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    <p>It works! In an <a href="https://stackoverflow.com/questions/2910186">earlier iteration</a> of the <a href="https://en.wikipedia.org/wiki/Johnson%27s_algorithm" rel="nofollow noreferrer">Johnson algorithm</a>, I had supposed that <code>A</code> was an <a href="http://en.wikipedia.org/wiki/Adjacency_matrix" rel="nofollow noreferrer">adjacency matrix</a>. Instead, it appears to represent an <a href="http://en.wikipedia.org/wiki/Adjacency_list" rel="nofollow noreferrer">adjacency list</a>. In that example, implemented below, the vertices <a href="http://en.wikipedia.org/wiki/Adjacency_list" rel="nofollow noreferrer">{a, b, c}</a> are numbered {0, 1, 2}, yielding the following circuits.</p> <p>Addendum: As noted in this proposed <a href="https://stackoverflow.com/review/suggested-edits/1478397">edit</a> and helpful <a href="https://stackoverflow.com/a/14824734/230513">answer</a>, the algorithm specifies that <code>unblock()</code> should remove the element having the <em>value</em> <code>w</code>, not the element having the <em>index</em> <code>w</code>.</p> <pre><code>list.remove(Integer.valueOf(w)); </code></pre> <p>Sample output:</p> <pre> 0 1 0 0 1 2 0 0 2 0 0 2 1 0 1 0 1 1 0 2 1 1 2 0 1 1 2 1 2 0 1 2 2 0 2 2 1 0 2 2 1 2 </pre> <p>By default, the program starts with <code>s = 0</code>; implementing <code>s := least vertex in V</code> as an optimization remains. A variation that produces only unique cycles is shown <a href="https://stackoverflow.com/a/35922906/230513">here</a>.</p> <pre class="lang-java prettyprint-override"><code>import java.util.ArrayList; import java.util.Arrays; import java.util.List; import java.util.Stack; /** * @see http://dutta.csc.ncsu.edu/csc791_spring07/wrap/circuits_johnson.pdf * @see https://stackoverflow.com/questions/2908575 * @see https://stackoverflow.com/questions/2939877 * @see http://en.wikipedia.org/wiki/Adjacency_matrix * @see http://en.wikipedia.org/wiki/Adjacency_list */ public final class CircuitFinding { final Stack&lt;Integer&gt; stack = new Stack&lt;Integer&gt;(); final List&lt;List&lt;Integer&gt;&gt; a; final List&lt;List&lt;Integer&gt;&gt; b; final boolean[] blocked; final int n; int s; public static void main(String[] args) { List&lt;List&lt;Integer&gt;&gt; a = new ArrayList&lt;List&lt;Integer&gt;&gt;(); a.add(new ArrayList&lt;Integer&gt;(Arrays.asList(1, 2))); a.add(new ArrayList&lt;Integer&gt;(Arrays.asList(0, 2))); a.add(new ArrayList&lt;Integer&gt;(Arrays.asList(0, 1))); CircuitFinding cf = new CircuitFinding(a); cf.find(); } /** * @param a adjacency structure of strong component K with * least vertex in subgraph of G induced by {s, s + 1, n}; */ public CircuitFinding(List&lt;List&lt;Integer&gt;&gt; a) { this.a = a; n = a.size(); blocked = new boolean[n]; b = new ArrayList&lt;List&lt;Integer&gt;&gt;(); for (int i = 0; i &lt; n; i++) { b.add(new ArrayList&lt;Integer&gt;()); } } private void unblock(int u) { blocked[u] = false; List&lt;Integer&gt; list = b.get(u); for (int w : list) { //delete w from B(u); list.remove(Integer.valueOf(w)); if (blocked[w]) { unblock(w); } } } private boolean circuit(int v) { boolean f = false; stack.push(v); blocked[v] = true; L1: for (int w : a.get(v)) { if (w == s) { //output circuit composed of stack followed by s; for (int i : stack) { System.out.print(i + " "); } System.out.println(s); f = true; } else if (!blocked[w]) { if (circuit(w)) { f = true; } } } L2: if (f) { unblock(v); } else { for (int w : a.get(v)) { //if (v∉B(w)) put v on B(w); if (!b.get(w).contains(v)) { b.get(w).add(v); } } } v = stack.pop(); return f; } public void find() { while (s &lt; n) { if (a != null) { //s := least vertex in V; L3: circuit(s); s++; } else { s = n; } } } } </code></pre>
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    1. POhelp in the Donalds B. Johnson's algorithm, i cannot understand the pseudo code (PART II)
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    1. CO+1 Wow, hope it wasn't his bachelor thesis.
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    2. CO@stacker: I hope not! Paraphrasing Knuth: "Beware of bugs in the above code; I have only tried it, not proved it correct."
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    3. CO@trashgod Thank you for your kind and very usefull help @stacker basically is my a small part of my MSC dissertation but it's no problem as i have already wrote most of the code plus i use totally different structures. I haven't tested your code but still there is a minor problem. The Ak refers to subgraph of strong components (in your example the network all an SCC .. but what happens if it can be divided in 2 SCC? how is going to be the Ak then? ) That stil remains the big question mark. My idea is that propably ( i have to test to it to check for the correctness) the Ak is the adjaceny list
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