线性规划与网络流24——航空路线问题

题目链接点这里

，，最大权不相交路径问题，，网络流24题中，，有3,4道这个类型的吧，，，

#include<iostream>
#include<map>
#include<stdio.h>
#include<algorithm>
#include<queue>
#include<set>
#include<string.h>
#include<string>
#include<vector>
#define MX 1111
#define INF 0x3f3f3f3f
#define mem(x,y) memset(x,y,sizeof(x))
#define FIN freopen("input.txt","r",stdin)
using namespace std;
int n,m,k;
int s,t;
int head[MX],rear;
struct Edge
{
int nxt,to,cap,cost;
} edge[MX*11];
void edge_init()
{
mem(head,-1);
rear=0;
}
void edge_add(int a,int b,int cap,int cost)
{
//cout<<a<<" "<<b<<endl;
edge[rear].cost=cost;
edge[rear].cap=cap;
edge[rear].nxt=head[a];
edge[rear].to=b;
head[a]=rear++;
}
int dis[MX],pre[MX]; //储存前驱顶点
bool vis[MX];
bool spfa(int s, int t)
{
mem(dis,0x3f);
mem(vis,0);
mem(pre,-1);
deque<int>q;
q.push_back(s);
dis[s]=0,vis[s]=1;
while (!q.empty())
{
int u = q.front();
q.pop_front();
vis[u] = 0;
for (int i= head[u]; ~i; i=edge[i].nxt)
{
int v=edge[i].to;
if (edge[i].cap&& dis[v]>dis[u]+edge[i].cost)
{
dis[v]=dis[u]+edge[i].cost;
pre[v] = i;
if (!vis[v])
{
vis[v]=1;
if(!q.empty()&&dis[v]<=dis[q.front()])q.push_front(v);//SLF优化
else q.push_back(v);
}
}
}
}
if (pre[t]==-1) return 0;
else return 1;
}
//返回的是最大流， cost存的是最小费用
int MCMF(int s,int t,int &cost)
{
int flow = 0;
cost = 0;
while (spfa(s, t))
{

int Min = INF;
for (int i = pre[t]; i != -1; i = pre[edge[i ^ 1].to])
if (Min > edge[i].cap) Min = edge[i].cap;
for (int i = pre[t]; i != -1; i = pre[edge[i ^ 1].to])
edge[i].cap -= Min,edge[i ^ 1].cap += Min;
cost += dis[t]* Min;
flow+=Min;
}
return flow;
}
string ss[111];
void dfs(int u,vector<int> &ans)
{
u=u-n;
ans.push_back(u);
for(int i=head[u]; ~i; i=edge[i].nxt)
{
int v=edge[i].to;
if(edge[i].cap)
{
dfs(v,ans);
}
}
}

int main()
{
FIN;
while(~scanf("%d%d",&n,&m))
{
map<string,int> stoi;
edge_init();
s=1,t=2*n;
for(int i=1; i<=n; i++)
{
string s;
cin>>s;
stoi[s]=i;
ss[i]=s;
}
edge_add(1,1+n,2,-1),edge_add(1+n,1,0,1);
edge_add(n,n+n,2,-1),edge_add(n+n,n,0,1);
for(int i=2; i<=n-1; i++) edge_add(i,i+n,1,-1),edge_add(i+n,i,0,1);
for(int i=1; i<=m; i++)
{
string aa,bb;
cin>>aa>>bb;
int a=stoi[aa],b=stoi[bb];
if(a>b)swap(a,b);
edge_add(n+a,b,1,0);
edge_add(b,n+a,0,0);
}

int cost,f;
f=MCMF(s,t,cost);
cost=-cost;
if(f==2)
{
if(cost!=2)
{
printf("%d\n",cost-2);
//cout<<-cost<<endl;
vector<int> ans;
dfs(t,ans);
int w;
for(int i=0; i<ans.size(); i++) if(ans[i]==s)
{
w=i;
break;
}

for(int i=ans.size()-1; i>=w+1; i--) cout<<ss[ans[i]]<<endl;
for(int i=0; i<=w; i++) cout<<ss[ans[i]]<<endl;
}
else cout<<2<<endl<<ss[1]<<endl<<ss
<<endl<<ss[1]<<endl;

}
else puts("No Solution!");
}
return 0;
}