[NOIP2013]货车运输

Posted 2020-09-20 QYP_2002

【题目描述】

思路{直接最大生成树+树链剖分即可。}

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<algorithm>
 5 #include<cmath>
 6 #include<queue>
 7 #include<vector>
 8 #include<set>
 9 #include<map>
10 #define LL long long 
11 #define dd double 
12 #define Inf 0x3f3f3f3f
13 #define maxx 10001
14 #define maxm 50001
15 #define rs ((o<<1)|1)
16 #define ls (o<<1)
17 #define mid ((l+r)>>1)
18 #define I(i) que[i]
19 #define RG register
20 using namespace std;
21 struct ee{int nxt,to,c;}e[maxm*2],E[maxm*2];int siz,W[maxx],w[maxx],hson[maxx];
22 int head[maxx],n,m,fa[maxx],col[maxx],HEAD[maxx],tot,TOT,colorr,f[maxx],top[maxx],sz[maxx],deep[maxx],id[maxx],cn,tree[maxx*4];
23 int find(int x){if(fa[x]!=x)fa[x]=find(fa[x]);return fa[x];}
24 int que[maxm*2];struct bi{int u,v,c;}b[maxm];vector<int>ha[maxx];
25 void ADD(int u,int v,int c){E[TOT].nxt=HEAD[u];E[TOT].to=v;E[TOT].c=c;HEAD[u]=TOT++;}
26 void add(int u,int v,int c){e[tot].nxt=head[u];e[tot].to=v;e[tot].c=c;head[u]=tot++;}
27 inline int read(){
28   int res=0,fh=1;char ch=getchar();
29   while((ch<‘0‘||ch>‘9‘)&&ch!=‘-‘)ch=getchar();
30   if(ch==‘-‘)fh=-1,ch=getchar();
31   while(ch<=‘9‘&&ch>=‘0‘)res=res*10+ch-‘0‘,ch=getchar();
32   return res*fh;
33 }
34 void DFS(int u,int faa){
35   for(int i=0;i<ha[u].size();++i)que[++que[0]]=ha[u][i];
36   for(int i=HEAD[u];i!=-1;i=E[i].nxt)if(!col[E[i].to]){
37       siz++;int v=E[i].to;col[v]=col[u];DFS(v,u);
38     }
39 }
40 bool comp(const int & aa,const int & bb){return b[aa].c>b[bb].c;}
41 void dfs(int u,int faa){
42   f[u]=faa;sz[u]=1;deep[u]=deep[faa]+1;
43   for(int i=head[u];i!=-1;i=e[i].nxt)if(!sz[e[i].to]){
44       int v=e[i].to;W[v]=e[i].c;dfs(v,u);
45       sz[u]+=sz[v];if(sz[hson[u]]<sz[v])hson[u]=v;
46     }
47 }
48 void dfs2(int u,int toop){top[u]=toop;
49   id[u]=++cn;w[cn]=W[u];if(hson[u])dfs2(hson[u],toop);
50   for(int i=head[u];i!=-1;i=e[i].nxt)if(e[i].to!=f[u]&&e[i].to!=hson[u])dfs2(e[i].to,e[i].to);
51 }
52 void kurusal(int u){siz=1;memset(que,0,sizeof(que));
53   col[u]=++colorr;DFS(u,u);sort(que+1,que+que[0]+1,comp);int cnt=0;
54   for(int i=1;i<=que[0]&&cnt+1!=siz;++i)
55     if(fa[find(b[I(i)].u)]!=fa[find(b[que[i]].v)])
56       fa[find(b[I(i)].u)]=fa[find(b[I(i)].v)],
57       add(b[I(i)].u,b[I(i)].v,b[I(i)].c),add(b[I(i)].v,b[I(i)].u,b[I(i)].c);
58   dfs(u,u);dfs2(u,u);
59 }
60 void build(int o,int l,int r){
61   if(l==r){tree[o]=w[l];return;}
62   build(ls,l,mid),build(rs,mid+1,r);
63   tree[o]=min(tree[rs],tree[ls]);
64 }
65 int query(int o,int l,int r,int L,int R){
66   if(L<=l&&r<=R)return tree[o];
67   if(mid<L)return query(rs,mid+1,r,L,R);
68   else if(mid>=R)return query(ls,l,mid,L,R);
69   else return min(query(rs,mid+1,r,L,R),query(ls,l,mid,L,R));
70 }
71 void lca(int x,int y){
72   int ans=Inf;
73   while(top[x]!=top[y]){
74     if(deep[top[x]]<deep[top[y]])swap(x,y);
75     ans=min(ans,query(1,1,n,id[top[x]],id[x]));
76     x=f[top[x]];
77   }
78   if(deep[x]<deep[y])swap(x,y);
79   if(id[y]<id[x])ans=min(ans,query(1,1,n,id[y]+1,id[x]));
80   printf("%d\n",ans);
81 }
82 int main(){
83   memset(HEAD,-1,sizeof(HEAD));
84   memset(head,-1,sizeof(head));scanf("%d%d",&n,&m);
85   for(RG int i=1;i<=n;++i)fa[i]=i;
86   for(int i=1;i<=m;++i)b[i].u=read(),b[i].v=read(),b[i].c=read(),ha[b[i].u].push_back(i),ADD(b[i].u,b[i].v,b[i].c),ADD(b[i].v,b[i].u,b[i].c);
87   for(int i=1;i<=n;++i)if(!col[i])kurusal(i);int kk;scanf("%d",&kk);build(1,1,n);
88   for(int i=1;i<=kk;++i){
89     int x,y;scanf("%d%d",&x,&y);
90     if(col[x]!=col[y]){cout<<"-1\n";continue;}
91    else lca(x,y);
92   }
93   return 0;
94 }