Java博里叶算法

Java博里叶算法

引言

博里叶算法（Boruvka's algorithm）是一种用于解决最小生成树（Minimum Spanning Tree，简称MST）问题的算法。最小生成树是在一个连通无向图中，通过选择一些边使得这些边构成的图是一棵树，并且这棵树的边权值之和最小。本文将介绍Java中的博里叶算法，并给出代码示例。

博里叶算法的原理

博里叶算法是基于贪心策略的算法，它的基本思想是从图的每个连通分量开始，找到连接该连通分量至外部的最小权重边，然后将这些边加入最小生成树的集合中。接着，将图中的每个连通分量缩减为一个节点，并重复上述步骤，直到只剩下一个节点。这样就能够得到最小生成树。

Java实现

下面我们来看一下在Java中如何实现博里叶算法。首先，我们需要定义一个表示图的类，包含顶点和边的信息。

import java.util.ArrayList;
import java.util.List;

class Graph {
    // 图的顶点数
    int V;

    // 图的边
    List<Edge> edges;

    // 边的类定义
    class Edge {
        int src, dest, weight;

        Edge(int src, int dest, int weight) {
            this.src = src;
            this.dest = dest;
            this.weight = weight;
        }
    }

    // 构造函数
    Graph(int V) {
        this.V = V;
        edges = new ArrayList<>();
    }

    // 添加边
    void addEdge(int src, int dest, int weight) {
        edges.add(new Edge(src, dest, weight));
    }
}

接下来，我们需要实现博里叶算法的主要逻辑。

class BoruvkaMST {
    // 执行博里叶算法
    void boruvkaMST(Graph graph) {
        int V = graph.V;
        int[] parent = new int[V];
        int[] cheapest = new int[V];
        Subset[] subsets = new Subset[V];
        List<Graph.Edge> mst = new ArrayList<>();
        int numTrees = 0;
        int MSTweight = 0;

        for (int v = 0; v < V; v++) {
            parent[v] = -1;
            cheapest[v] = -1;
            subsets[v] = new Subset();
            subsets[v].parent = v;
            subsets[v].rank = 0;
            numTrees = V;
        }

        while (numTrees > 1) {
            for (int v = 0; v < V; v++) {
                cheapest[v] = -1;
            }

            for (int i = 0; i < graph.edges.size(); i++) {
                int set1 = find(subsets, graph.edges.get(i).src);
                int set2 = find(subsets, graph.edges.get(i).dest);

                if (set1 == set2) {
                    continue;
                }

                if (cheapest[set1] == -1 ||
                        graph.edges.get(i).weight < graph.edges.get(cheapest[set1]).weight) {
                    cheapest[set1] = i;
                }

                if (cheapest[set2] == -1 ||
                        graph.edges.get(i).weight < graph.edges.get(cheapest[set2]).weight) {
                    cheapest[set2] = i;
                }
            }

            for (int i = 0; i < V; i++) {
                if (cheapest[i] != -1) {
                    int set1 = find(subsets, graph.edges.get(cheapest[i]).src);
                    int set2 = find(subsets, graph.edges.get(cheapest[i]).dest);

                    if (set1 == set2) {
                        continue;
                    }

                    mst.add(graph.edges.get(cheapest[i]));
                    MSTweight += graph.edges.get(cheapest[i]).weight;

                    union(subsets, set1, set2);
                    numTrees--;
                }
            }
        }

        System.out.println("Minimum Spanning Tree:");
        for (int i = 0; i < mst.size(); i++) {
            System.out.println(mst.get(i).src + " - " +
                    mst.get(i).dest + ": " + mst.get(i).weight);
        }
        System.out.println("Weight of MST: " + MSTweight);
    }

    // 查找节点所属的集合
    int find(Subset[] subsets, int i) {
        if