public void TestIndexMinHeap()
{
int n = 1000000;
Random random = new Random();
var heap = new IndexMinHeap <int>(n);
for (int i = 0; i < n; i++)
{
heap.Add((int)(random.Next() * n));
}
var arr = new int[n];
for (var i = 0; i < n; i++)
{
arr[i] = heap.ExtractMin();
}
var success = true;
for (var i = 1; i < n; i++)
{
if (arr[i - 1] > arr[i])
{
success = false;
}
}
Assert.AreEqual(true, success);
}
// X - set of explored vertices of graph G
// V-X - set of unexplored vertices of graph G
//
// Invariant.
// The key of a vertex w belongs to V-X is the min Dijkstra score of an edge with tail v belongs to X
// and head w, or +infinity if no such edge exists.
// key(w) = min len(v) + l(vw)
//
// DijkstraSearch(graph G, vertex s):
// // Initialization
// X = empty set
// H = empty min heap
// key(s) = 0
// for each vertex V in G.vertices do: key(V) = +infinity
// for each vertex V in G.vertices do: H.Insert(V)
// // Main loop
// while H is not empty do:
// w* = H.ExtractMin()
// X.Add(w*)
// len(w*) = key(w*)
// // Update Heap to maintain Invariant
// for every edge(w*, y) do:
// H.Delete(y) // Delete: given a heap H and a pointer to an object y in H, delete y from H.
// key(y) = min {key(y), len(w*) + l(w*y)}
// H.Insert(y)
public static int[] DijkstraMinHeap(IDirectedWeightedGraph <int> weightedGraph, int startVertex)
{
var minHeap = new IndexMinHeap <int>(weightedGraph.VerticesCount);
var exploredVertices = new HashSet <int> {
startVertex
};
var len = new int[weightedGraph.VerticesCount + 1];
for (int i = 1; i <= weightedGraph.VerticesCount; i++)
{
var score = i == startVertex ? 0 : 1000000;
len[i] = score;
minHeap.Insert(i, score);
}
while (!minHeap.IsEmpty())
{
int u = minHeap.GetMin();
len[u] = minHeap.GetItemKey(u);
minHeap.ExtractMin();
exploredVertices.Add(u);
foreach ((int v, int weight) in weightedGraph.GetAdjacentVertices(u))
{
if (!exploredVertices.Contains(v))
{
if (len[v] > len[u] + weight)
{
int vKey = minHeap.GetItemKey(v);
int newScore = Math.Min(len[u] + weight, vKey);
// can use (minHeap.Delete + minHeap.Insert) instead of DecreaseKey
// but this would be less effective
minHeap.DecreaseKey(v, newScore);
len[v] = newScore;
}
}
}
}
return(len);
}
public KruskalMST(IGraph <TWeight> graph)
{
G = graph;
ipq = new IndexMinHeap <Edge <TWeight> >(2 * G.E);
marked = new bool[G.V];
MSTEdges = new List <Edge <TWeight> >();
for (var i = 0; i < G.V; i++)
{
foreach (Edge <TWeight> e in G.GetAdjIterator(i))
{
ipq.Add(e);
}
}
var uf = new UnionFind(G.V);
while (!ipq.IsEmpty() && MSTEdges.Count < graph.V - 1)
{
var e = ipq.ExtractMin();
if (uf.IsConnected(e.V, e.W))
{
continue;
}
MSTEdges.Add(e);
uf.UnionElements(e.V, e.W);
}
var value = 0.0;
var converter = TypeDescriptor.GetConverter(typeof(TWeight));
foreach (var edge in MSTEdges)
{
value += (double)converter.ConvertTo(edge.Weight, typeof(double));
}
MSTWeight = (TWeight)converter.ConvertTo(value, typeof(TWeight));
}
static void Main(string[] args)
{
// 使用两种图的储存方式来读取文件
string fileName = "TextG1.txt";
SparseGraph graph = new SparseGraph(13, false);
ReadGraph readGraph = new ReadGraph(graph, fileName);
Console.WriteLine("test g1 in sparse graph ");
graph.Show();
Console.WriteLine();
DenseGraph graph1 = new DenseGraph(13, false);
ReadGraph readGraph1 = new ReadGraph(graph1, fileName);
Console.WriteLine("test g1 in dense graph ");
graph1.Show();
Console.WriteLine("===========================================");
DenseGraph graph2 = new DenseGraph(13, false);
ReadGraph readGraph2 = new ReadGraph(graph2, fileName);
Path path = new Path(graph2, 0);
Console.WriteLine("test path g1 in dense graph ");
path.ShowPath(4);
Console.WriteLine("===========================================");
WeightedDenseGraph <double> wgraph3 = new WeightedDenseGraph <double>(8, false);
ReadWeightedGraph readGraph3 = new ReadWeightedGraph(wgraph3, "testG1.txt");
Console.WriteLine("test in weighted dense graph ");
wgraph3.Show();
Console.WriteLine("===========================================");
SparseWeightedGraph <double> wgraph4 = new SparseWeightedGraph <double>(8, false);
ReadWeightedGraph readGraph4 = new ReadWeightedGraph(wgraph4, "testG1.txt");
Console.WriteLine("test in weighted sparse graph ");
wgraph4.Show();
Console.WriteLine("Test MinHeap");
int n = 100000;
MinHeap <int> heap = new MinHeap <int>(n);
Random rand = new Random();
for (int i = 0; i < n; i++)
{
heap.Add(rand.Next(n));
}
List <int> list = new List <int>();
for (int i = 0; i < n; i++)
{
list.Add(heap.ExtractMin());
}
for (int i = 0; i < n - 1; i++)
{
if (list[i] > list[i + 1])
{
throw new Exception("MinHeap error");
}
}
Console.WriteLine("===========================================");
Console.WriteLine("Test MST");
SparseWeightedGraph <double> wgraph5 = new SparseWeightedGraph <double>(8, false);
ReadWeightedGraph readGraph5 = new ReadWeightedGraph(wgraph5, "testG1.txt");
LazyPrimeMST <double> mst = new LazyPrimeMST <double>(wgraph5);
List <Edge <double> > mstPath = mst.MstEdges();
for (int i = 0; i < mstPath.Count; i++)
{
Console.WriteLine(mstPath[i]);
}
Console.WriteLine("Test Index MinHeap");
IndexMinHeap <int> heap1 = new IndexMinHeap <int>(n);
for (int i = 0; i < n; i++)
{
heap1.Add(i, rand.Next(n));
}
for (int i = 0; i < n / 2; i++)
{
heap1.Update(i, rand.Next(n));
}
List <int> list1 = new List <int>();
for (int i = 0; i < n; i++)
{
list1.Add(heap1.ExtractMin());
}
for (int i = 0; i < n - 1; i++)
{
if (list1[i] > list1[i + 1])
{
throw new Exception("IndexMinHeap error");
}
}
Console.WriteLine("===========================================");
Console.WriteLine("Test MST Optimization");
SparseWeightedGraph <double> wgraph6 = new SparseWeightedGraph <double>(8, false);
ReadWeightedGraph readGraph6 = new ReadWeightedGraph(wgraph6, "testG1.txt");
PrimMST <double> mst1 = new PrimMST <double>(wgraph6);
List <Edge <double> > mstPath1 = mst1.MstEdges();
for (int i = 0; i < mstPath1.Count; i++)
{
Console.WriteLine(mstPath1[i]);
}
}