4144: [AMPPZ2014]Petrol (多源最短路+最小生成树+启发式合并)

  1 #include<bits/stdc++.h>
  2 #define clr(x) memset(x,0,sizeof(x))
  3 #define clr_1(x) memset(x,-1,sizeof(x))
  4 #define INF 0x3f3f3f3f
  5 #define LL long long
  6 #define pb push_back
  7 #define mod 1000000007
  8 #define ls(i) (i<<1)
  9 #define rs(i) (i<<1|1)
 10 #define mp make_pair
 11 #define fi first
 12 #define se second
 13 using namespace std;
 14 typedef pair<LL,int > pli;
 15 const int N = 2e5+10;
 16 bool need[N];
 17 vector<pli> e[N];
 18 struct node
 19 {
 20     int u,v;
 21     LL w;
 22     node(int _u=0,int _v=0,LL _w=0):u(_u),v(_v),w(_w) {}
 23 };
 24 vector<node> ve;
 25 int n,s,m,T;
 26 priority_queue<pli,vector<pli>,greater<pli> > que;
 27 int fuel[N];
 28 int fa[N],rfa[N],rk[N],dep[N];
 29 LL dis[N],val[N];
 30 bool vis[N];
 31 int pre[N];
 32 void dij()
 33 {
 34     while(!que.empty())
 35     {
 36         pli now=que.top();
 37         que.pop();
 38         LL dist=now.fi;
 39         int u=now.se;
 40         if(vis[u]) continue;
 41         vis[u]=1;
 42         int sz=e[u].size();
 43         for(int i=0;i<sz;i++)
 44         {
 45             pli p=e[u][i];
 46             int w=p.fi;
 47             int v=p.se;
 48             if(!pre[v] || dis[v]>dis[u]+w)
 49             {
 50                 dis[v]=dis[u]+w;
 51                 pre[v]=pre[u];
 52                 que.push(mp(dis[v],v));
 53             }
 54             else if(pre[u] != pre[v])
 55                 ve.pb(node(pre[u],pre[v],dis[u]+dis[v]+w));
 56         }
 57     }
 58     return ;
 59 }
 60 bool cmp(node a,node b)
 61 {
 62     return a.w<b.w;
 63 }
 64 int Find(int u)
 65 {
 66     if(fa[u]!=u)
 67         fa[u]=Find(fa[u]);
 68     return fa[u];
 69 }
 70 void Union()
 71 {
 72     sort(ve.begin(),ve.end(),cmp);
 73     for(int i=1;i<=s;i++)
 74     {
 75         fa[fuel[i]]=fuel[i];
 76         rk[fuel[i]]=1;
 77     }
 78     int sz=ve.size();
 79     for(int i=0;i<sz;i++)
 80     {
 81         node p=ve[i];
 82         int u = p.u, v = p.v;
 83         LL w = p.w;
 84         u = Find(u), v = Find(v);
 85         if(u==v) continue;
 86         if(rk[u]<rk[v]) swap(u,v);
 87         if(rk[u]==rk[v]) rk[u]++;
 88         rfa[v]=u,fa[v]=u,val[v]=w;
 89     }
 90     return ;
 91 }
 92 void dealdep(int u)
 93 {
 94     if(dep[u]>0) return ;
 95     if(fa[u]==u)
 96     {
 97         dep[u]=1;
 98         return ;
 99     }
100     dealdep(rfa[u]);
101     dep[u]=dep[rfa[u]]+1;
102     return ;
103 }
104 bool solve(int u,int v,LL b)
105 {
106     if(Find(u)!=Find(v)) return 0;
107     if(dep[u]<dep[v]) swap(u,v);
108     while(dep[u]>dep[v])
109     {
110         if(b<val[u]) return 0;
111         u=rfa[u];
112     }
113     if(u==v) return 1;
114     while(u!=v)
115     {
116         if(b<val[u]) return 0;
117         if(b<val[v]) return 0;
118         u=rfa[u];
119         v=rfa[v];
120     }
121     return 1;
122 }
123 int main()
124 {
125     scanf("%d%d%d",&n,&s,&m);
126     clr_1(dis);
127     for(int i=1;i<=s;i++)
128     {
129         scanf("%d",fuel+i);
130         que.push(mp(0,fuel[i]));
131         pre[fuel[i]]=fuel[i];
132         dis[fuel[i]]=0;
133     }
134     for(int i=1;i<=m;i++)
135     {
136         int u,v;
137         LL w;
138         scanf("%d%d%lld",&u,&v,&w);
139         e[u].pb(mp(w,v));
140         e[v].pb(mp(w,u));
141     }
142     dij();
143     Union();
144     for(int i=1;i<=s;i++)
145         dealdep(fuel[i]);
146     int u,v;
147     LL b,maxn;
148     int q;
149     scanf("%d",&q);
150     while(q--)
151     {
152         scanf("%d%d%lld",&u,&v,&b);
153         if(solve(u,v,b))
154             printf("TAK\n");
155         else
156             printf("NIE\n");
157     }
158     return 0;
159 }