public LazyPrimMST(EdgeWeightedGraph graph)
{
prioryQueue = new MinPQ <Edge>();
marked = new bool[graph.Vertecies];
mst = new Queue <Edge>();
Visit(graph, 0);
while (!prioryQueue.IsEmpty())
{
var edge = prioryQueue.DelMin();
int vertex = edge.Either();
int otherVertex = edge.Other(vertex);
if (marked[vertex] && marked[otherVertex])
{
continue;
}
mst.Enqueue(edge);
if (!marked[vertex])
{
Visit(graph, vertex);
}
if (!marked[otherVertex])
{
Visit(graph, otherVertex);
}
}
}
public KruskalMst(EdgeWeightedGraph graph)
{
mst = new Queue <Edge>();
var prioryQueue = new MinPQ <Edge>();
foreach (var edge in graph.GetEdges())
{
prioryQueue.Insert(edge);
}
var ds = new DisjointSet(graph.Vertices);
while (!prioryQueue.IsEmpty() && mst.Count < graph.Vertices - 1)
{
var edge = prioryQueue.DelMin();
int vertex = edge.Either();
int otherVertex = edge.Other(vertex);
if (ds.Connected(vertex, otherVertex))
{
continue;
}
ds.Union(vertex, otherVertex);
mst.Enqueue(edge);
}
}
public KruskalMST(EdgeWeightedGraph ewg)
{
this.mst = new Queue();
MinPQ minPQ = new MinPQ();
Iterator iterator = ewg.edges().iterator();
while (iterator.hasNext())
{
Edge edge = (Edge)iterator.next();
minPQ.insert(edge);
}
UF uF = new UF(ewg.V());
while (!minPQ.isEmpty() && this.mst.size() < ewg.V() - 1)
{
Edge edge = (Edge)minPQ.delMin();
int num = edge.either();
int i = edge.other(num);
if (!uF.connected(num, i))
{
uF.union(num, i);
this.mst.enqueue(edge);
this.weight += edge.weight();
}
}
if (!KruskalMST.s_assertionsDisabled && !this.check(ewg))
{
throw new AssertionError();
}
}
public void Initialize()
{
_target = new MinPQ<Distance>();
_target.Insert(new Distance { V = 0, Dist = 3 });
_target.Insert(new Distance { V = 1, Dist = 1 });
_target.Insert(new Distance { V = 2, Dist = 2 });
}
public KruskalMST(EdgeWeightedGraph G)
{
_mst = new Queue <Edge>();
var pq = new MinPQ <Edge>(G.Edges().Count());
var uf = new WeightedQuickUnion(G.V);
foreach (var edge in G.Edges())
{
if (edge is null)
{
continue;
}
pq.Insert(edge);
}
while (!pq.IsEmpty && _mst.Count() < G.V - 1)
{
var e = pq.DelMin(); // Get min weight edge on pq
var v = e.Either();
var w = e.Other(v); // and its vertices.
if (uf.Connected(v, w))
{
continue; // Ignore ineligible edges.
}
uf.Union(v, w); // Merge components.
_mst.Enqueue(e); // Add edge to mst.
}
}
private KruskalMSTAlgorithm(EdgeWeightedGraph graph)
{
// It is more efficient to build a heap by passing array of edges.
MinPQ <Edge> crossingEdgesByWeight = new MinPQ <Edge>(1);
this._mst = new Queue <Edge>();
foreach (Edge edge in graph.GetEdges())
{
crossingEdgesByWeight.Add(edge);
}
// Greedy algorithm
UnionFinder uf = new UnionFinder(graph.VerticesCount);
while (!crossingEdgesByWeight.IsEmpty && this._mst.Count < graph.VerticesCount - 1)
{
Edge edge = crossingEdgesByWeight.DeleteMin();
Int32 sourceVertice = edge.Source;
Int32 targetVertice = edge.Target;
if (!uf.IsConnected(sourceVertice, targetVertice))
{
// sourceVertice - targetVertice does not create a cycle.
uf.Union(sourceVertice, targetVertice); // Merge sourcerVertice and targetVertice components.
this._mst.Enqueue(edge); // Add edge to minimum spanning tree.
this.Weight += edge.Weight;
}
}
}
/// <summary>
/// Compute a minimum spanning tree (or forest) of an edge-weighted graph.
