/// <summary>
/// Gets the minimum-weight path to a goal using the A* algorithm.
/// </summary>
/// <remarks>Because the heuristic is not known to be consistent, we cannot use the closed set optimization.</remarks>
/// <typeparam name="TNode">The type of a node.</typeparam>
/// <typeparam name="TKey">The type of a node key.</typeparam>
/// <param name="sources">The set of nodes from which to start the search, weighted by their initial cost.</param>
/// <param name="key">The function which maps a node to its key.</param>
/// <param name="next">The function which maps a node to its adjacent nodes.</param>
/// <param name="goal">The goal predicate.</param>
/// <param name="heuristic">The possibly-inconsistent heuristic function.</param>
/// <returns>The minimum-weight path, or null if none exists.</returns>
private static IWeighted <IEnumerable <TNode> > AStarInconsistent <TNode, TKey>(
IEnumerable <IWeighted <TNode> > sources,
Func <TNode, TKey> key,
Func <TNode, IEnumerable <IWeighted <TNode> > > next,
Func <TNode, bool> goal,
Func <TNode, double> heuristic)
{
var came_from = new Dictionary <TKey, TNode>();
IPriorityQueue <double, AStarOpen <TNode> > open_queue = new PairingHeap <double, AStarOpen <TNode> >();
var open_lookup = new Dictionary <TKey, IPriorityQueueHandle <double, AStarOpen <TNode> > >();
foreach (var source in sources)
{
var u = source.Value;
var key_u = key(u);
var g_u = source.Weight;
var f_u = g_u + heuristic(u);
var open_u = new AStarOpen <TNode>(u, g_u);
open_u.Handle = open_queue.Add(f_u, open_u);
open_lookup.Add(key_u, open_u.Handle);
}
while (open_queue.Count > 0)
{
var handle_u = open_queue.Min;
var u = handle_u.Value.Node;
var key_u = key(u);
if (goal(u))
{
var path = ReconstructPath(key, came_from, u);
return(new Weighted <IEnumerable <TNode> >(path, handle_u.Value.G));
}
open_queue.Remove(handle_u);
open_lookup.Remove(key_u);
foreach (var uv in next(u))
{
var v = uv.Value;
var key_v = key(v);
var g_v = handle_u.Value.G + uv.Weight;
var f_v = g_v + heuristic(v);
IPriorityQueueHandle <double, AStarOpen <TNode> > handle_v;
if (open_lookup.TryGetValue(key_v, out handle_v))
{
if (f_v < handle_v.Key)
{
open_queue.UpdateKey(handle_v, f_v);
handle_v.Value.G = g_v;
came_from[key_v] = u;
}
}
else
{
var open_v = new AStarOpen <TNode>(v, g_v);
open_v.Handle = open_queue.Add(f_v, open_v);
open_lookup.Add(key_v, open_v.Handle);
came_from[key_v] = u;
}
}
}
return(null);
}
/// <summary>
/// Gets the minimum-weight path to a goal using uniform cost search.
/// </summary>
/// <typeparam name="TNode">The type of a node.</typeparam>
/// <typeparam name="TKey">The type of a node key.</typeparam>
/// <param name="sources">The set of nodes from which to start the search, weighted by their initial cost.</param>
/// <param name="key">The function which maps a node to its key.</param>
/// <param name="next">The function which maps a node to its adjacent nodes.</param>
/// <param name="goal">The goal predicate.</param>
/// <returns>The minimum-weight path, or null if none exists.</returns>
public static IWeighted <IEnumerable <TNode> > UniformCostSearch <TNode, TKey>(
this IEnumerable <IWeighted <TNode> > sources,
Func <TNode, TKey> key,
Func <TNode, IEnumerable <IWeighted <TNode> > > next,
Func <TNode, bool> goal)
{
var came_from = new Dictionary <TKey, TNode>();
var open_lookup = new Dictionary <TKey, IPriorityQueueHandle <double, TNode> >();
IPriorityQueue <double, TNode> open_queue = new PairingHeap <double, TNode>();
var closed = new HashSet <TKey>();
foreach (var source in sources)
{
var u = source.Value;
var g_u = source.Weight;
open_lookup.Add(key(u), open_queue.Add(g_u, u));
}
while (open_queue.Count > 0)
{
var handle_u = open_queue.Min;
var u = handle_u.Value;
var key_u = key(u);
var g_u = handle_u.Key;
if (goal(u))
{
var path = ReconstructPath(key, came_from, u);
return(new Weighted <IEnumerable <TNode> >(path, g_u));
}
open_lookup.Remove(key_u);
open_queue.Remove(handle_u);
closed.Add(key_u);
foreach (var uv in next(u))
{
var v = uv.Value;
var key_v = key(v);
if (closed.Contains(key_v))
{
continue;
}
IPriorityQueueHandle <double, TNode> v_handle;
var g_uv = g_u + uv.Weight;
if (open_lookup.TryGetValue(key_v, out v_handle))
{
if (g_uv < v_handle.Key)
{
open_queue.UpdateKey(v_handle, g_uv);
came_from[key_v] = u;
}
}
else
{
open_lookup.Add(key_v, open_queue.Add(g_uv, v));
came_from[key_v] = u;
}
}
}
return(null);
}
public IEnumerable<Tuple<Word, int>> Derive()
{
var derivedWords = new HashSet<string>();
var pq = new PairingHeap<Word, int>();
pq.Add(new Word(Grammar.StartSymbol), 0);
var rules = Grammar.Rules.OrderBy(r => r.WordToInsert.Length - r.WordToReplace.Length).ToArray();
while (pq.Count > 0)
{
var elementToDerive = pq.Min;
pq.Remove(elementToDerive);
var wordToDerive = elementToDerive.Key;
foreach (var nw in rules.SelectMany(rule => wordToDerive.ReplaceAll(rule.WordToReplace, rule.WordToInsert))
.Where(nw => !derivedWords.Contains(nw.ToString())))
{
derivedWords.Add(nw.ToString());
pq.Add(nw, nw.Length);
yield return Tuple.Create(nw, wordToDerive.Length);
}
}
}
