洛谷 4172 [WC2006]水管局长
【题解】
我们把操作倒过来做，就变成了加边而不是删边。于是用LCT维护动态加边的最小生成树就好了。同样要注意把边权变为点权。
1 #include<cstdio> 2 #include<algorithm> 3 #define N 200010 4 #define rg register 5 #define ls (c[u][0]) 6 #define rs (c[u][1]) 7 using namespace std; 8 int n,m,q,top,tot; 9 int f[N],fa[N],c[N][2],rev[N],mx[N],pos[N],val[N],st[N],ans[N],num[1001][1001]; 10 bool bro[1001][1001]; 11 struct edge{ 12 int u,v,dis; 13 }e[N]; 14 struct question{ 15 int opt,x,y; 16 }que[N]; 17 inline int read(){ 18 int k=0,f=1; char c=getchar(); 19 while(c<'0'||c>'9')c=='-'&&(f=-1),c=getchar(); 20 while('0'<=c&&c<='9')k=k*10+c-'0',c=getchar(); 21 return k*f; 22 } 23 inline int find(int x){return f[x]==x?x:f[x]=find(f[x]);} 24 inline bool cmp(edge a,edge b){return a.dis<b.dis;} 25 inline int max(int x,int y){return x>y?x:y;} 26 inline bool isroot(int u){return c[fa[u]][0]!=u&&c[fa[u]][1]!=u;} 27 inline bool which(int u){return c[fa[u]][1]==u;} 28 inline void pushup(int u){ 29 pos[u]=u; mx[u]=val[u]; 30 if(mx[ls]>mx[u]) pos[u]=pos[ls],mx[u]=mx[ls]; 31 if(mx[rs]>mx[u]) pos[u]=pos[rs],mx[u]=mx[rs]; 32 } 33 inline void pushdown(int u){ 34 rev[u]=0; rev[ls]^=1; rev[rs]^=1; swap(ls,rs); 35 } 36 inline void rotate(int u){ 37 int f=fa[u],g=fa[f],wh=which(u); 38 if(!isroot(f)) c[g][which(f)]=u; 39 fa[u]=g; fa[f]=u; fa[c[u][wh^1]]=f; 40 c[f][wh]=c[u][wh^1]; c[u][wh^1]=f; 41 pushup(f); pushup(u); 42 } 43 inline void splay(int u){ 44 st[top=1]=u; 45 for(rg int i=u;!isroot(i);i=fa[i]) st[++top]=fa[i]; 46 for(rg int i=top;i;i--) if(rev[st[i]]) pushdown(st[i]); 47 while(!isroot(u)){ 48 if(!isroot(fa[u])) rotate(which(u)==which(fa[u])?fa[u]:u); 49 rotate(u); 50 } 51 } 52 inline void access(int u){ 53 for(rg int s=0;u;s=u,u=fa[u]) splay(u),c[u][1]=s,pushup(u); 54 } 55 inline void makeroot(int u){access(u); splay(u); rev[u]^=1;} 56 inline int findroot(int u){ 57 access(u); splay(u); 58 while(ls) u=ls; return u; 59 } 60 inline void split(int x,int y){makeroot(x); access(y); splay(y);} 61 inline void link(int x,int y){makeroot(x); fa[x]=y;} 62 inline void cut(int x,int y){ 63 split(x,y); int t=c[y][0]; 64 if(t==x&&!c[t][1]) fa[x]=0,c[y][0]=0; 65 else{ 66 while(c[t][1]) t=c[t][1]; 67 if(t==x) fa[x]=0,c[y][0]=0; 68 } 69 } 70 inline void build(){ 71 sort(e+1,e+1+m,cmp); 72 for(rg int i=1;i<=n;i++) f[i]=i; 73 for(rg int i=1;i<=m;i++){ 74 val[i+n]=e[i].dis; 75 num[e[i].u][e[i].v]=num[e[i].v][e[i].u]=i; 76 } 77 int cnt=0; 78 for(rg int i=1;i<=m;i++){ 79 int u=e[i].u,v=e[i].v; 80 if(bro[u][v]) continue; 81 if(find(u)!=find(v)){ 82 cnt++; link(u,i+n); link(v,i+n); 83 f[find(u)]=find(v); 84 } 85 if(cnt>=n-1) break; 86 } 87 } 88 inline void work(){ 89 for(rg int i=q;i;i--){ 90 int opt=que[i].opt,x=que[i].x,y=que[i].y; 91 if(opt==1){ 92 split(x,y); ans[++tot]=mx[y]; 93 } 94 else{ 95 int ne=num[x][y]; 96 split(x,y); 97 if(e[ne].dis<mx[y]){ 98 int oe=pos[y]-n; 99 cut(e[oe].u,oe+n); cut(e[oe].v,oe+n); 100 link(e[ne].u,ne+n); link(e[ne].v,ne+n); 101 } 102 } 103 } 104 for(rg int i=tot;i;i--) printf("%d\n",ans[i]); 105 } 106 int main(){ 107 n=read(),m=read(),q=read(); 108 for(rg int i=1;i<=m;i++) { 109 e[i].u=read(),e[i].v=read(),e[i].dis=read(); 110 } 111 for(rg int i=1;i<=q;i++){ 112 que[i].opt=read(); que[i].x=read(); que[i].y=read(); 113 if(que[i].opt==2) 114 bro[que[i].x][que[i].y]=bro[que[i].y][que[i].x]=1; 115 } 116 build(); 117 work(); 118 return 0; 119 }