/// </summary>
/// <param name="g">g the edge-weighted graph</param>
public KruskalMST(EdgeWeightedGraph g)
{
// more efficient to build heap by passing array of edges
var pq = new MinPQ<EdgeW>();
foreach (var e in g.Edges())
{
pq.Insert(e);
}
// run greedy algorithm
var uf = new UF(g.V);
while (!pq.IsEmpty() && _mst.Size() < g.V - 1)
{
var e = pq.DelMin();
var v = e.Either();
var w = e.Other(v);
if (!uf.Connected(v, w))
{ // v-w does not create a cycle
uf.Union(v, w); // merge v and w components
_mst.Enqueue(e); // add edge e to mst
_weight += e.Weight;
}
}
// check optimality conditions
//assert check(G);
}
public static void Main(string[] arg)
{
string filename = "words3.txt";
string[] a = Util.readWords(filename);
MaxPQ<string> pqMax = new MaxPQ<string>();
foreach (var item in a)
{
pqMax.insert(item);
}
// se vor afisa cuvintele in ordine descrescatoare
Console.WriteLine("MaxPQ");
while (!pqMax.isEmpty())
{
Console.WriteLine(pqMax.delMax());
}
MinPQ<string> pqMin = new MinPQ<string>();
foreach (var item in a)
{
pqMin.insert(item);
}
// se vor afisa cuvintele in ordine crescatoare
Console.WriteLine("\nMinPQ");
while (!pqMin.isEmpty())
{
Console.WriteLine(pqMin.delMin());
}
}
/**
* Simulates the system of particles for the specified amount of time.
*
* @param limit the amount of time
*/
public void simulate(double limit) {
// initialize PQ with collision events and redraw event
pq = new MinPQ<Event>();
for (int i = 0; i < particles.length; i++) {
predict(particles[i], limit);
}
pq.insert(new Event(0, null, null)); // redraw event
// the main event-driven simulation loop
while (!pq.isEmpty()) {
// get impending event, discard if invalidated
Event e = pq.delMin();
if (!e.isValid()) continue;
Particle a = e.a;
Particle b = e.b;
// physical collision, so update positions, and then simulation clock
for (int i = 0; i < particles.length; i++)
particles[i].move(e.time - t);
t = e.time;
// process event
if (a != null && b != null) a.bounceOff(b); // particle-particle collision
else if (a != null && b == null) a.bounceOffVerticalWall(); // particle-wall collision
else if (a == null && b != null) b.bounceOffHorizontalWall(); // particle-wall collision
else if (a == null && b == null) redraw(limit); // redraw event
// update the priority queue with new collisions involving a or b
predict(a, limit);
predict(b, limit);
}
}
public LazyPrimMST(EdgeWeightedGraph g)
{
_pq = new MinPQ <Edge>(g.E);
_marked = new List <bool>(new bool[g.V]);
_mst = new Queue <Edge>();
Visit(g, 0);
while (!_pq.IsEmpty)
{
var e = (Edge)_pq.DeleteMin();
int v = e.Either(), w = e.Other(v);
if (_marked[v] && _marked[w])
{
continue;
}
_mst.Enqueue(e);
if (!_marked[v])
{
Visit(g, v);
}
if (!_marked[w])
{
Visit(g, w);
}
}
}
private Queue <Edge> mst = new Queue <Edge>(); // edges in MST
public KruskalMST(EdgeWeightedGraph G)
{
// more efficient to build heap by passing array of edges
EdgeComparer comparer = new EdgeComparer();
