public void Min_FibonacciHeap_Test()
{
int nodeCount = 1000 * 10;
var minHeap = new FibonacciHeap <int>();
for (int i = 0; i <= nodeCount; i++)
{
minHeap.Insert(i);
}
for (int i = 0; i <= nodeCount; i++)
{
minHeap.UpdateKey(i, i - 1);
}
int min = 0;
for (int i = 0; i <= nodeCount; i++)
{
min = minHeap.Extract();
Assert.AreEqual(min, i - 1);
}
//IEnumerable tests.
Assert.AreEqual(minHeap.Count, minHeap.Count());
var rnd = new Random();
var testSeries = Enumerable.Range(0, nodeCount - 1).OrderBy(x => rnd.Next()).ToList();
foreach (var item in testSeries)
{
minHeap.Insert(item);
}
for (int i = 0; i < testSeries.Count; i++)
{
var decremented = testSeries[i] - rnd.Next(0, 1000);
minHeap.UpdateKey(testSeries[i], decremented);
testSeries[i] = decremented;
}
testSeries.Sort();
for (int i = 0; i < nodeCount - 2; i++)
{
min = minHeap.Extract();
Assert.AreEqual(testSeries[i], min);
}
//IEnumerable tests.
Assert.AreEqual(minHeap.Count, minHeap.Count());
}
public void Max_FibonacciHeap_Test()
{
int nodeCount = 1000 * 10;
var maxHeap = new FibonacciHeap <int>(SortDirection.Descending);
for (int i = 0; i <= nodeCount; i++)
{
maxHeap.Insert(i);
}
for (int i = 0; i <= nodeCount; i++)
{
maxHeap.UpdateKey(i, i + 1);
}
int max = 0;
for (int i = nodeCount; i >= 0; i--)
{
max = maxHeap.Extract();
Assert.AreEqual(max, i + 1);
}
//IEnumerable tests.
Assert.AreEqual(maxHeap.Count, maxHeap.Count());
var rnd = new Random();
var testSeries = Enumerable.Range(0, nodeCount - 1).OrderBy(x => rnd.Next()).ToList();
foreach (var item in testSeries)
{
maxHeap.Insert(item);
}
for (int i = 0; i < testSeries.Count; i++)
{
var incremented = testSeries[i] + rnd.Next(0, 1000);
maxHeap.UpdateKey(testSeries[i], incremented);
testSeries[i] = incremented;
}
testSeries = testSeries.OrderByDescending(x => x).ToList();
for (int i = 0; i < nodeCount - 2; i++)
{
max = maxHeap.Extract();
Assert.AreEqual(testSeries[i], max);
}
//IEnumerable tests.
Assert.AreEqual(maxHeap.Count, maxHeap.Count());
}
private void CheckHeap(FibonacciHeap <int> heap)
{
FibonacciNode <int> prePeak = null;
while (!heap.IsEmpty)
{
var peak = heap.Extract();
Console.WriteLine();
Console.WriteLine($"Extract {peak}");
heap.Traverse(heap.Peak,
(node) =>
{
Console.Write($"{node} ");
}
);
if (prePeak == null)
{
prePeak = peak;
}
else
{
Assert.IsTrue(prePeak.Key < peak.Key);
prePeak = peak;
}
}
}
/// <summary>
/// Get shortest distance to target.
/// </summary>
public ShortestPathResult <T, W> FindShortestPath(IGraph <T> graph, T source, T destination)
{
//regular argument checks
if (graph?.GetVertex(source) == null || graph.GetVertex(destination) == null)
{
throw new ArgumentException();
}
if (this.@operator == null)
{
throw new ArgumentException("Provide an operator implementation for generic type W during initialization.");
}
if (!graph.IsWeightedGraph)
{
if ([email protected]() != typeof(int))
{
throw new ArgumentException("Edges of unweighted graphs are assigned an imaginary weight of one (1)." +
"Provide an appropriate IShortestPathOperators<int> operator implementation during initialization.");
}
}
//track progress for distance to each Vertex from source
var progress = new Dictionary <T, W>();
//trace our current path by mapping current vertex to its Parent
var parentMap = new Dictionary <T, T>();
//min heap to pick next closest vertex
var minHeap = new FibonacciHeap <MinHeapWrap <T, W> >();
//keep references of heap Node for decrement key operation
var heapMapping = new Dictionary <T, MinHeapWrap <T, W> >();
//add vertices to min heap and progress map
foreach (var vertex in graph.VerticesAsEnumberable)
{
//init parent
parentMap.Add(vertex.Key, default(T));
//init to max value
progress.Add(vertex.Key, @operator.MaxValue);
if (vertex.Key.Equals(source))
{
continue;
}
}
//start from source vertex as current
var current = new MinHeapWrap <T, W>()
{
Distance = @operator.DefaultValue,
Vertex = source
};
minHeap.Insert(current);
heapMapping.Add(current.Vertex, current);
//until heap is empty
while (minHeap.Count > 0)
{
//next min vertex to visit
current = minHeap.Extract();
