biconnected.c

/*	biconnected.c
	Identify articulation vertices in a graph

	by: Steven Skiena
	begun: March 27, 2002
*/

/*
Copyright 2003 by Steven S. Skiena; all rights reserved. 

Permission is granted for use in non-commerical applications
provided this copyright notice remains intact and unchanged.

This program appears in my book:

"Programming Challenges: The Programming Contest Training Manual"
by Steven Skiena and Miguel Revilla, Springer-Verlag, New York 2003.

See our website www.programming-challenges.com for additional information.

This book can be ordered from Amazon.com at

http://www.amazon.com/exec/obidos/ASIN/0387001638/thealgorithmrepo/

*/

#include <stdio.h>

#include "bool.h"
#include "bfs-dfs.h"
#include "queue.h"

extern bool processed[];    /* which vertices have been processed */
extern bool discovered[];   /* which vertices have been found */
extern int parent[];        /* discovery relation */

extern int entry_time[MAXV+1];  /* time of vertex entry */
extern int exit_time[MAXV+1];   /* time of vertex exit */

/* [[[ ratod_cut */
int reachable_ancestor[MAXV+1]; /* earliest reachable ancestor of v */
int tree_out_degree[MAXV+1];    /* DFS tree outdegree of v */
/* ]]] */

/* [[[ pvearlydfs_cut */
void process_vertex_early(int v) {
    reachable_ancestor[v] = v;
}
/* ]]] */

/* [[[ pvlatedfs_cut */
void process_vertex_late(int v) {
    bool root;       /* is a given vertex the root of the DFS tree? */
    int time_v;      /* earliest reachable time for v */
    int time_parent; /* earliest reachable time for parent[v] */

    if (parent[v] < 1) {	/* test if v is the root */
        if (tree_out_degree[v] > 1) {
            printf("root articulation vertex: %d \n", v);
        }
        return;
    }

    root = (parent[parent[v]] < 1);    /* test if parent[v] is root */

    if (!root) {
        if (reachable_ancestor[v] == parent[v]) {
            printf("parent articulation vertex: %d \n", parent[v]);
        }

        if (reachable_ancestor[v] == v) {
            printf("bridge articulation vertex: %d \n",parent[v]);

            if (tree_out_degree[v] > 0) {    /* test if v is not a leaf */
                printf("non-leaf articulation vertex: %d \n", v);
            }
        }
    }

    time_v = entry_time[reachable_ancestor[v]];
    time_parent = entry_time[reachable_ancestor[parent[v]]];

    if (time_v < time_parent) {
        reachable_ancestor[parent[v]] = reachable_ancestor[v];
    }
}
/* ]]] */

/* [[[ pedgedfs_cut */
void process_edge(int x, int y) {
    int class;    /* edge class */

    class = edge_classification(x, y);

    if (class == TREE) {
        tree_out_degree[x] = tree_out_degree[x] + 1;
    }

    if ((class == BACK) && (parent[x] != y)) {
        if (entry_time[y] < entry_time[reachable_ancestor[x]]) {
            reachable_ancestor[x] = y;
        }
    }
}
/* ]]] */

void articulation_vertices(graph *g) {
    int i;    /* counter */

    for (i = 1; i <= (g->nvertices); i++) {
        tree_out_degree[i] = 0;
    }

    initialize_search(g);

    for (i = 1; i <= (g->nvertices); i++) {
        if (discovered[i] == FALSE) {
            dfs(g, i);
        }
    }
}

int main(void) {
    graph g;
    int i;

    read_graph(&g, FALSE);
    print_graph(&g);

    articulation_vertices(&g);

    return 0;
}