UVA 315 Network (no-map-cut point)

The main idea: to give you an no-map, the number of cut points. Input data first row one n means there are n points followed by a number of lines, until read into a 0, the entire map read into the end, and then read into a 0, the end of the file data.  Each row has the first number a, which means that the next number is connected to a. Knowledge Summary: Cut point: In the undirected connected graph, if a point is deleted, the graph becomes disconnected, then the point is called a cut point. Here the cutting point and the bridge are the concept of the non-direction diagram, we do not confuse here. To cut points a vertex u is a cut point, when and only if satisfies (1) or (2) (1) U is a root, and U has more than one subtree. (2) U is not a root, and satisfies the presence (U,V) as a branch edge (or parent-child edge, that is, U is the father of V in the search tree), making DFN (U) <=low (v). (That is, V has no way to bypass the U-point to reach a smaller point than U DFN) Note: The tree mentioned here refers to the search tree under DFS. Cut point Tarjan Low and dfndfn[u] definition is similar to the previous, but low[u] defined as U or u in a subtree can be traced through non-parent-child edge of the first node of the DFS start time in the Tarjan algorithm to cut point we want to add an array father[u], Determine whether the two are parent-child side

#include <cstdio> #include <cstdlib> #include <cmath> #include <iostream> #include < algorithm> #include <cstring> #include <vector>using namespaceStd;#define MAXN 10005intDfn[Maxn];/// represents the first time to traverse to this pointintLow[Maxn];/// The earliest point of time before this point can be reachedintFather[Maxn];/// Save this node's father nodeintN,M,Time,Top;///time point in time, top for stack operationsVector<Vector<int> >G;voidInit(){G.Clear();G.Resize(N+1);Memset(Low,0,sizeof(Low));Memset(Dfn,0,sizeof(Dfn));Memset(Father,0,sizeof(Father));Time =0;}voidTarjan(intU,intFa){Low[U] =Dfn[U] = ++Time;Father[U] =Fa;intLen =G[U].Size(),V; for(intI=0;I<Len;I++) {V =G[U][I];if(!Dfn[V]) {Tarjan(V,U);Low[U] =Min(Low[U],Low[V]); }else if(Fa !=V)if we write here Low[u] = min (Low[v], low[u]), then it is equivalent to the node before v backLow[U] =Min(Dfn[V],Low[U]); }}voidSolve(){/** cut point a vertex u is a cut point, when and only if satisfies (1) or (2) (1) U is a root, and U has more than one subtree. (2) U is not a root, and satisfies the presence (U,V) as a branch edge (or parent-child edge, that is, U is the father of V in the search tree), making DFN (U) <=low (v). (That is, V has no way to bypass the U-point to reach a smaller point than U DFN) Note: The tree mentioned here refers to the search tree under DFS */intRootson =0,Ans =0;/// root node number of sonsBOOLCut[Maxn] = {false};/// tag array to determine if this point is a cut pointTarjan(1,0); for(intI=2;I<=N;I++) {intV =Father[I];if(V ==1)/// I also say I's father is the root nodeRootson ++;else if(Dfn[V] <=Low[I])Cut[V] =true; } for(intI=2;I<=N;I++) {if(Cut[I])Ans ++; }if(Rootson>1)Ans++;Printf("%d\n",Ans);}intMain(){ while(scanf("%d", &N),N) {intA,B;CharCh;Init(); while(scanf("%d", &A),A) { while(scanf("%d%c",&B,&Ch)) {G[A].Push_back(B);G[B].Push_back(A);if(Ch ==' \ n ') Break; } }Solve(); }return0;}

UVA 315 Network (no-map-cut point)