// 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();
}
double EPSILON = 1E-12;
if (Math.abs(total - weight()) > EPSILON) {
System.err.printf("Weight of edges does not equal weight(): %f vs. %f\n", total, weight());
return false;
}
// 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 : 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()) {
int v = e.either(), w = e.other(v);
// 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;
}
/** Add the undirected edge e to this graph. */
public void addEdge(Edge e) {
int v = e.either();
int w = e.other(v);
adj[v].add(e);
adj[w].add(e);
E++;
}
/**
* Returns all edges in the edge-weighted graph. To iterate over the edges in the edge-weighted
* graph, use foreach notation: <tt>for (Edge e : G.edges())</tt>.
*
* @return all edges in the edge-weighted graph as an Iterable.
*/
public Iterable<Edge> edges() {
Bag<Edge> list = new Bag<Edge>();
for (int v = 0; v < V; v++) {
int selfLoops = 0;
for (Edge e : adj(v)) {
if (e.other(v) > v) {
list.add(e);
}
// only add one copy of each self loop (self loops will be consecutive)
else if (e.other(v) == v) {
if (selfLoops % 2 == 0) list.add(e);
selfLoops++;
}
}
}
return list;
}
private void visit(EdgeWeightedGraph G, int v) {
// Mark v and add to pq all edges from v to unmarked vertices.
marked[v] = true;
for (Edge e : G.adj(v)) {
if (!marked[e.other(v)]) {
pq.insert(e);
}
}
}
public Iterable<Edge> edges() {
Bag<Edge> edges = new Bag<Edge>();
for (int i = 0; i < V; i++) {
for (Edge be : adj(i)) {
if (i < be.other(i)) edges.add(be);
}
}
return edges;
}
/**
* Adds the undirected edge <tt>e</tt> to the edge-weighted graph.
*
* @param e the edge
* @throws java.lang.IndexOutOfBoundsException unless both endpoints are between 0 and V-1
*/
public void addEdge(Edge e) {
int v = e.either();
int w = e.other(v);
if (v < 0 || v >= V)
throw new IndexOutOfBoundsException("vertex " + v + " is not between 0 and " + (V - 1));
if (w < 0 || w >= V)
throw new IndexOutOfBoundsException("vertex " + w + " is not between 0 and " + (V - 1));
adj[v].add(e);
adj[w].add(e);
E++;
}
public Set<Node> getConnectedNodes(Node node) {
Set<Edge> edges = this.getEdges(node);
if (edges == null) {
return null;
}
Set<Node> nodes = new HashSet<>();
for (Edge e : edges) {
nodes.add(e.other(node));
}
return nodes;
}
public void visit(int v) {
marked[v] = true;
for (Edge e : G.adj(v)) {
int w = e.other(v);
if (marked[w]) continue;
if (disTo[w] > e.weight()) {
disTo[w] = e.weight();
if (!pq.contains(w)) {
pq.insert(w, e.weight());
} else pq.changeKey(w, e.weight());
edgeTo[w] = v;
}
}
}
private void visit(EdgeWeightedGraph G, int v) // Add v to tree; update data structures.
{
marked[v] = true;
for (Edge e : G.adj(v)) {
int w = e.other(v);
if (marked[w]) continue; // v-w is ineligible.
if (e.weight() < distTo[w]) // Edge e is new best connection from tree to w.