MinPQ <Edge> pq = new MinPQ <Edge>((Comparer <Edge>)comparer);
foreach (Edge e in G.edges())
{
pq.insert(e);
}
// run greedy algorithm
UF uf = new UF(G.V());
while (!pq.isEmpty() && mst.size() < G.V() - 1)
{
Edge e = pq.delMin();
int v = e.either();
int w = e.other(v);
if (!uf.connected(v, w))
{ // v-w does not create a cycle
uf.union(v, w); // merge v and w components
mst.Enqueue(e); // add edge e to mst
weight += e.Weight();
}
}
}
static void Main(string[] args)
{
var processorNum = int.Parse(Console.ReadLine());
var jobNum = int.Parse(Console.ReadLine());
var jobs = new Job[jobNum];
for (var i = 0; i < jobNum; i++)
{
var jobDesc = Console.ReadLine().Split(' ');
jobs[i] = new Job(jobDesc[0], double.Parse(jobDesc[1]));
}
Array.Sort(jobs);
var processors = new MinPQ <Processor>(processorNum);
for (var i = 0; i < processorNum; i++)
{
processors.Insert(new Processor());
}
for (var i = jobs.Length - 1; i >= 0; i--)
{
var min = processors.DelMin();
min.Add(jobs[i]);
processors.Insert(min);
}
while (!processors.IsEmpty())
{
Console.WriteLine(processors.DelMin());
}
}
/// <summary>
/// 向下访问叶节点，并将slide添加到优先列表中
/// </summary>
/// <param name="node"></param>
/// <param name="p"></param>
/// <param name="pq"></param>
/// <returns></returns>
private TreeNode Explore2Leaf(TreeNode node, Point p, MinPQ pq)
{
TreeNode unexpl;
var expl = node;
TreeNode prev;
while (expl != null && (expl.left != null || expl.right != null))
{
prev = expl;
var axis = expl.axis;
var val = expl.point.vector[axis];
if (p.vector[axis] <= val)
{
unexpl = expl.right;
expl = expl.left;
}
else
{
unexpl = expl.left;
expl = expl.right;
}
if (unexpl != null)
{
pq.insert(new PQNode(unexpl, Math.Abs(val - p.vector[axis])));
}
if (expl == null)
{
return(prev);
}
}
return(expl);
}
private readonly Collections.Queue <EdgeW> _mst = new Collections.Queue <EdgeW>(); // edges in MST
/// <summary>
/// Compute a minimum spanning tree (or forest) of an edge-weighted graph.
/// </summary>
/// <param name="g">g the edge-weighted graph</param>
public KruskalMST(EdgeWeightedGraph g)
{
// more efficient to build heap by passing array of edges
var pq = new MinPQ <EdgeW>();
foreach (var e in g.Edges())
{
pq.Insert(e);
}
// run greedy algorithm
var uf = new UF(g.V);
while (!pq.IsEmpty() && _mst.Size() < g.V - 1)
{
var e = pq.DelMin();
var v = e.Either();
var w = e.Other(v);
if (!uf.Connected(v, w))
{ // v-w does not create a cycle
uf.Union(v, w); // merge v and w components
_mst.Enqueue(e); // add edge e to mst
_weight += e.Weight;
}
}
// check optimality conditions
//assert check(G);
}
public Kruskal(WeightedGraph G)
{
var V = G.V();
var uf = new QuickUnion(V);
var pq = new MinPQ <Edge>();
mst = new List <Edge>();
foreach (Edge e in G.edges())
{
pq.Enqueue(e);
}
while (!pq.IsEmpty && mst.Count < V - 1)
{
var e = pq.DelMin();
var v = e.either();
var w = e.other(v);
if (!uf.IsConnected(v, w))
{
uf.Union(v, w);
mst.Add(e);
}
}
}
public void Test_Empty_OnCreation()
{
MinPQ <Int32> pq = new MinPQ <Int32>(1);
