cf1051F. The Shortest Statement(最短路/dfs树)

You are given a weighed undirected connected graph, consisting of nn vertices and mm edges.

You should answer qq queries, the ii-th query is to find the shortest distance between vertices uiui and vivi.

Input

The first line contains two integers n and m (1n,m105,mn20) — the number of vertices and edges in the graph.

Next m lines contain the edges: the i-th edge is a triple of integers vi,ui,di (1≤ui,vi≤n,1≤di≤109,ui≠vi). This triple means that there is an edge between vertices ui and vi of weight di. It is guaranteed that graph contains no self-loops and multiple edges.

The next line contains a single integer q (1q105)— the number of queries.

Each of the next qq lines contains two integers uiui and vi (1ui,vin)vi (1≤ui,vi≤n) — descriptions of the queries.

Pay attention to the restriction mn  20

Output

Print q lines.

The i-th line should contain the answer to the i-th query — the shortest distance between vertices ui and vi.

解题思路:

题目非常良心地强调了m-n<=20

建一颗dfs树,对于未加入树的边两端跑Dij

询问只要枚举未入树边更新即可。

代码:

  1 #include<queue>
  2 #include<cstdio>
  3 #include<cstring>
  4 #include<algorithm>
  5 typedef long long lnt;
  6 struct pnt{
  7     int hd;
  8     int dp;
  9     int no;
 10     int fa[22];
 11     lnt dis;
 12     lnt tds;
 13     bool vis;
 14     bool cop;
 15     bool friend operator < (pnt x,pnt y)
 16     {
 17         return x.dis>y.dis;
 18     }
 19 }p[1000000];
 20 struct ent{
 21     int twd;
 22     int lst;
 23     lnt vls;
 24 }e[1000000];
 25 std::priority_queue<pnt>Q;
 26 int n,m;
 27 int q;
 28 int cnt;
 29 int sct;
 30 lnt dist[50][200000];
 31 int sta[50];
 32 void ade(int f,int t,lnt v)
 33 {
 34     cnt++;
 35     e[cnt].twd=t;
 36     e[cnt].vls=v;
 37     e[cnt].lst=p[f].hd;
 38     p[f].hd=cnt;
 39     return ;
 40 }
 41 void Dij(int x)
 42 {
 43     if(p[x].cop)
 44         return ;
 45     p[x].cop=true;
 46     sta[++sct]=x;
 47     for(int i=1;i<=n;i++)
 48     {
 49         p[i].dis=0x3f3f3f3f3f3f3f3fll;
 50         p[i].no=i;
 51         p[i].vis=false;
 52     }
 53     p[x].dis=0;
 54     while(!Q.empty())
 55         Q.pop();
 56     Q.push(p[x]);
 57     while(!Q.empty())
 58     {
 59         x=Q.top().no;
 60         Q.pop();
 61         if(p[x].vis)
 62             continue;
 63         p[x].vis=true;
 64         for(int i=p[x].hd;i;i=e[i].lst)
 65         {
 66             int to=e[i].twd;
 67             if(p[to].dis>p[x].dis+e[i].vls)
 68             {
 69                 p[to].dis=p[x].dis+e[i].vls;
 70                 Q.push(p[to]);
 71             }
 72         }
 73     }
 74     for(int i=1;i<=n;i++)
 75         dist[sct][i]=p[i].dis;
 76     return ;
 77 }
 78 void dfs(int x,int f)
 79 {
 80     p[x].fa[0]=f;
 81     p[x].dp=p[f].dp+1;
 82     for(int i=1;i<=20;i++)
 83         p[x].fa[i]=p[p[x].fa[i-1]].fa[i-1];
 84     for(int i=p[x].hd;i;i=e[i].lst)
 85     {
 86         int to=e[i].twd;
 87         if(to==f)
 88             continue;
 89         if(p[to].tds)
 90         {
 91             Dij(x);
 92             Dij(to);
 93         }else{
 94             p[to].tds=p[x].tds+e[i].vls;
 95             dfs(to,x);
 96         }
 97     }
 98 }
 99 int Lca(int x,int y)
100 {
101     if(p[x].dp<p[y].dp)
102         std::swap(x,y);
103     for(int i=20;i>=0;i--)
104         if(p[p[x].fa[i]].dp>=p[y].dp)
105             x=p[x].fa[i];
106     if(x==y)
107         return x;
108     for(int i=20;i>=0;i--)
109         if(p[x].fa[i]!=p[y].fa[i])
110         {
111             x=p[x].fa[i];
112             y=p[y].fa[i];
113         }
114     return p[x].fa[0];
115 }
116 int main()
117 {
118     scanf("%d%d",&n,&m);
119     for(int i=1;i<=m;i++)
120     {
121         int a,b,c;
122         scanf("%d%d%d",&a,&b,&c);
123         ade(a,b,c);
124         ade(b,a,c);
125     }
126     p[1].tds=1;
127     dfs(1,1);
128     scanf("%d",&q);
129     while(q--)
130     {
131         int x,y;
132         scanf("%d%d",&x,&y);
133         int f=Lca(x,y);
134         lnt ans=p[x].tds+p[y].tds-2*p[f].tds;
135         for(int i=1;i<=sct;i++)
136             ans=std::min(ans,dist[i][x]+dist[i][y]);
137         printf("%I64d\n",ans);
138     }
139     return 0;
140 }
posted @ 2018-10-26 17:55  Unstoppable728  阅读(406)  评论(0编辑  收藏  举报