315 – Network

Problem Statement

Given a connected undirected graph, find its critical nodes (articulation points). A critical node is a node which its removal leaves the graph disconnected.

A straight-forward solution –to remove each node and do a DFS check for connectivity– will get an AC, but this is an implementation that uses Tarjan’s DFS algorithm for finding Articulation Point:

#include <algorithm>
#include <iostream>
#include <fstream>
#include <cstring>
#include <limits>
#include <sstream>
#include <string>
#include <stack>
#include <queue>
#include <map>
#include <set>
using namespace std;

set<int> apNodes, apVis;
set<pair<int, int> > apEdges;
void articulationPointAndBridge(map<int, map<int, int> > &graph, int s) {
//     cout << "ARTICULATION POINT AND BRIDGE" << endl;
    map<int, int> parent, num_dfs, num_low;
    int children_s = 0, num_dfs_size = 0;
    stack<int> stk;
    parent[s] = s, stk.push(s);
    // dfs
    while (stk.size()) {
        int u = stk.top();
        // grey
        if (apVis.find(u) == apVis.end()) {
            num_dfs[u] = num_low[u] = num_dfs_size++;
            apVis.insert(u);
            children_s += u != s && parent[u] == s;
            for (map<int, int>::reverse_iterator v = graph[u].rbegin();
                 v != graph[u].rend(); ++v)
                // grey to white
                if (apVis.find(v->first) == apVis.end())
                    parent[v->first] = u, stk.push(v->first);
                // grey to grey
                else if (parent[u] != v->first)
                    num_low[u] = min(num_low[u], num_dfs[v->first]);
        }
        // black
        else {
            if (parent[u] != u) {
                // POINTS
                if (num_dfs[parent[u]] <= num_low[u])
                    apNodes.insert(parent[u]);
                // BRIDGES
                if (num_dfs[parent[u]] < num_low[u])
                    if (u < parent[u])
                        apEdges.insert(make_pair(u, parent[u]));
                    else
                        apEdges.insert(make_pair(parent[u], u));
                num_low[parent[u]] = min(num_low[parent[u]], num_low[u]);
            }
            stk.pop();
        }
    }
    apNodes.erase(s);
    if (children_s > 1)
        apNodes.insert(s);
}

int main() {
    int n;
    string line;
    while (cin >> n && n) {
        // input
        getline(cin, line);
        bool inputDone = false;
        map<int, map<int, int> > graph;
        while (!inputDone) {
            getline(cin, line);
            stringstream ss(line);
            int u, v;
            ss >> u;
            if (!u)
                inputDone = true;
            while (ss >> v)
                graph[u][v] = 1, graph[v][u] = 1;
        }
        // solve
        apVis.clear(), apNodes.clear(), apEdges.clear();
        articulationPointAndBridge(graph, graph.begin()->first);
        cout << apNodes.size() << endl;
    }
}