图的结构 .图的广度优先遍历(BFS),深度优先遍历(DFS)

本文链接：https://blog.youkuaiyun.com/Smartbbbb/article/details/123634886

本文详细介绍了如何在Java中实现广度优先搜索(BFS)和深度优先搜索(DFS)，通过实例展示了如何使用栈和队列数据结构处理图的节点，包括有向图的构建与遍历。理解这两种基本图算法有助于在实际项目中高效解决问题。

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图的BFS,DFS

BFS: 利用栈可控制遍历正常结束,尤其对于有环图,是不可缺少的. 在每次出队时打印!

//给定图的一个节点,实现图的广度优先遍历
    public static void bfs(Node<Integer> node){
        if(node == null){
            return;
        }
        Queue<Node<Integer>> queue = new LinkedList<>();
        HashSet<Node<Integer>> set = new HashSet<>();
        queue.add(node);
        set.add(node);
        while (!queue.isEmpty()){
            Node<Integer> curr = queue.poll();
            System.out.println(curr.val);
            for (Node<Integer> next : curr.nexts) {
                if(!set.contains(next)){
                    queue.add(next);
                    set.add(next);
                }
            }
        }
    }

DFS: 深度优先遍历,每次入栈时打印

//给定一个节点,实现图的深度优先遍历
    private static void dfs(Node<Integer> node) {
        if(node == null){
            return;
        }
        Stack<Node<Integer>> stack = new Stack<>();
        HashSet<Node<Integer>> set = new HashSet<>();
        stack.add(node);
        set.add(node);
        System.out.println(node.val);
        while (!stack.empty()){
            Node<Integer> curr = stack.pop();
            for (Node<Integer> next : curr.nexts) {
                if(!set.contains(next)){
                    stack.push(curr);
                    stack.push(next);
                    set.add(next);
                    System.out.println(next.val);
                    break;
                }
            }
        }
    }

图结构的定义:

1.图的构成: 点集边集

public class Graph<T> {
    //点集
    public HashMap<Integer,Node<T>> nodes;
    //边集
    public HashSet<Edge<T>> edges;

    public Graph() {
        this.nodes = new HashMap<>();
        this.edges = new HashSet<>();
    }

}

2.点集的构成: 节点

public class Node<T> {
    
    public T val; //存储的数据
    public int in; //入度
    public int out; //出度
    public ArrayList<Node<T>> nexts; //指向的节点
    public ArrayList<Edge<T>> edges; //该节点含有的边

    public Node(T val) {
        this.val = val;
        this.in = 0;
        this.out = 0;
        this.nexts = new ArrayList<>();
        this.edges = new ArrayList<>();
    }
}

3.边集的构成: 边

public class Edge<T> {
    public Integer weight; //权重
    public Node<T> from; //起点
    public Node<T> to; //重点

    public Edge(Integer weight, Node<T> from, Node<T> to) {
        this.weight = weight;
        this.from = from;
        this.to = to;
    }
}

4.给定一个矩阵生成对应的图


public class GraphGenerator {
    public static void main(String[] args) {
        int[][] matrix = {
                {5, 1, 5},
                {10, 4, 1},
                {12, 6, 1},
                {7, 6, 5},
                {8, 8, 6},
                {1, 5, 8},
                {4, 8, 4}
        };

        createGraph(matrix);
    }

    /**
     * @param matrix 生成图的数据 3 * N, 每组中分别代表 权重,from,to
     * @return 生成的图
     */
    public static Graph<Integer> createGraph(int[][] matrix) {
        Graph<Integer> graph = new Graph<>();
        for (int i = 0; i < matrix.length; i++) {
            Integer weight = matrix[i][0];
            Integer from = matrix[i][1];
            Integer to = matrix[i][2];

            if (!graph.nodes.containsKey(matrix[i][1])) {
                graph.nodes.put(from, new Node<>(from));
            }
            if (!graph.nodes.containsKey(matrix[i][2])) {
                graph.nodes.put(to, new Node<>(to));
            }

            Node<Integer> fromNode = graph.nodes.get(from);
            Node<Integer> toNode = graph.nodes.get(to);
            Edge<Integer> edge = new Edge<>(weight, fromNode, toNode);

            fromNode.nexts.add(toNode);
            fromNode.out++;
            toNode.in++;
            fromNode.edges.add(edge);
            graph.edges.add(edge);
        }
        return graph;
    }
}

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