private readonly int[] _rank; // rank[v] = order where vertex v appers in order
/// <summary>
/// Determines whether the digraph <tt>G</tt> has a topological order and, if so,
/// finds such a topological order.
/// </summary>
/// <param name="g">g the digraph</param>
public TopologicalX(Digraph g)
{
// indegrees of remaining vertices
var indegree = new int[g.V];
for (var v = 0; v < g.V; v++)
{
indegree[v] = g.Indegree(v);
}
// initialize
_rank = new int[g.V];
_order = new Collections.Queue <Integer>();
var count = 0;
// initialize queue to contain all vertices with indegree = 0
var queue = new Collections.Queue <Integer>();
for (var v = 0; v < g.V; v++)
{
if (indegree[v] == 0)
{
queue.Enqueue(v);
}
}
for (var j = 0; !queue.IsEmpty(); j++)
{
int v = queue.Dequeue();
_order.Enqueue(v);
_rank[v] = count++;
foreach (int w in g.Adj(v))
{
indegree[w]--;
if (indegree[w] == 0)
{
queue.Enqueue(w);
}
}
}
// there is a directed cycle in subgraph of vertices with indegree >= 1.
if (count != g.V)
{
_order = null;
}
//assert check(G);
}
// all keys in subtrie rooted at x with given prefix
private static void Collect(Node <TValue> x, StringBuilder prefix, Collections.Queue <string> queue)
{
if (x == null)
{
return;
}
Collect(x.Left, prefix, queue);
if (x.Value != null)
{
queue.Enqueue(prefix.ToString() + x.Ch);
}
Collect(x.Mid, prefix.Append(x.Ch), queue);
prefix.Remove(prefix.Length - 1, 1);
Collect(x.Right, prefix, queue);
}
/// <summary>
/// Returns all of the keys in the set that start with <tt>prefix</tt>.
/// </summary>
/// <param name="prefix">prefix the prefix</param>
/// <returns>all of the keys in the set that start with <tt>prefix</tt>, as an iterable</returns>
public IEnumerable <string> KeysWithPrefix(string prefix)
{
var queue = new Collections.Queue <string>();
var x = Get(_root, prefix, 0);
if (x == null)
{
return(queue);
}
if (x.Value != null)
{
queue.Enqueue(prefix);
}
Collect(x.Mid, new StringBuilder(prefix), queue);
return(queue);
}
private void Collect(Node <TValue> x, StringBuilder prefix, Collections.Queue <string> results)
{
if (x == null)
{
return;
}
if (x.Value != null)
{
results.Enqueue(prefix.ToString());
}
for (var c = 0; c < R; c++)
{
var ch = (char)c;
prefix.Append(ch);
Collect(x.Next[c], prefix, results);
prefix.Remove(prefix.Length - 1, 1);
}
}
/// <summary>
/// Returns the Keys in the BST in level order (for debugging).
/// </summary>
/// <returns>the Keys in the BST in level order traversal, as an Iterable</returns>
public IEnumerable <TKey> LevelOrder()
{
var keys = new Collections.Queue <TKey>();
var queue = new Collections.Queue <Node <TKey, TValue> >();
queue.Enqueue(_root);
while (!queue.IsEmpty())
{
var x = queue.Dequeue();
if (x == null)
{
continue;
}
keys.Enqueue(x.Key);
queue.Enqueue(x.Left);
queue.Enqueue(x.Right);
}
return(keys);
}
/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="queue"></param>
/// <param name="lo"></param>
/// <param name="hi"></param>
private void Keys(Node <TKey, TValue> x, Collections.Queue <TKey> queue, TKey lo, TKey hi)
{
if (x == null)
{
return;
}
var cmplo = lo.CompareTo(x.Key);
var cmphi = hi.CompareTo(x.Key);
if (cmplo < 0)
{
Keys(x.Left, queue, lo, hi);
}
if (cmplo <= 0 && cmphi >= 0)
{
queue.Enqueue(x.Key);
}
if (cmphi > 0)
{
Keys(x.Right, queue, lo, hi);
}
}
private IEnumerable <DirectedEdge> _cycle; // negative cycle (or null if no such cycle)
/// <summary>
/// Computes a shortest paths tree from <tt>s</tt> to every other vertex in
/// the edge-weighted digraph <tt>G</tt>.
