POJ3694 Network (Tarjan dual-link LCA bridge)

Links: http://poj.org/problem?id=3694

Test instructions: Given a connected graph, add one edge at a time to find the number of bridges remaining.

Ideas:

Given an undirected connected graph, add a u->v Edge to the effect of this edge on the number of bridges remaining in the graph :

If the u,v is in the same strong unicom component, is no effect added. Otherwise , all the bridges from u,v 's LCA to the u,v side are no longer bridges.

     in u,v belong to different strong connected components, DFN ( set to v) merge up until DFN[V] < Dfn[u] u Span style= "font-family: the song Body;" > merge up until u = v 1 .

Merging uses and checks to optimize the path during the merge process, or time out.

#include <iostream>#include<cstdio>#include<string>#include<cstring>#include<cstdlib>#include<queue>#include<vector>#include<algorithm>Const intINF =0x3f3f3f3f;using namespaceStd;typedefLong LongLL;Const intn=100008, m=400008;intHead[n],tot,n,m,dfn[n],deep;intBridge;intFa[n], cnt[n], pre[n];structnode{intTo,next;} E[M];voidinit () {memset (head,-1,sizeof(head)); Tot=0; Bridge=0;  for(inti =1; I <= N; i++) {Fa[i]=i; Cnt[i]=1; }}intFind (intx) {     while(X! =Fa[x]) {x=Fa[x]; }    returnx;}BOOLUnion (intXinty) {    intFX =Find (x); intFY =Find (y); if(fx!=FY) {    if(cnt[fx]>Cnt[fy]) {Fa[fy]=FX; CNT[FX]+=Cnt[fy]; }Else{FA[FX]=fy; CNT[FY]+=CNT[FX]; }        return true; }Else{        return false; }}inlinevoidAddintUintTo ) {e[tot].to=to ; E[tot].next=Head[u]; Head[u]=tot++;}intDfsintUintFA) {    intLowu = Dfn[u] = ++deep;//Lowu is the farthest ancestor that u and its descendants can reach.     for(intI=head[u];~i;i=E[i].next) {        intv =e[i].to; if(!dfn[v]) {//leaf Edge, u to V and v not accessedPRE[V] =u; intLOWV =Dfs (v, u); Lowu=min (Lowu, LOWV); if(Lowv >Dfn[u]) {Bridge++; }Else{Union (U, v); }        }Else if(Dfn[v] < Dfn[u] && v! =FA) {Lowu= Min (Lowu, dfn[v]);//Back to Edge        }    }    returnLowu;}voidTarjan () {memset (DFN,0,sizeof(DFN)); deep=0;  for(intI=1; i<=n;i++){        if(!Dfn[i]) {Pre[i]=i; DFS (i,-1); }    }}intLCA (intUintv) {    if(Find (u) = =Find (v)) {        returnBridge; }    if(Dfn[u] >Dfn[v])    {Swap (U, v); }     while(Dfn[u] <Dfn[v]) {        if(Union (V, Pre[v])) {Bridge--; } v=Pre[v]; }     while(U! =v) {        if(Union (U, Pre[u])) {Bridge--; } u=Pre[u]; }    returnBridge;}intMain () {intt =0;  while(~SCANF ("%d%d", &n, &m) && (n | |m))        {init (); intA, B, q;  while(m--) {scanf ("%d%d", &a, &b);            Add (A, b);        Add (b, a);        } Tarjan (); scanf ("%d", &q); printf ("Case %d:\n",++t);  while(q--) {scanf ("%d%d", &a, &b); printf ("%d\n", LCA (A, b)); } printf ("\ n"); }    return 0;}

POJ3694 Network (Tarjan dual-link LCA bridge)