PAT甲级 All Roads Lead to Rome （dijkstra+dfs回溯）

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <queue>
  5 #include <vector>
  6 #include <map>
  7 #include <algorithm>
  8 #define inf 0x3f3f3f3f
  9 using namespace std;
 10 const int maxn=220;
 11 int n,m;
 12 string s1,s2,st;
 13 int cnt;
 14 int fhappy=0;
 15 double fhave=0;
 16 
 17 map<string,int>mp1;
 18 map<int,string>mp2;
 19 struct node{
 20     int pos;
 21     int cost;
 22     node(){}
 23     node(int pos,int cost):pos(pos),cost(cost){}
 24     friend bool operator < (node a,node b)
 25     {
 26         return a.cost>b.cost;
 27     } 
 28 }head,tail;
 29 vector<node>g[maxn];
 30 vector<int> pre[maxn];
 31 vector<int> path;
 32 vector<int> tpath;
 33 int vis[maxn],dis[maxn];
 34 int happy[maxn];
 35 void dijkstra(int st)
 36 {
 37     priority_queue<node> q;
 38     dis[st]=0;
 39     head.pos=st;
 40     head.cost=0;
 41     q.push(head);
 42     while(!q.empty())
 43     {
 44         head=q.top();
 45         q.pop();
 46         if(vis[head.pos]) continue;
 47         vis[head.pos]=1;
 48         int now=head.pos;
 49         for(int i=0;i<g[now].size();i++)
 50         {
 51             tail=g[now][i];
 52             int v=tail.pos;
 53             int len=tail.cost;
 54             if(dis[v]>dis[head.pos]+len)
 55             {
 56                 dis[v]=dis[head.pos]+len;
 57                 pre[v].clear();
 58                 pre[v].push_back(head.pos);
 59                 q.push(tail);
 60             }
 61             else if(dis[v]==dis[head.pos]+len)
 62             {
 63                 pre[v].push_back(head.pos);
 64                 q.push(tail);
 65             }            
 66         }
 67     }
 68 }
 69 void dfs(int now)
 70 {
 71     if(now==0)
 72     {
 73         cnt++;
 74         tpath.push_back(now);
 75         int hval=0;
 76         for(int i=tpath.size()-2;i>=0;i--)
 77         {
 78         //    cout<<"lala"<<tpath[i]<<endl;
 79             hval+=happy[tpath[i]];
 80         }
 81         double have=1.0*hval/(tpath.size()-1);
 82         if(hval>fhappy)
 83         {
 84             fhappy=hval;
 85             fhave=have;
 86             path=tpath;
 87         }
 88         else if(hval==fhappy&&have>fhave)
 89         {
 90             fhappy=hval;
 91             fhave=have;
 92             path=tpath;
 93         }
 94         tpath.pop_back();
 95         return;
 96     }
 97     tpath.push_back(now);
 98     for(int i=0;i<pre[now].size();i++)
 99     {
100         dfs(pre[now][i]);
101     }
102     tpath.pop_back();
103 }
104 int main()
105 {
106     cin>>n>>m>>st;
107     memset(dis,inf,sizeof(dis)); 
108     mp1[st]=0;
109     mp2[0]=st;
110     int t;
111     for(int i=1;i<=n-1;i++)
112     {
113         cin>>s1>>happy[i];
114         mp1[s1]=i;
115         mp2[i]=s1;
116     } 
117     for(int i=0;i<m;i++)
118     {
119         cin>>s1>>s2>>t;
120         int id1=mp1[s1];
121         int id2=mp1[s2];
122         node tmp;
123         tmp.pos=id2;
124         tmp.cost=t;
125         g[id1].push_back(tmp);
126         tmp.pos=id1;
127         g[id2].push_back(tmp);
128     }
129     int ed=mp1["ROM"];
130     dijkstra(0);
131     dfs(ed);
132     printf("%d %d %d %d\n",cnt,dis[ed],fhappy,(int)fhave);
133     for(int i=path.size()-1;i>=0;i--)
134     {
135         cout<<mp2[path[i]];
136         if(i!=0)
137         {
138             printf("->");
139         } 
140     }
141     return 0;
142 }