【网络流24题-11】洛谷P2770 航空路线问题

https://www.luogu.org/problemnew/show/P2770
建图方法：$s$到$1$容量为2，费用为0，$n^{\prime }$到$t$容量为2，费用为0，$1->1^{\prime }和n->n^{\prime }$容量为2，费用为-1，其余$x->x^{\prime }$容量为1，费用为-1，再连接航线即可。

#include
using namespace std;
const int maxn=100*2+100;
const int INF=0x3f3f3f3f;
typedef long long ll;

struct Edge{
	int from,to,cap,flow,cost;
};

struct MCMF{
	int n,m,s,t;
	vector<Edge> edges;
	vector<int> G[maxn];
	int inq[maxn];
	ll d[maxn];
	int p[maxn];
	int a[maxn];
	map<string,int> city;
	map<int,string> city2;
	bool linked;

	void init()
	{
		int m0;
		string str,str2;
		cin>>n>>m0;
		s=0,t=1;
		AddEdge(s,1*2,2,0);
		AddEdge(n*2+1,t,2,0);
		for(int i=1;i<=n;i++)
		{
			cin>>str;
			city[str]=i;
			city2[i]=str;
			AddEdge(i*2,i*2+1,i==1||i==n?2:1,-1);
		}
		for(int i=1;i<=m0;i++)
		{
			cin>>str>>str2;
			int from=city[str],to=city[str2];
			if(from>to)swap(from,to);
			if(from==1&&to==n)linked=1;
			AddEdge(from*2+1,to*2,1,0);
		}
	}

	void AddEdge(int from,int to,int cap,int cost)
	{
		edges.push_back((Edge){from,to,cap,0,cost});
		edges.push_back((Edge){to,from,0,0,-cost});
		m=edges.size();
		G[from].push_back(m-2);
		G[to].push_back(m-1);
	}

	bool BellmanFord(int& flow,int& cost)
	{	
		for(int i=0;i<=2*n+1;i++)d[i]=INF;
		memset(inq,0,sizeof(inq));
		d[s]=0;inq[s]=1;p[s]=0;a[s]=INF;

		queue<int> Q;
		Q.push(s);
		while(!Q.empty())
		{
			int u=Q.front();Q.pop();
			inq[u]=0;
			for(int i=0;i<G[u].size();i++)
			{
				Edge& e=edges[G[u][i]];
				if(e.cap>e.flow && d[e.to]>d[u]+e.cost)
				{
					d[e.to]=d[u]+e.cost;
					p[e.to]=G[u][i];
					a[e.to]=min(a[u],e.cap-e.flow);
					if(inq[e.to]==0){inq[e.to]=1;Q.push(e.to);}
				}
			}
		}
		if(d[t]==INF)return false;
		flow+=a[t];
		cost+=a[t]*d[t];	
		int u=t;
		while(u!=s)
		{
			edges[p[u]].flow+=a[t];
			edges[p[u]^1].flow-=a[t];
			u=edges[p[u]].from;
		}
		return true;
	}

	int Mincost()
	{
		int flow=0,cost=0;
		while(BellmanFord(flow,cost));
		if(flow!=2)
		{
			if(linked)
			{
				cout<<2<<"\n";
				cout<<city2[1]<<"\n"<<city2[n]<<"\n"<<city2[1]<<"\n";
				exit(0);
			}
			puts("No Solution!");
			exit(0);
		}
		return cost;
	}

	void print(int cost)
	{
		cout<<cost<<endl;
		int nxt[maxn]={0},nxt2[maxn]={0};
		for(int i=0;i<m;i+=2)
		{
			int from=edges[i].from,to=edges[i].to,flow=edges[i].flow;
			if(from==s||from==t||to==s||to==t||from/2==to/2||flow==0)continue;
			if(!nxt[from/2])nxt[from/2]=to/2;
			else nxt2[from/2]=to/2;
		}		
		int u=1;
		while(u!=n)
		{
			cout<<city2[u]<<"\n";
			u=nxt[u];
		}
		stack<string> stk;
		stk.push(city2[1]);
		u=nxt2[1];
		while(u)
		{
			stk.push(city2[u]);
			u=nxt[u];
		}
		while(!stk.empty())cout<<stk.top()<<"\n",stk.pop();
	}
}ans;

int main()
{
	//freopen("input.in","r",stdin);
	ans.init();
	int cost=-ans.Mincost()-2;
	ans.print(cost);
	return 0;
}