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ArticulationPointsAdjacencyList.java
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ArticulationPointsAdjacencyList.java
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/**
* Finds all articulation points on an undirected graph.
*
* <p>Tested against HackerEarth online judge at:
* https://www.hackerearth.com/practice/algorithms/graphs/articulation-points-and-bridges/tutorial
*
* @author William Fiset, william.alexandre.fiset@gmail.com
*/
package com.williamfiset.algorithms.graphtheory;
import static java.lang.Math.min;
import java.util.ArrayList;
import java.util.List;
public class ArticulationPointsAdjacencyList {
private int n, id, rootNodeOutcomingEdgeCount;
private boolean solved;
private int[] low, ids;
private boolean[] visited, isArticulationPoint;
private List<List<Integer>> graph;
public ArticulationPointsAdjacencyList(List<List<Integer>> graph, int n) {
if (graph == null || n <= 0 || graph.size() != n) throw new IllegalArgumentException();
this.graph = graph;
this.n = n;
}
// Returns the indexes for all articulation points in the graph even if the
// graph is not fully connected.
public boolean[] findArticulationPoints() {
if (solved) return isArticulationPoint;
id = 0;
low = new int[n]; // Low link values
ids = new int[n]; // Nodes ids
visited = new boolean[n];
isArticulationPoint = new boolean[n];
for (int i = 0; i < n; i++) {
if (!visited[i]) {
rootNodeOutcomingEdgeCount = 0;
dfs(i, i, -1);
isArticulationPoint[i] = (rootNodeOutcomingEdgeCount > 1);
}
}
solved = true;
return isArticulationPoint;
}
private void dfs(int root, int at, int parent) {
if (parent == root) rootNodeOutcomingEdgeCount++;
visited[at] = true;
low[at] = ids[at] = id++;
List<Integer> edges = graph.get(at);
for (Integer to : edges) {
if (to == parent) continue;
if (!visited[to]) {
dfs(root, to, at);
low[at] = min(low[at], low[to]);
if (ids[at] <= low[to]) {
isArticulationPoint[at] = true;
}
} else {
low[at] = min(low[at], ids[to]);
}
}
}
/* Graph helpers */
// Initialize a graph with 'n' nodes.
public static List<List<Integer>> createGraph(int n) {
List<List<Integer>> graph = new ArrayList<>(n);
for (int i = 0; i < n; i++) graph.add(new ArrayList<>());
return graph;
}
// Add an undirected edge to a graph.
public static void addEdge(List<List<Integer>> graph, int from, int to) {
graph.get(from).add(to);
graph.get(to).add(from);
}
/* Example usage: */
public static void main(String[] args) {
testExample2();
}
private static void testExample1() {
int n = 9;
List<List<Integer>> graph = createGraph(n);
addEdge(graph, 0, 1);
addEdge(graph, 0, 2);
addEdge(graph, 1, 2);
addEdge(graph, 2, 3);
addEdge(graph, 3, 4);
addEdge(graph, 2, 5);
addEdge(graph, 5, 6);
addEdge(graph, 6, 7);
addEdge(graph, 7, 8);
addEdge(graph, 8, 5);
ArticulationPointsAdjacencyList solver = new ArticulationPointsAdjacencyList(graph, n);
boolean[] isArticulationPoint = solver.findArticulationPoints();
// Prints:
// Node 2 is an articulation
// Node 3 is an articulation
// Node 5 is an articulation
for (int i = 0; i < n; i++)
if (isArticulationPoint[i]) System.out.printf("Node %d is an articulation\n", i);
}
// Tests a graph with 3 nodes in a line: A - B - C
// Only node 'B' should be an articulation point.
private static void testExample2() {
int n = 3;
List<List<Integer>> graph = createGraph(n);
addEdge(graph, 0, 1);
addEdge(graph, 1, 2);
ArticulationPointsAdjacencyList solver = new ArticulationPointsAdjacencyList(graph, n);
boolean[] isArticulationPoint = solver.findArticulationPoints();
// Prints:
// Node 1 is an articulation
for (int i = 0; i < n; i++)
if (isArticulationPoint[i]) System.out.printf("Node %d is an articulation\n", i);
}
}