{
edgeTo[w] = e;
distTo[w] = e.weight();
if (pq.contains(w)) pq.change(w, distTo[w]);
else pq.insert(w, distTo[w]);
}
}
}
public KruskalMST(EdgeWeightedGraph G) {
mst = new Queue<Edge>();
MaxPQ<Edge> pq = new MaxPQ<Edge>();
for (Edge e : G.edges()) pq.insert(e); // 将所有的边进入优先队列，按照权重升序排列
UF uf = new UF(G.V()); // 构建union-find对象
while (!pq.isEmpty() && mst.size() < G.V() - 1) {
Edge e = pq.delMax(); // 从pq得到权重最小的边和他的顶点
int v = e.either(), w = e.other(v);
if (uf.connected(v, w)) continue; // 忽略失效的边，两个顶点已经在生成树中了
uf.union(v, w); // 否则将两者合并，在一个树中,顶点
mst.enqueue(e); // 将边添加到最小生成树中
}
}
public LazyPrimMST(EdgeWeightedGraph G) {
pq = new PriorityQueue<>(Collections.reverseOrder());
marked = new boolean[G.V()];
mst = new LinkedList<>();
visit(G, 0);
while (!pq.isEmpty()) {
Edge e = pq.poll();
int v = e.either();
int w = e.other(v);
if (marked[v] && marked[w]) continue;
mst.offer(e);
if (!marked[v]) visit(G, v);
if (!marked[w]) visit(G, w);
}
}
private Node exploreNode(Set<Node> nodes, Node node) {
this.permanentNodes.add(node);
nodes.remove(node);
Set<Edge> edges = this.graph.getEdges(node);
if (edges == null) {
throw new IllegalStateException("Node not connected. Node: " + node);
}
int nodeLabel = this.getLabel(node);
for (Edge edge : edges) {
Node other = edge.other(node);
if (this.permanentNodes.contains(other)) {
continue;
}
this.setLabel(other, nodeLabel + edge.getWeight());
nodes.add(other);
}
return this.closestNode(nodes);
}
KruskalMST(EdgeWeightedGraph G) {
MinPQ<Edge> pq = new MinPQ<Edge>(); // we dont need to pass a new comparator let it
// follow the natural ordering of edges
double temp_wt = 0;
for (Edge e : G.edges()) pq.insert(e);
UF set = 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 (!set.connected(v, w)) {
set.union(v, w);
mst.add(e);
temp_wt += e.weight();
}
}
this.weight = temp_wt;
}
/**
* Dado un grafo no dirigido y con pesos, ejecuta el algoritmo de Kruskal para la obtención del su
* árbol de cobertura mínima.
*
* @param G Grafo no dirigido con pesos al cual se le deesea obtener su arbol de cobertura mínima.
*/
public void minimumSpanningTree(EdgeWeightedGraph G) // By Kruskal's algorithm
{
LinkedList<Edge> mst = new LinkedList<>();
MinPQ<Edge> pq = new MinPQ<>(G.E());
for (Edge edge : G.edges()) // Bag<Edge> != Comparator<Edge> :c
pq.insert(edge);
UF uf = new UF(G.V());
while (!pq.isEmpty() && mst.size() < G.V() - 1) {
Edge edge = pq.delMin();
int v = edge.either(), w = edge.other(v);
if (!uf.connected(v, w)) {
uf.union(v, w);
mst.add(edge);
}
}
System.out.println("");
for (Edge edge : mst) System.out.println(edge);
}
public LazyPrimMST(EdgeWeightedGraph G) {
pq = new MinPQ<Edge>();
marked = new boolean[G.V()];
mst = new Queue<Edge>();
visit(G, 0); // assumes G is connected (see ex. 4.3.22)
while (!pq.isEmpty()) {
Edge e = pq.delMin(); // Get lowest-weight from pq.
int v = e.either();
int w = e.other(v);
if (marked[v] && marked[w]) {
continue; // Skip if ineligible
}
mst.enqueue(e); // Add edge to tree
if (!marked[v]) { // Add vertex to tree (either v or w).
visit(G, v);
}
if (!marked[w]) {
visit(G, w);
}
}
}
// Kruskal's algorithm
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);
}
public void addEdge(Edge e){//这个要着重看下很重要哦,这个才是图形成的关键
int v = e.either();w=e.other();
adj[v].add(e);
adj[w].add(e);
E++;
}
private void visit(EdgeWeightedGraph G, int v) {
marked[v] = true;
for (Edge e : G.adj(v)) {
if (!marked[e.other(v)]) pq.offer(e);
}
}