/// </summary>
/// <param name="g">g the acyclic digraph</param>
/// <param name="s">s the source vertex</param>
/// <exception cref="ArgumentException">unless 0 le; <tt>s</tt> le; <tt>V</tt> - 1</exception>
public BellmanFordSP(EdgeWeightedDigraph g, int s)
{
_distTo = new double[g.V];
_edgeTo = new DirectedEdge[g.V];
_onQueue = new bool[g.V];
for (var v = 0; v < g.V; v++)
{
_distTo[v] = double.PositiveInfinity;
}
_distTo[s] = 0.0;
// Bellman-Ford algorithm
_queue = new Collections.Queue <Integer>();
_queue.Enqueue(s);
_onQueue[s] = true;
while (!_queue.IsEmpty() && !HasNegativeCycle())
{
int v = _queue.Dequeue();
_onQueue[v] = false;
Relax(g, v);
}
}
private void Collect(Node <TValue> x, StringBuilder prefix, string pattern, Collections.Queue <string> results)
{
if (x == null)
{
return;
}
var d = prefix.Length;
if (d == pattern.Length && x.Value != null)
{
results.Enqueue(prefix.ToString());
}
if (d == pattern.Length)
{
return;
}
var c = pattern[d];
if (c == '.')
{
for (var ch = 0; ch < R; ch++)
{
var chr = (char)ch;
prefix.Append(chr);
Collect(x.Next[ch], prefix, pattern, results);
prefix.Remove(prefix.Length - 1, 1);
}
}
else
{
prefix.Append(c);
Collect(x.Next[c], prefix, pattern, results);
prefix.Remove(prefix.Length - 1, 1);
}
}
/// <summary>
/// run Prim's algorithm
/// </summary>
/// <param name="g"></param>
/// <param name="s"></param>
private void Prim(EdgeWeightedGraph g, int s)
{
Scan(g, s);
while (!_pq.IsEmpty())
{ // better to stop when mst has V-1 edges
var e = _pq.DelMin(); // smallest edge on pq
int v = e.Either(), w = e.Other(v); // two endpoints
//assert marked[v] || marked[w];
if (_marked[v] && _marked[w])
{
continue; // lazy, both v and w already scanned
}
_mst.Enqueue(e); // add e to MST
_weight += e.Weight;
if (!_marked[v])
{
Scan(g, v); // v becomes part of tree
}
if (!_marked[w])
{
Scan(g, w); // w becomes part of tree
}
}
}
private readonly Collections.Stack <Integer> _cycle; // the directed cycle; null if digraph is acyclic
public DirectedCycleX(Digraph g)
{
// indegrees of remaining vertices
var indegree = new int[g.V];
for (var v = 0; v < g.V; v++)
{
indegree[v] = g.Indegree(v);
}
// initialize queue to contain all vertices with indegree = 0
var queue = new Collections.Queue <Integer>();
for (var v = 0; v < g.V; v++)
{
if (indegree[v] == 0)
{
queue.Enqueue(v);
}
}
for (var j = 0; !queue.IsEmpty(); j++)
{
int v = queue.Dequeue();
foreach (int w in g.Adj(v))
{
indegree[w]--;
if (indegree[w] == 0)
{
queue.Enqueue(w);
}
}
}
// there is a directed cycle in subgraph of vertices with indegree >= 1.
var edgeTo = new int[g.V];
var root = -1; // any vertex with indegree >= -1
for (var v = 0; v < g.V; v++)
{
if (indegree[v] == 0)
{
continue;
}
root = v;
foreach (int w in g.Adj(v))
{
if (indegree[w] > 0)
{
edgeTo[w] = v;
}
}
}
if (root != -1)
{
// find any vertex on cycle
var visited = new bool[g.V];
while (!visited[root])
{
visited[root] = true;
root = edgeTo[root];
}
// extract cycle
_cycle = new Collections.Stack <Integer>();
var v = root;
do
{
_cycle.Push(v);
v = edgeTo[v];
} while (v != root);
_cycle.Push(root);
}
//assert check();
}
/// <summary>
/// Log a diagnostic level message.
/// </summary>
/// <param name="category">The category of the message.</param>
/// <param name="message">The message format string.</param>
/// <param name="args">Arguments for the message format string.</param>
public static void Diag(int category, string message, params object[] args)
{
_logQueue.Enqueue(new Entry
{
Level = LogLevel.Diagnostic,
Category = category,
Message = string.Format(message, args),
Except = null
});
}
/// <summary>
/// BFS from multiple sources
/// </summary>
/// <param name="g"></param>
/// <param name="sources"></param>
private void Bfs(Digraph g, IEnumerable<Integer> sources)
{
var q = new Collections.Queue<Integer>();
foreach (int s in sources)
{
_marked[s] = true;
_distTo[s] = 0;
q.Enqueue(s);
}
while (!q.IsEmpty())
{
int v = q.Dequeue();
foreach (int w in g.Adj(v))
{
if (!_marked[w])
{
_edgeTo[w] = v;
_distTo[w] = _distTo[v] + 1;
_marked[w] = true;
q.Enqueue(w);
}
}
}
}