Assert.True(pq.IsEmpty);
Assert.Equal(0, pq.Count);
}
public static void Main(string[] args)
{
int M = 5;
MinPQ<int> pq = new MinPQ<int>(M + 1);
//StreamReader fs = new StreamReader("tinyW.txt");
//StreamReader fs = new StreamReader("tinyT.txt");
//StreamReader fs = new StreamReader("largeW.txt");
StreamReader fs = new StreamReader("largeT.txt");
string line;
while (!fs.EndOfStream)
{
line = fs.ReadLine();
pq.insert(int.Parse(line));
// eliminam valoarea minima din coada cu prioritate daca sunt M+1 elemente in coada
if (pq.size() > M)
pq.delMin();
} // cele mai mari M elemente sunt in coada
// afisam elementele din coada cu prioritate in ordine inversa
Stack<int> stack = new Stack<int>();
foreach (var item in pq)
stack.push(item);
foreach (var item in stack)
{
Console.WriteLine(item);
}
}
public void MinPQTest()
{
string[] graphItems = {
"4 5 0.35",
"4 7 0.37",
"5 7 0.28",
"0 7 0.16",
"1 5 0.32",
"0 4 0.38",
"2 3 0.17",
"1 7 0.19",
"0 2 0.26",
"1 2 0.36",
"1 3 0.29",
"2 7 0.34",
"6 2 0.40",
"3 6 0.52",
"6 0 0.58",
"6 4 0.93"
};
var graph = new EdgeWeightedGraph(8, 16, graphItems);
var pq = new MinPQ<Edge>();
foreach (Edge edge in graph.Edges())
{
pq.insert(edge);
}
while (pq.isEmpty() == false)
{
pq.delMin();
}
}
public LazyPrimMST(IEdgeWeightGraph g)
{
pq = new MinPQ <IEdge>();
marked = new bool[g.V];
mst = new Chapter1.Queue <IEdge>();
Visit(g, 0);//假设G是联通的
while (!pq.IsEmpty)
{
IEdge e = pq.Delete(); //找到权重最小的边
int v = e.Either;
int w = e.Other(v);
if (marked[v] && marked[w]) //跳过失效的边
{
continue;
}
mst.Enqueue(e); //将边添加到树中
if (!marked[v])
{
Visit(g, v);
}
if (!marked[w])
{
Visit(g, w);
}
}
}
public MaxPQWithSize(int max, IComparer <T> comparer)
{
//m_pq = new T[max + 2];
m_max = max;
m_minPQ = new MinPQ <T>(max, comparer);
m_comparer = comparer;
}
public KruskalMST(EdgeWeightedGraph ewg)
{
this.g = ewg;
minPQ = new MinPQ <Edge>(g.E());
mstEdges = new Queue <Edge>();
//first we need to create a priority queue to store all Edges
int either, other;
foreach (Edge edge in ewg.Edges())
{
//either = edge.Either();
//other = edge.Other(either);
//if(either<other) //insert the same edge once only when either<other;
minPQ.Insert(edge);
}
Edge currrent;
Utils.UF uf = new Utils.UF(g.V()); //instantiate the union find variable
//second, we take min from the PQ one at a time and insert to the queue if both ends are not connected yet
while (!minPQ.IsEmpty() && mstEdges.Count < (this.g.V() - 1))
{
currrent = minPQ.DelMin();
either = currrent.Either();
other = currrent.Other(either);
if (!uf.IsConnected(either, other)) //only add the edge into the final queue if both ends are not connected
{
mstEdges.Enqueue(currrent);
uf.Union(either, other);
}
}
}
static T ExtractMin <T>(MinPQ <T> pq) where T : IComparable <T>
{
T x = pq.Top;
pq.Pop();
return(x);
}
/// <summary>
/// Returns a uniformly random tree on <tt>V</tt> vertices.
/// This algorithm uses a Prufer sequence and takes time proportional to <em>V log V</em>.
