

void adde (int u,int v,double f) {
	e[++cnt].v = v;
	e[cnt].f = f;
	e[cnt].next = head[u];
	head[u] = cnt;
}

double dfs (int u,double minf) {
	if(u == n + 1)
		return minf;
	
	int chan = n + 1;
	double leftf = minf;
	
	for(int i = head[u];i != -1;i = e[i].next) {
		int v = e[i].v;
		
		if(e[i].f) {
			if(h[v] == h[u] - 1) {
				double t = dfs(v,min(leftf,e[i].f));
				e[i].f -= t;
				e[i ^ 1].f += t;
				leftf -= t;
				
				if(h[0] >= n + 2)
					return minf - leftf;
				if(!leftf)
					 break;
			}
			chan = min(chan,h[v]);
		}
	}
	
	if(leftf == minf) {
		if(--gap[h[u]] == 0)
			h[0] = n + 2;
		++gap[h[u] = chan + 1];
	}
	return minf - leftf;
}

bool work (double k) {
	cnt = -1;
	memset(head,-1,sizeof head);
	
	for(int i = 1;i <= n;++i) {
		adde(0,i,m);
		adde(i,0,0);
		adde(i,n + 1,k * 2 - d[i] + m);
		adde(n + 1,i,0);
	}
	for(int i = 1;i <= m;++i) {
		adde(U[i],V[i],1);
		adde(V[i],U[i],1);
	}
	
	memset(gap,0,sizeof gap);
	memset(h,0,sizeof h);
	gap[0] = n + 2;
	double re = 0;
	while(h[0] < n + 2)
		re += dfs(0,0x3f3f3f3f);
	
	re -= n * m;
	re *= -1;
	
	if(re == 0)
		return 1;
	return 0;
}

void dfs1 (int u) {
	vis[u] = 1;
	if(u >= 1 && u <= n)
		ans[++hehe] = u;
	
	for(int i = head[u];i != -1;i = e[i].next) {
		int v = e[i].v;
		
		if(e[i].f && !vis[v])
			dfs1(v);
	}
}

int main () {
	n = read_int();
	m = read_int();
	if(m == 0) {
		printf("1\n1\n");
		return 0;
	}	
	for(int i = 1;i <= m;++i) {
		U[i] = read_int();
		V[i] = read_int();
		++d[U[i]];
		++d[V[i]];
	}
	
	double l = 0,r = m,mid;
	while(r - l >= 1.0 / (n * n)) {
		mid = (l + r) / 2;
		if(work(mid))
			r = mid;
		else l = mid;
	}
	
	work(l);

	dfs1(0);
	sort(ans + 1,ans + 1 + hehe);
	printf("%d\n",hehe);
	for(int i = 1;i <= hehe;++i)
		printf("%d\n",ans[i]);
}