java实现图的最小生成树（森林）MST克鲁斯卡尔（Kruskal）算法

/******************************************************************************
*  Compilation:  javac KruskalMST.java
*  Execution:    java  KruskalMST filename.txt
*  Dependencies: EdgeWeightedGraph.java Edge.java Queue.java
*                UF.java In.java StdOut.java
*  Data files:   http://algs4.cs.princeton.edu/43mst/tinyEWG.txt *                http://algs4.cs.princeton.edu/43mst/mediumEWG.txt *                http://algs4.cs.princeton.edu/43mst/largeEWG.txt *
*  Compute a minimum spanning forest using Kruskal's algorithm.
*
*  %  java KruskalMST tinyEWG.txt
*  0-7 0.16000
*  2-3 0.17000
*  1-7 0.19000
*  0-2 0.26000
*  5-7 0.28000
*  4-5 0.35000
*  6-2 0.40000
*  1.81000
*
*  % java KruskalMST mediumEWG.txt
*  168-231 0.00268
*  151-208 0.00391
*  7-157   0.00516
*  122-205 0.00647
*  8-152   0.00702
*  156-219 0.00745
*  28-198  0.00775
*  38-126  0.00845
*  10-123  0.00886
*  ...
*  10.46351
*
******************************************************************************/

package edu.princeton.cs.algs4;

/**
*  The <tt>KruskalMST</tt> class represents a data type for computing a
*  <em>minimum spanning tree</em> in an edge-weighted graph.
*  The edge weights can be positive, zero, or negative and need not
*  be distinct. If the graph is not connected, it computes a <em>minimum
*  spanning forest</em>, which is the union of minimum spanning trees
*  in each connected component. The <tt>weight()</tt> method returns the
*  weight of a minimum spanning tree and the <tt>edges()</tt> method
*  returns its edges.
*  <p>
*  This implementation uses <em>Krusal's algorithm</em> and the
*  union-find data type.
*  The constructor takes time proportional to <em>E</em> log <em>E</em>
*  and extra space (not including the graph) proportional to <em>V</em>,
*  where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
*  Afterwards, the <tt>weight()</tt> method takes constant time
*  and the <tt>edges()</tt> method takes time proportional to <em>V</em>.
*  <p>
*  For additional documentation,
*  see <a href="http://algs4.cs.princeton.edu/43mst">Section 4.3</a> of
*  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*  For alternate implementations, see {@link LazyPrimMST}, {@link PrimMST},
*  and {@link BoruvkaMST}.
*
*  @author Robert Sedgewick
*  @author Kevin Wayne
*/
public class KruskalMST {
private static final double FLOATING_POINT_EPSILON = 1E-12;

private double weight;                        // weight of MST
private Queue<Edge> mst = new Queue<Edge>();  // edges in MST

/**
* Compute a minimum spanning tree (or forest) of an edge-weighted graph.
* @param G the edge-weighted graph
*/
public KruskalMST(EdgeWeightedGraph G) {
// more efficient to build heap by passing array of edges
MinPQ<Edge> pq = new MinPQ<Edge>();
for (Edge e : 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();
}
}

// check optimality conditions
assert check(G);
}

/**
* Returns the edges in a minimum spanning tree (or forest).
* @return the edges in a minimum spanning tree (or forest) as
*    an iterable of edges
*/
public Iterable<Edge> edges() {
return mst;
}

/**
* Returns the sum of the edge weights in a minimum spanning tree (or forest).
* @return the sum of the edge weights in a minimum spanning tree (or forest)
*/
public double weight() {
return weight;
}

// check optimality conditions (takes time proportional to E V lg* V)
private boolean check(EdgeWeightedGraph G) {

// check total weight
double total = 0.0;
for (Edge e : edges()) {
total += e.weight();
}
if (Math.abs(total - weight()) > FLOATING_POINT_EPSILON) {
System.err.printf("Weight of edges does not equal weight(): %f vs. %f\n", total, weight());
return false;

97e2
}

// check that it is acyclic
UF uf = new UF(G.V());
for (Edge e : edges()) {
int v = e.either(), w = e.other(v);
if (uf.connected(v, w)) {
System.err.println("Not a forest");
return false;
}
uf.union(v, w);
}

// check that it is a spanning forest
for (Edge e : G.edges()) {
int v = e.either(), w = e.other(v);
if (!uf.connected(v, w)) {
System.err.println("Not a spanning forest");
return false;
}
}

// check that it is a minimal spanning forest (cut optimality conditions)
for (Edge e : edges()) {

// all edges in MST except e
uf = new UF(G.V());
for (Edge f : mst) {
int x = f.either(), y = f.other(x);
if (f != e) uf.union(x, y);
}

// check that e is min weight edge in crossing cut
for (Edge f : G.edges()) {
int x = f.either(), y = f.other(x);
if (!uf.connected(x, y)) {
if (f.weight() < e.weight()) {
System.err.println("Edge " + f + " violates cut optimality conditions");
return false;
}
}
}

}

return true;
}

/**
* Unit tests the <tt>KruskalMST</tt> data type.
*/
public static void main(String[] args) {
In in = new In(args[0]);
EdgeWeightedGraph G = new EdgeWeightedGraph(in);
KruskalMST mst = new KruskalMST(G);
for (Edge e : mst.edges()) {
StdOut.println(e);
}
StdOut.printf("%.5f\n", mst.weight());
}

}