/// http://www.proofwiki.org/wiki/Labeled_Tree_from_Prüfer_Sequence
/// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.6484&rep=rep1&type=pdf
/// </summary>
/// <param name="v">V the number of vertices in the tree</param>
/// <returns>a uniformly random tree on <tt>V</tt> vertices</returns>
public static Graph Tree(int v)
{
var g = new Graph(v);
// special case
if (v == 1)
{
return(g);
}
// Cayley's theorem: there are V^(V-2) labeled trees on V vertices
// Prufer sequence: sequence of V-2 values between 0 and V-1
// Prufer's proof of Cayley's theorem: Prufer sequences are in 1-1
// with labeled trees on V vertices
var prufer = new int[v - 2];
for (var i = 0; i < v - 2; i++)
{
prufer[i] = StdRandom.Uniform(v);
}
// degree of vertex v = 1 + number of times it appers in Prufer sequence
var degree = new int[v];
for (var vi = 0; vi < v; vi++)
{
degree[vi] = 1;
}
for (var i = 0; i < v - 2; i++)
{
degree[prufer[i]]++;
}
// pq contains all vertices of degree 1
var pq = new MinPQ <Integer>();
for (var vi = 0; vi < v; vi++)
{
if (degree[vi] == 1)
{
pq.Insert(vi);
}
}
// repeatedly delMin() degree 1 vertex that has the minimum index
for (var i = 0; i < v - 2; i++)
{
int vmin = pq.DelMin();
g.AddEdge(vmin, prufer[i]);
degree[vmin]--;
degree[prufer[i]]--;
if (degree[prufer[i]] == 1)
{
pq.Insert(prufer[i]);
}
}
g.AddEdge(pq.DelMin(), pq.DelMin());
return(g);
}
public void Hamlet_MinPQ()
{
// arrange
var pq = new MinPQ <string>();
// act
ArrayPQHamlet(pq, new[] { "be", "be", "not", "or", "that", "to" }, new[] { "is", "to" });
}
public LazyPrimMST(EdgeWeightedGraph g)
{
this.MST = new Queue<Edge>();
this._pq = new MinPQ<Edge>();
this._marked = new bool[g.V()];
for (int v = 0; v < g.V(); v++)
if (!this._marked[v])
this.prim(g, v);
}
private MinPQ<Edge> pq; // edges with one endpoint in tree
/**
* Compute a minimum spanning tree (or forest) of an edge-weighted graph.
* @param G the edge-weighted graph
*/
public LazyPrimMST(EdgeWeightedGraph G) {
mst = new Queue<Edge>();
pq = new MinPQ<Edge>();
marked = new boolean[G.V()];
for (int v = 0; v < G.V(); v++) // run Prim from all vertices to
if (!marked[v]) prim(G, v); // get a minimum spanning forest
// check optimality conditions
assert check(G);
}
public void Test_NotEmpty_WhenAdding()
{
MinPQ <Int32> pq = new MinPQ <Int32>(2);
pq.Add(18);
pq.Add(2);
Assert.False(pq.IsEmpty);
Assert.Equal(2, pq.Count);
}
public void Test_Empty_WhenCleaning()
{
MinPQ <Int32> pq = new MinPQ <Int32>(1);
pq.Add(2);
pq.DeleteMin();
Assert.True(pq.IsEmpty);
Assert.Equal(0, pq.Count);
}
private double _weight; // total weight of MST
#endregion Fields
#region Constructors
/// <summary>
/// Compute a minimum spanning tree (or forest) of an edge-weighted graph.
/// </summary>
/// <param name="g">g the edge-weighted graph</param>
public LazyPrimMST(EdgeWeightedGraph g)
{
_mst = new Collections.Queue<EdgeW>();
_pq = new MinPQ<EdgeW>();
_marked = new bool[g.V];
for (var v = 0; v < g.V; v++) // run Prim from all vertices to
if (!_marked[v]) Prim(g, v); // get a minimum spanning forest
// check optimality conditions
//assert check(G);
}
public void ShouldReturnSize(int[] values, int expectedCount)
{
// Arrange
var minPQ = new MinPQ <int>(values);
// Act
var actualCount = minPQ.Size();
// Assert
Assert.AreEqual(expectedCount, actualCount);
}
public void Test_Add_Min()
{
MinPQ <Int32> pq = new MinPQ <Int32>(10);
for (int i = 1; i < 11; i++)
{
pq.Add(i);
}
