【数据结构-图】最小生成树

news2024/11/27 7:23:52

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博客目录

- 一.Prim
- 二.Kruskal

一.Prim

public class Prim {
    public static void main(String[] args) {
        Vertex v1 = new Vertex("v1");
        Vertex v2 = new Vertex("v2");
        Vertex v3 = new Vertex("v3");
        Vertex v4 = new Vertex("v4");
        Vertex v5 = new Vertex("v5");
        Vertex v6 = new Vertex("v6");
        Vertex v7 = new Vertex("v7");

        v1.edges = List.of(new Edge(v2, 2), new Edge(v3, 4), new Edge(v4, 1));
        v2.edges = List.of(new Edge(v1, 2), new Edge(v4, 3), new Edge(v5, 10));
        v3.edges = List.of(new Edge(v1, 4), new Edge(v4, 2), new Edge(v6, 5));
        v4.edges = List.of(new Edge(v1, 1), new Edge(v2, 3), new Edge(v3, 2),
                new Edge(v5, 7), new Edge(v6, 8), new Edge(v7, 4));
        v5.edges = List.of(new Edge(v2, 10), new Edge(v4, 7), new Edge(v7, 6));
        v6.edges = List.of(new Edge(v3, 5), new Edge(v4, 8), new Edge(v7, 1));
        v7.edges = List.of(new Edge(v4, 4), new Edge(v5, 6), new Edge(v6, 1));

        List<Vertex> graph = List.of(v1, v2, v3, v4, v5, v6, v7);

        prim(graph, v1);

    }

    static void prim(List<Vertex> graph, Vertex source) {
        ArrayList<Vertex> list = new ArrayList<>(graph);
        source.dist = 0;

        while (!list.isEmpty()) {
            Vertex min = chooseMinDistVertex(list);
            updateNeighboursDist(min);
            list.remove(min);
            min.visited = true;
            System.out.println("---------------");
            for (Vertex v : graph) {
                System.out.println(v);
            }
        }
    }

    private static void updateNeighboursDist(Vertex curr) {
        for (Edge edge : curr.edges) {
            Vertex n = edge.linked;
            if (!n.visited) {
                int dist = edge.weight;
                if (dist < n.dist) {
                    n.dist = dist;
                    n.prev = curr;
                }
            }
        }
    }

    private static Vertex chooseMinDistVertex(ArrayList<Vertex> list) {
        Vertex min = list.get(0);
        for (int i = 1; i < list.size(); i++) {
            if (list.get(i).dist < min.dist) {
                min = list.get(i);
            }
        }
        return min;
    }
}

二.Kruskal

public class Kruskal {
    static class Edge implements Comparable<Edge> {
        List<Vertex> vertices;
        int start;
        int end;
        int weight;

        public Edge(List<Vertex> vertices, int start, int end, int weight) {
            this.vertices = vertices;
            this.start = start;
            this.end = end;
            this.weight = weight;
        }

        public Edge(int start, int end, int weight) {
            this.start = start;
            this.end = end;
            this.weight = weight;
        }

        @Override
        public int compareTo(Edge o) {
            return Integer.compare(this.weight, o.weight);
        }

        @Override
        public String toString() {
            return vertices.get(start).name + "<->" + vertices.get(end).name + "(" + weight + ")";
        }
    }

    public static void main(String[] args) {
        Vertex v1 = new Vertex("v1");
        Vertex v2 = new Vertex("v2");
        Vertex v3 = new Vertex("v3");
        Vertex v4 = new Vertex("v4");
        Vertex v5 = new Vertex("v5");
        Vertex v6 = new Vertex("v6");
        Vertex v7 = new Vertex("v7");

        List<Vertex> vertices = List.of(v1, v2, v3, v4, v5, v6, v7);
        PriorityQueue<Edge> queue = new PriorityQueue<>(List.of(
                new Edge(vertices,0, 1, 2),
                new Edge(vertices,0, 2, 4),
                new Edge(vertices,0, 3, 1),
                new Edge(vertices,1, 3, 3),
                new Edge(vertices,1, 4, 10),
                new Edge(vertices,2, 3, 2),
                new Edge(vertices,2, 5, 5),
                new Edge(vertices,3, 4, 7),
                new Edge(vertices,3, 5, 8),
                new Edge(vertices,3, 6, 4),
                new Edge(vertices,4, 6, 6),
                new Edge(vertices,5, 6, 1)
        ));

        kruskal(vertices.size(), queue);
    }

    static void kruskal(int size, PriorityQueue<Edge> queue) {
        List<Edge> result = new ArrayList<>();
        DisjointSet set = new DisjointSet(size);
        while (result.size() < size - 1) {
            Edge poll = queue.poll();
            int s = set.find(poll.start);
            int e = set.find(poll.end);
            if (s != e) {
                result.add(poll);
                set.union(s, e);
            }
        }

        for (Edge edge : result) {
            System.out.println(edge);
        }
    }
}