#6122. 「网络流 24 题」航空路线问题

#include<iostream>
#include<cstdio>
#include<cstring>
#include<map>
#include<queue>
#define maxn 110
using namespace std;
int dis[maxn],head[maxn],n,m,S,T,num=1,ans;
bool v[maxn],vis[maxn];
map<string,int>p;
struct node{int to,pre,v,w;}e[maxn*maxn];
struct Node{int e,v;}pre[maxn*maxn];
string pp[maxn],s1,s2;
void Insert(int from,int to,int v,int w){e[++num].to=to;e[num].v=v;e[num].w=w;e[num].pre=head[from];head[from]=num;e[++num].to=from;e[num].v=0;e[num].w=-w;e[num].pre=head[to];head[to]=num;
}
bool spfa(int x){memset(dis,0,sizeof(dis));memset(vis,0,sizeof(vis));queue<int>q;q.push(x);vis[x]=1;while(!q.empty()){int now=q.front();q.pop();vis[now]=0;for(int i=head[now];i;i=e[i].pre){int to=e[i].to;if(e[i].v>0&&dis[now]+e[i].w>dis[to]){dis[to]=dis[now]+e[i].w;pre[to].e=i;pre[to].v=now;if(!vis[to]){vis[to]=1;q.push(to);}}}}return dis[T];
}
int max_flow(int f){int res=0,d;while(f){if(!spfa(S))return -1;d=f;for(int i=T;i!=S;i=pre[i].v)d=min(e[pre[i].e].v,d);res+=d*dis[T];f-=d;for(int i=T;i!=S;i=pre[i].v){e[pre[i].e].v-=d;e[pre[i].e^1].v+=d;}}return res;
}
int main(){scanf("%d%d",&n,&m);S=1,T=n*2;for(int i=1;i<=n;i++){cin>>pp[i];p[pp[i]]=i;}for(int i=1;i<=m;i++){cin>>s1>>s2;int a1=p[s1],a2=p[s2];if(a1>a2)swap(a1,a2);if(a1==1&&a2==n)Insert(a1+n,a2,2,0);else Insert(a1+n,a2,1,0);}Insert(S,1+n,2,1);Insert(n,T,2,1);for(int i=2;i<n;i++)Insert(i,i+n,1,1);ans=max_flow(2);if(ans<0){puts("No Solution!");return 0;}printf("%d\n",ans-2);cout<<pp[1]<<endl;for(int i=head[S+n];i;i=e[i].pre)if(!e[i].v&&!(i&1)){int to=e[i].to;while(to){cout<<pp[to]<<endl;v[to]=1;int j;for(j=head[to+n],to=0;j;j=e[j].pre)if(!e[j].v&&!(j&1)){to=e[j].to;break;}}break;}for(int i=head[T-n];i;i=e[i].pre)if(!e[i^1].v&&(i&1)&&!v[e[i].to-n]){int to=e[i].to-n;while(to){cout<<pp[to]<<endl;v[to]=1;int j;for(j=head[to],to=0;j;j=e[j].pre)if(!e[j^1].v&&(j&1)){to=e[j].to-n;break;}}break;}
}