Assert.Equal(1, pq.Min());
}
public void ShouldReturnTrueIfMinPqIsEmpty()
{
// Arrange
var minPQ = new MinPQ <int>();
// Act
var result = minPQ.IsEmpty();
// Assert
Assert.IsTrue(result);
}
public EagerPrimMST(EdgeWeightedGraph g)
{
_edgeTo = new Edge[g.V()];
_distTo = new double[g.V()];
for (var i = 0; i < g.V(); i++)
{
_distTo[i] = double.PositiveInfinity;
}
_marked = new bool[g.V()];
_pq = new MinPQ <double>(g.E());
Visit(g, 0);
}
static void Main(string[] args)
{
// 输入格式： buy 20.05 100
var buyer = new MaxPQ <Ticket>();
var seller = new MinPQ <Ticket>();
var n = int.Parse(Console.ReadLine());
for (var i = 0; i < n; i++)
{
var ticket = new Ticket();
var item = Console.ReadLine().Split(' ');
ticket.Price = double.Parse(item[1]);
ticket.Share = int.Parse(item[2]);
if (item[0] == "buy")
{
buyer.Insert(ticket);
}
else
{
seller.Insert(ticket);
}
}
while (!buyer.IsEmpty() && !seller.IsEmpty())
{
if (buyer.Max().Price < seller.Min().Price)
{
break;
}
var buy = buyer.DelMax();
var sell = seller.DelMin();
Console.Write("sell $" + sell.Price + " * " + sell.Share);
if (buy.Share > sell.Share)
{
Console.WriteLine(" -> " + sell.Share + " -> $" + buy.Price + " * " + buy.Share + " buy");
buy.Share -= sell.Share;
buyer.Insert(buy);
}
else if (buy.Share < sell.Share)
{
sell.Share -= buy.Share;
seller.Insert(sell);
Console.WriteLine(" -> " + buy.Share + " -> $" + buy.Price + " * " + buy.Share + " buy");
}
else
{
Console.WriteLine(" -> " + sell.Share + " -> $" + buy.Price + " * " + buy.Share + " buy");
}
}
}
public void ShouldReturnFalseIfMinPqIsNotEmpty()
{
// Arrange
var minPQ = new MinPQ <int>();
minPQ.Insert(5);
// Act
var result = minPQ.IsEmpty();
// Assert
Assert.IsFalse(result);
}
public void TestMinPQ() {
var arr = CreateRandomArray(10);
Insertion<int>.Sort(arr);
StdOut.WriteLine(arr);
var pq = new MinPQ<int>();
foreach (int i in arr) {
pq.Insert(i);
}
while (!pq.IsEmpty) {
StdOut.WriteLine("delete min: {0}", pq.DelMin());
}
}
public Dijkstra(EdgeWeightedDigraph graph, int source)
{
pq = new MinPQ <double>(graph.V());
edgeTo = new DirectedWeightedEdge[graph.V()];
distTo = new double[graph.V()];
for (int i = 0; i < graph.V(); ++i)
{
distTo[i] = double.MaxValue;
}
distTo[source] = 0.0;
dijkstra(graph, 0);
}
public void Min_pq_delete_tests()
{
var p = new MinPQ<int>(5);
p.Insert(5);
p.Insert(4);
p.Insert(99);
p.Insert(14);
p.Insert(0);
Assert.AreEqual(0, p.DelMin());
Assert.AreEqual(4, p.DelMin());
Assert.AreEqual(5, p.DelMin());
Assert.AreEqual(14, p.DelMin());
Assert.AreEqual(99, p.DelMin());
}
public Astar(EdgeWeightedDigraph graph, int source, int target)
{
pq = new MinPQ <double>(graph.V());
edgeTo = new DirectedWeightedEdge[graph.V()];
distTo = new double[graph.V()];
for (int i = 0; i < graph.V(); ++i)
{
distTo[i] = double.MaxValue;
}
distTo[source] = 0.0;
AstarSP(graph, 0, target);
}
public void Min_priority_queue()
{
var p = new MinPQ<int>(5);
p.Insert(5);
Assert.AreEqual("5", string.Join(",", p.CurrentPQ()));
p.Insert(4);
Assert.AreEqual("4,5", string.Join(",", p.CurrentPQ()));
p.Insert(99);
Assert.AreEqual("4,5,99", string.Join(",", p.CurrentPQ()));
p.Insert(14);
Assert.AreEqual("4,5,99,14", string.Join(",", p.CurrentPQ()));
p.Insert(0);
Assert.AreEqual("0,4,99,14,5", string.Join(",", p.CurrentPQ()));
}
public void Run()
{
Console.WriteLine("Choose file:"); // Prompt
Console.WriteLine("1 - tinyPQ.txt"); // Prompt
Console.WriteLine("or quit"); // Prompt
var fileNumber = Console.ReadLine();
