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articulation-points.cpp
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articulation-points.cpp
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/*
DFS(G,u)
state[u] = “discovered”
process vertex u if desired
entry[u] = time
time = time + 1
for each v ∈ Adj[u] do
process edge (u,v) if desired
if state[v] = “undiscovered” then
p[v] = u
DFS(G,v)
state[u] = “processed”
exit[u] = time
time = time + 1
*/
#include <algorithm>
#include <iostream>
#include <queue>
#include <string>
#include <vector>
using namespace std;
struct Edge_Node {
int src, desc;
};
class Graph {
public:
vector<vector<int>> adjList;
int V, nedges;
vector<int> parent;
vector<bool> discovered;
vector<bool> processed;
vector<int> entry_time, exit_time;
vector<int> reachable_ancestor;
vector<int> tree_out_degree;
bool isfinished = false;
bool isCycledetceted = false;
Graph(int V, vector<Edge_Node> edges) {
this->V = V;
parent.resize(V + 1);
adjList.resize(V);
discovered.resize(V);
entry_time.resize(V);
exit_time.resize(V);
processed.resize(V);
reachable_ancestor.resize(V + 1);
tree_out_degree.resize(V + 1);
fill(discovered.begin(), discovered.end(), false);
std::fill(std::begin(parent), std::end(parent), -1);
for (auto edge : edges) {
insert_edge(edge.src, edge.desc);
}
}
void insert_edge(int x, int y) {
adjList[x].push_back(y);
adjList[y].push_back(x);
}
void DFS(int u, int time) {
if (isfinished)
return;
discovered[u] = true;
time += 1;
entry_time[u] = time;
process_vertex_early(u);
for (auto v : adjList[u]) {
if (discovered[v] == false) {
parent[v] = u;
process_edge(u, v);
if (isfinished)
return;
DFS(v, time);
} else if (processed[v] == false) {
process_edge(u, v);
}
}
time += 1;
process_vertex_late(u);
processed[u] = true;
}
/*
run it only after bfs so that parent get filled
*/
void find_paths(int u, int v) {
// std::cout << "Path from " << u << " to " << v << " : " << std::endl;
find_pathUtil(u, v);
}
void find_pathUtil(int u, int v) {
if (u == v || v == -1) {
std::cout << u << std::endl;
} else {
find_pathUtil(u, parent[v]);
std::cout << v << std::endl;
}
}
void process_vertex_early(int vertex) {
reachable_ancestor[vertex] = vertex;
// std::cout << "Early Vertex Process : " << vertex
// << " time : " << entry_time[vertex] << std::endl;
}
std::string edge_classification(int u, int v) {
if (parent[u] != v) {
return "BACK";
} else {
return "TREE";
}
}
void process_edge(int u, int v) {
std::string edge_class = edge_classification(u, v);
if (edge_class == "TREE")
tree_out_degree[u] = tree_out_degree[u] + 1;
if (edge_class == "BACK" && (parent[u] != v))
if (entry_time[v] < entry_time[reachable_ancestor[u]])
reachable_ancestor[u] = v;
// std::cout << "Process Edge : " << u << " " << v << std::endl;
}
void process_vertex_late(int v) {
bool root; /* is the 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) {
std::cout << "root articulation vertex " << v << " " << std::endl;
}
return;
}
root = (parent[parent[v]] < 1); /* is parent[v] the root? */
if (reachable_ancestor[v] == parent[v] && (!root)) {
std::cout << "parent articulation vertex " << parent[v] << " "
<< std::endl;
}
if (reachable_ancestor[v] == v) {
std::cout << "bridge articulation vertex " << parent[v] << " "
<< std::endl;
if (tree_out_degree[v] > 0) { /* test if v is not a leaf */
std::cout << "bridge articulation vertex " << v << std::endl;
}
}
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];
}
// std::cout << "late Vertex Process : " << vertex
// << " time : " << exit_time[vertex] << std::endl;
}
void printGraph() {
for (int i = 0; i < V; i++) {
// print the current vertex number
cout << i << " ——> ";
// print all neighboring vertices of a vertex `i`
for (int v : adjList[i]) {
cout << v << " ";
}
cout << endl;
}
}
};
int main(int argc, const char **argv) {
vector<Edge_Node> edges = {{0, 1}, {1, 4}, {1, 2}, {2, 3},
{3, 4}, {4, 5}, {5, 3}};
int V = 6;
Graph graph = Graph(V, edges);
graph.DFS(0, 0);
return 0;
}