Minimum Spanning Tree Algorithm
At the beginning, each node is a set. Starting from the minimum weight of the edge, it is judged whether the left and right nodes of the current edge are in the same set, and if not, they are divided into the same set. Then loop until all nodes are in the same set.
So the data structures we use: union search, heap. The union search is mainly used to merge sets, and the small root heap is mainly used to pop up edges from small to large according to the weight of the edges.
https://juejin.cn/post/7161250651702296612
package algorithmbasic.class17;
import java.util.*;
//最小生成树算法
public class Kruskal {
public static Set<Edge> kruskalMST(Graph graph) {
//生成好我的并查集。
UnionFind unionFind = new UnionFind();
//图中的每个节点都是一个集合。
unionFind.makeCollection(graph);
//小根堆：根据边的权重比较。
PriorityQueue<Edge> queue = new PriorityQueue<>(new myComparator());
for (Edge e : graph.edges) {
queue.add(e);
}
Set<Edge> set = new HashSet<>();
while (!queue.isEmpty()) {
Edge e = queue.poll();
if (!unionFind.isSameSet(e.from, e.to)) {
unionFind.union(e.from, e.to);
set.add(e);
}
}
return set;
}
public static class UnionFind {
static HashMap<Node, Node> fatherMap = new HashMap<>();
static HashMap<Node, Integer> sizeMap = new HashMap<>();
static Stack<Node> stack = new Stack<>();
public static void makeCollection(Graph graph) {
//**
fatherMap.clear();
sizeMap.clear();
for (Node node : graph.nodes.values()) {
fatherMap.put(node, node);
sizeMap.put(node, 1);
}
}
public static boolean isSameSet(Node a, Node b) {
return findAncestor(a) == findAncestor(b);
}
public static void union(Node a, Node b) {
Node fatherA = findAncestor(a);
Node fatherB = findAncestor(b);
if (fatherA != fatherB) {
Node big = sizeMap.get(fatherA) > sizeMap.get(fatherB) ? fatherA : fatherB;
Node small = big == fatherA ? fatherB : fatherA;
fatherMap.put(small, big);
sizeMap.put(small, 0);
sizeMap.put(big, sizeMap.get(big) + sizeMap.get(small));
}
}
//出入一个节点，寻找这个节点的祖先节点
public static Node findAncestor(Node node) {
while (fatherMap.get(node) != node) {
stack.add(node);
node = fatherMap.get(node);
}
//fatherMap.get(node) == node
//先进行优化
while (!stack.isEmpty()) {
Node cur = stack.pop();
fatherMap.put(cur, node);
}
return node;
}
}
public static class myComparator implements Comparator<Edge> {
@Override
public int compare(Edge o1, Edge o2) {
return o1.weight - o2.weight;
}
}
}
for test
public static void main(String[] args) {
Graph graph = new Graph();
Node a = new Node(1);
Node b = new Node(2);
Node c = new Node(3);
Node e = new Node(5);
Node f = new Node(6);
Node g = new Node(7);
Node h = new Node(8);
graph.nodes.put(1, a);
graph.nodes.put(2, b);
graph.nodes.put(3, c);
graph.nodes.put(5, e);
graph.nodes.put(6, f);
graph.nodes.put(7, g);
graph.nodes.put(8, h);
Edge ac = new Edge(1, a, c);
Edge bc = new Edge(1, b, c);
Edge ab = new Edge(3, a, b);
Edge be = new Edge(10, b, e);
Edge ec = new Edge(12, e, c);
Edge fc = new Edge(50, f, c);
Edge eg = new Edge(1, g, e);
Edge fg = new Edge(3, f, g);
Edge fh = new Edge(6, f, h);
Edge gh = new Edge(9, g, h);
graph.edges.add(ac);
graph.edges.add(bc);
graph.edges.add(ab);
graph.edges.add(be);
graph.edges.add(ec);
graph.edges.add(fc);
graph.edges.add(eg);
graph.edges.add(fg);
graph.edges.add(fh);
graph.edges.add(gh);
Set<Edge> set = new HashSet<>();
set = kruskalMST(graph);
System.out.println(1);
}