Poj--1966--cable TV Network "undirected graph vertex Connectivity"

Links:http://poj.org/problem?id=1966

Test Instructions: an undirected graph, n points, M edges, to find the vertex connectivity of this graph.

idea: vertex connectivity, that is, the number of cut points in the minimum cut point set, the general method of finding the vertex connectivity of undirected graphs is to transform to the minimum cut of the network flow.

Build diagram:

(1) The original image of each point I split, split for I ' and I ', I ' to I ', an arc capacity of 1.

(2) for edges present in the original image (U, v), with two arcs (U ', V ') and (V ', U '), capacity INF.

(3) Find a source point I, this point cannot be adjacent to all other points are not able to find the minimum cut, with this point I ' as the source point, enumerate the meeting point J '.

After the diagram has been built, the maximum flow is n-1, and the least of the answers is the vertex connectivity of the graph, and I-I ' to I ' is the smallest cut-point set.

#include <cstring> #include <string> #include <fstream> #include <iostream> #include < iomanip> #include <cstdio> #include <cctype> #include <algorithm> #include <queue> #include <map> #include <set> #include <vector> #include <stack> #include <ctime> #include < cstdlib> #include <functional> #include <cmath>using namespace std; #define PI ACOs ( -1.0) #define MAXN 1010 #define EPS 1e-7#define INF 0x3f3f3f3f//0x7fffffff#define llinf 0x7fffffffffffffff#define seed 1313131#define MOD 10 00000007#define ll Long long#define ull unsigned ll#define lson l,m,rt<<1#define Rson m+1,r,rt<<1|1struct nod e{int u,v,w,next;} Edge[500000],edge2[500000];int Head[120],dist[120],cur[120],fa[120],num[120],vis[120];int N,m,k,cnt,nn,src,sink;    void Add_edge (int a,int b,int c) {edge2[cnt].u = A;    EDGE2[CNT].V = b;    EDGE2[CNT].W = C;    Edge2[cnt].next = Head[a]; Head[a] = cnt++;}    void BFs () {int x,i,j; Queue<int> q;    memset (dist,-1,sizeof (Dist));    memset (num,0,sizeof (num));    Q.push (sink);    Dist[sink] = 0;    Num[0] = 1;        while (!q.empty ()) {x = Q.front ();        Q.pop ();                for (I=head[x];i!=-1;i=edge[i].next) {if (dist[edge[i].v]<0) {DIST[EDGE[I].V] = dist[x] + 1;                num[dist[edge[i].v]]++;            Q.push (EDGE[I].V);    }}}}int augment () {int x=sink,a=inf;        while (X!=SRC) {a = min (A,EDGE[FA[X]].W);    x = edge[fa[x]].u;    } X=sink;        while (X!=SRC) {edge[fa[x]].w-= A;        EDGE[FA[X]^1].W + = A;    x = edge[fa[x]].u; } return A;    int Isap () {int i,x,ok,minm,flow=0;    BFS ();    for (i=0;i<=nn+5;i++) cur[i] = Head[i];    X=SRC;            while (DIST[SRC]&LT;NN) {if (X==sink) {flow + = augment ();        x = src;        } ok=0;               for (I=cur[x];i!=-1;i=edge[i].next) {if (EDGE[I].W && dist[x]==dist[edge[i].v]+1) { ok=1;                FA[EDGE[I].V] = i;                CUR[X] = i;                x = EDGE[I].V;            Break            }} if (!ok) {minm = nn; for (I=head[x];i!=-1;i=edge[i].next) if (edge[i].w && dist[edge[i].v]<minm) MINM=DIST[EDGE[I].V]            ;            if (--num[dist[x]]==0) break;            num[dist[x]=minm+1]++;            CUR[X]=HEAD[X];        if (X!=SRC) x=edge[fa[x]].u; }} return flow;}    int main () {int i,j;    int A, B;        while (scanf ("%d%d", &n,&m)!=eof) {memset (head,-1,sizeof (head));        CNT = 0;            for (i=0;i<n;i++) {Add_edge (i,i+n,1);        Add_edge (i+n,i,0);            } for (i=0;i<m;i++) {scanf ("(%d,%d)", &a,&b);            Add_edge (A+n,b,inf);            Add_edge (b,a+n,0);            Add_edge (B+n,a,inf);        Add_edge (a,b+n,0);        } int ans = INF;        nn = n * 2;            for (i=0;i<n;i++) {memset (vis,0,sizeof (VIS));            for (J=head[i];j!=-1;j=edge2[j].next) {VIS[EDGE2[J].V] = 1;            } int sum = 0;            for (j=0;j<n;j++) {if (vis[j]) sum++;                } if (Sum < n-1) {src = i + N;            Break            }} for (i=1;i<n;i++) {sink = i;            memcpy (edge,edge2,sizeof (node) *cnt);            int temp = ISAP ();        ans = min (ans, temp);        } if (ans = = INF) ans = n;    printf ("%d\n", ans); } return 0;}

Poj--1966--cable TV Network "undirected graph vertex Connectivity"