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package algs41;
import stdlib.*;
/* ***********************************************************************
 *  Compilation:  javac Biconnected.java
 *  Dependencies: Graph.java
 *
 *  Identify articulation points and print them out.
 *  This can be used to decompose a graph into biconnected components.
 *  Runs in O(E + V) time.
 *
 *  http://www.cs.brown.edu/courses/cs016/book/slides/Connectivity2x2.pdf
 *
 *************************************************************************/

public class XBiconnected {
  private final int[] low;
  private final int[] pre;
  private int cnt;
  // private int bridges;
  private final boolean[] articulation;

  public XBiconnected(Graph G) {
    low = new int[G.V()];
    pre = new int[G.V()];
    articulation = new boolean[G.V()];
    for (int v = 0; v < G.V(); v++) low[v] = -1;
    for (int v = 0; v < G.V(); v++) pre[v] = -1;

    for (int v = 0; v < G.V(); v++)
      if (pre[v] == -1)
        dfs(G, v, v);
  }

  private void dfs(Graph G, int u, int v) {
    int children = 0;
    pre[v] = cnt++;
    low[v] = pre[v];
    for (int w : G.adj(v)) {
      if (pre[w] == -1) {
        children++;
        dfs(G, v, w);

        // update low number
        low[v] = Math.min(low[v], low[w]);

        // non-root of DFS is an articulation point if low[w] >= pre[v]
        if (low[w] >= pre[v] && u != v)
          articulation[v] = true;
      }

      // update low number - ignore reverse of edge leading to v
      else if (w != u)
        low[v] = Math.min(low[v], pre[w]);
    }

    // root of DFS is an articulation point if it has more than 1 child
    if (u == v && children > 1)
      articulation[v] = true;
  }

  // is vertex v an articulation point?
  public boolean isArticulation(int v) { return articulation[v]; }

  // test client
  public static void main(String[] args) {
    int V = Integer.parseInt(args[0]);
    int E = Integer.parseInt(args[1]);
    Graph G = new Graph(V, E);
    StdOut.println(G);

    XBiconnected bic = new XBiconnected(G);

    // print out articulation points
    StdOut.println();
    StdOut.println("Articulation points");
    StdOut.println("-------------------");
    for (int v = 0; v < G.V(); v++)
      if (bic.isArticulation(v)) StdOut.println(v);
  }


}