heapMapping.Remove(current.Vertex);
//no path exists, so return max value
if (current.Distance.Equals(@operator.MaxValue))
{
return(new ShortestPathResult <T, W>(null, @operator.MaxValue));
}
//visit neighbours of current
foreach (var neighbour in graph.GetVertex(current.Vertex).Edges.Where(x => !x.TargetVertexKey.Equals(source)))
{
//new distance to neighbour
var newDistance = @operator.Sum(current.Distance,
graph.GetVertex(current.Vertex).GetEdge(neighbour.TargetVertex).Weight <W>());
//current distance to neighbour
var existingDistance = progress[neighbour.TargetVertexKey];
//update distance if new is better
if (newDistance.CompareTo(existingDistance) < 0)
{
progress[neighbour.TargetVertexKey] = newDistance;
if (!heapMapping.ContainsKey(neighbour.TargetVertexKey))
{
var wrap = new MinHeapWrap <T, W>()
{
Distance = newDistance, Vertex = neighbour.TargetVertexKey
};
minHeap.Insert(wrap);
heapMapping.Add(neighbour.TargetVertexKey, wrap);
}
else
{
//decrement distance to neighbour in heap
var decremented = new MinHeapWrap <T, W>()
{
Distance = newDistance, Vertex = neighbour.TargetVertexKey
};
minHeap.UpdateKey(heapMapping[neighbour.TargetVertexKey], decremented);
heapMapping[neighbour.TargetVertexKey] = decremented;
}
//trace parent
parentMap[neighbour.TargetVertexKey] = current.Vertex;
}
}
}
return(tracePath(graph, parentMap, source, destination));
}
/// <summary>
/// Search path to target using the heuristic.
/// </summary>
public ShortestPathResult <T, W> FindShortestPath(WeightedDiGraph <T, W> graph, T source, T destination)
{
//regular argument checks
if (graph?.FindVertex(source) == null || graph.FindVertex(destination) == null)
{
throw new ArgumentException();
}
//track progress for distance to each Vertex from source
var progress = new Dictionary <T, W>();
//trace our current path by mapping current vertex to its Parent
var parentMap = new Dictionary <T, T>();
//min heap to pick next closest vertex
var minHeap = new FibonacciHeap <AStarWrap <T, W> >();
//keep references of heap Node for decrement key operation
var heapMapping = new Dictionary <T, AStarWrap <T, W> >();
//add vertices to min heap and progress map
foreach (var vertex in graph.Vertices)
{
//init parent
parentMap.Add(vertex.Key, default(T));
//init to max value
progress.Add(vertex.Key, operators.MaxValue);
if (vertex.Key.Equals(source))
{
continue;
}
}
//start from source vertex as current
var current = new AStarWrap <T, W>(heuristic, destination)
{
Distance = operators.DefaultValue,
Vertex = source
};
//insert neighbour in heap
minHeap.Insert(current);
heapMapping[source] = current;
//until heap is empty
while (minHeap.Count > 0)
{
//next min vertex to visit
current = minHeap.Extract();
heapMapping.Remove(current.Vertex);
//no path exists, so return max value
if (current.Distance.Equals(operators.MaxValue))
{
return(new ShortestPathResult <T, W>(null, operators.MaxValue));
}
//visit neighbours of current
foreach (var neighbour in graph.Vertices[current.Vertex].OutEdges.Where(x => !x.Key.Value.Equals(source)))
{
//new distance to neighbour
var newDistance = operators.Sum(current.Distance,
graph.Vertices[current.Vertex].OutEdges[neighbour.Key]);
//current distance to neighbour
var existingDistance = progress[neighbour.Key.Value];
//update distance if new is better
if (newDistance.CompareTo(existingDistance) < 0)
{
progress[neighbour.Key.Value] = newDistance;
if (heapMapping.ContainsKey(neighbour.Key.Value))
{
//decrement distance to neighbour in heap
var decremented = new AStarWrap <T, W>(heuristic, destination)
{
Distance = newDistance, Vertex = neighbour.Key.Value
};
minHeap.UpdateKey(heapMapping[neighbour.Key.Value], decremented);
heapMapping[neighbour.Key.Value] = decremented;
}
else
{
//insert neighbour in heap
var discovered = new AStarWrap <T, W>(heuristic, destination)
{
Distance = newDistance, Vertex = neighbour.Key.Value
};
minHeap.Insert(discovered);
heapMapping[neighbour.Key.Value] = discovered;
}
//trace parent
parentMap[neighbour.Key.Value] = current.Vertex;
}
}
}
return(tracePath(graph, parentMap, source, destination));
}