var fieName = string.Empty;
switch (fileNumber)
{
case "1":
fieName = "tinyPQ.txt";
break;
case "quit":
return;
default:
return;
}
var @in = new In(string.Format("Files\\Sorting\\{0}", fieName));
var words = @in.ReadAllStrings();
//var list = words.Select(word => new StringComparable(word)).ToList();
//var listComparable = list.Cast<IComparable>().ToList();
//var arrayComparable = list.Cast<IComparable>().ToArray();
var listStrings = words.ToList();
var pq = new MinPQ<string>(new StringComparer());
//Fill Priority Queue
foreach (var word in listStrings)
{
pq.Insert(word);
}
// print results
foreach (var item in pq)
{
Console.WriteLine(item);
}
Console.ReadLine();
}
public KruskalMST(EdgeWeightedGraph g)
{
MinPQ<Edge> pq = new MinPQ<Edge>();
foreach (Edge e in g.Edges())
pq.Insert(e);
Part1.QuickUnion uf = new Part1.QuickUnion(g.V());
while (!pq.IsEmpty() && this._mst.Count < g.V() - 1)
{
Edge e = pq.DelMin();
int v = e.Either();
int w = e.Other(v);
if (!uf.IsConnected(v, w))
{
uf.Union(v, w);
this._mst.Enqueue(e);
this.Weight += e.Weight();
}
}
}
public LazyPrimMST(EdgeWeightedGraph graph)
{
pq = new MinPQ<Edge>();
marked = new bool[graph.V];
mst = new Queue<Edge>();
visit(graph, 0);
while (!pq.isEmpty())
{
Edge e = pq.delMin();
int v = e.Either, w = e.Other(v);
if (marked[v] && marked[w]) continue;
mst.Enqueue(e);
if (!marked[v]) visit(graph, v);
if (!marked[w]) visit(graph, w);
}
}
public IEnumerable<int> KSE_MinHeap(int[] A, int K){
var heap = new int[K];
for(int i=0; i<heap.Length; i++)
heap[i] = A[i];
var pq = new MinPQ(heap);
for(int i=K; i<A.Length; i++)
pq.InsertAtTop(A[i]);
foreach(var i in pq.PQ())
yield return i;
}
public static void Test(){
var a = new int[] { 23, 12, 9, 30, 2, 1, 50 };
MinPQ pq = new MinPQ(a);
foreach(var i in pq.PQ()){
Out(i+" ");
}
}
/// <summary>
/// Returns a uniformly random tree on <tt>V</tt> vertices.
/// This algorithm uses a Prufer sequence and takes time proportional to <em>V log V</em>.
/// http://www.proofwiki.org/wiki/Labeled_Tree_from_Prüfer_Sequence
/// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.6484&rep=rep1&type=pdf
/// </summary>
/// <param name="v">V the number of vertices in the tree</param>
/// <returns>a uniformly random tree on <tt>V</tt> vertices</returns>
public static Graph Tree(int v)
{
var g = new Graph(v);
// special case
if (v == 1) return g;
// Cayley's theorem: there are V^(V-2) labeled trees on V vertices
// Prufer sequence: sequence of V-2 values between 0 and V-1
// Prufer's proof of Cayley's theorem: Prufer sequences are in 1-1
// with labeled trees on V vertices
var prufer = new int[v - 2];
for (var i = 0; i < v - 2; i++)
prufer[i] = StdRandom.Uniform(v);
// degree of vertex v = 1 + number of times it appers in Prufer sequence
var degree = new int[v];
for (var vi = 0; vi < v; vi++)
degree[vi] = 1;
for (var i = 0; i < v - 2; i++)
degree[prufer[i]]++;
// pq contains all vertices of degree 1
var pq = new MinPQ<Integer>();
for (var vi = 0; vi < v; vi++)
if (degree[vi] == 1) pq.Insert(vi);
// repeatedly delMin() degree 1 vertex that has the minimum index
for (var i = 0; i < v - 2; i++)
{
int vmin = pq.DelMin();
g.AddEdge(vmin, prufer[i]);
degree[vmin]--;
degree[prufer[i]]--;
if (degree[prufer[i]] == 1) pq.Insert(prufer[i]);
}
g.AddEdge(pq.DelMin(), pq.DelMin());
return g;
}
public TopM(ICollection<string> a)
{
_m = a.Count;
_pq = new MinPQ<Transaction>(_m + 1);
InsertTransactions(a);
}
