/**
* Find k clusters in given graph. Returns maximum spacing between clusters.
*
* @param k - number of cluster to find
* @return spacing between clusters
*/
public int findClusters(final int k) {
Preconditions.checkArgument(k >= 2);
final Edge[] edges = g.getEdges();
Arrays.sort(edges);
final UF uf = new UF(g.getVertexCount());
for (Edge edge : edges) {
if (uf.connected(edge.from, edge.to)) continue;
if (uf.count() > k) uf.union(edge.from, edge.to);
else return edge.weight;
}
throw new IllegalStateException("Failed to reach " + k + " clusters. This should not happen.");
}
public static int count(int N) {
int edges = 0;
UF uf = new UF(N);
while (uf.count() > 1) {
int i = StdRandom.uniform(N);
int j = StdRandom.uniform(N);
if (j == i) j = StdRandom.uniform(N);
// if (uf.connected(i,j)) continue;
uf.union(i, j);
edges++;
}
return edges;
}
public static void main(String[] args) {
int N = StdIn.readInt();
UF uf = new UF(N);
// read in a sequence of pairs of integers (each in the range 0 to N-1),
// calling find() for each pair: If the members of the pair are not already
// call union() and print the pair.
while (!StdIn.isEmpty()) {
int p = StdIn.readInt();
int q = StdIn.readInt();
if (uf.connected(p, q)) continue;
uf.union(p, q);
StdOut.println(p + " " + q);
}
StdOut.println("# components: " + uf.count());
}
public static void main(String[] args) {
StdOut.println("Quick-union-weighted");
int N = StdIn.readInt();
UF uf = new UF(N);
while (!StdIn.isEmpty()) {
int p = StdIn.readInt();
int q = StdIn.readInt();
if (!uf.connected(p, q)) {
uf.union(p, q);
// StdOut.println(p + " " + q);
StdOut.println(uf);
}
}
}
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
}
}
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;
}
// 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;
}
// 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);
}
/**
* 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);
}
/** @param args */
public static void main(String[] args) {
try {
int N = StdIn.readInt();
indexArray = new int[N];
for (int i = 0; i < N; i++) {
indexArray[i] = i;
}
UF uf = new WeightedQuickUnionUF(N);
while (!StdIn.isEmpty()) {
int p = StdIn.readInt();
if (p == -1) {
p = StdIn.readInt();
int q = StdIn.readInt();
StdOut.print(p + " and " + q + " are");
if (!uf.connected(p, q)) {
StdOut.print(" not");
}
StdOut.println(" connected.");
} else {
int q = StdIn.readInt();
if (!uf.connected(p, q)) {
uf.union(p, q);
StdOut.println("connecting " + p + " " + q);
}
}
printArray(indexArray);
printArray(uf.idArray());
printArray(uf.sizeArray());
StdOut.println();
}
} catch (InputMismatchException e) {
System.exit(0);
}
}
