1.图的基础知识

该图片来自于：  https://b23.tv/KHCF2m6

2.稀疏图与稠密图

G(V,E)：V顶点个数，E边的个数

稀疏图：E<<V²        一般用邻接表表示(数组+链表)

稠密图：E接近V²        一般用邻接矩阵表示（二维数组）

3.图的两种表示

邻接表法：

class Graph {
    int[][] matrix;
    int size;

    public Graph(int size) {
        this.size = size;
        matrix = new int[size][size];
    }

    public void addEdge(int from, int to) {
        matrix[from][to] = 1;
        matrix[to][from] = 1; // 如果是无向图，需要加上这一行
    }
    
    public void printGraph() {
		for (int i = 0; i < matrix.length; i++) {
			for (int j = 0; j < matrix[i].length; j++) {
				System.out.print(matrix[i][j]+"  ");
			}
			System.out.println();
		}
	}
    
    public static void main(String[] args) {
		Graph graph = new Graph(5);
		graph.addEdge(0, 1);
		graph.addEdge(0, 2);
		graph.addEdge(0, 3);
		graph.addEdge(0, 4);
		
		graph.addEdge(1, 2);
		graph.addEdge(1, 3);
		graph.addEdge(1, 4);
		
		graph.addEdge(2, 3);
		graph.addEdge(2, 4);
		
		graph.addEdge(3, 4);
		graph.printGraph();
	}

 

邻接矩阵法：

public class Graph2 {
    int V;	//图的顶点个数
    LinkedList<Integer> adjListArray[];//数组链表：数组位置存储的是链表，链表里的元素是Integer

    Graph2(int V) {
        this.V = V;

        adjListArray = new LinkedList[V];

        for (int i = 0; i < V; i++) {
            adjListArray[i] = new LinkedList<>();
        }
    }

    void addEdge(int src, int dest) {//添加边
        adjListArray[src].add(dest);
        adjListArray[dest].add(src); // 如果是无向图，需要加上这一行
    }

    void printGraph() {
        for (int v = 0; v < V; v++) {
            System.out.println("Adjacency list of vertex " + v);
            System.out.print("head");
            for (Integer pCrawl : adjListArray[v]) {
                System.out.print(" -> " + pCrawl);
            }
            System.out.println("\n");
        }
    }
    
    public static void main(String[] args) {
		Graph2 graph2 = new Graph2(5);
		System.out.println("顶点个数为："+graph2.V);
		
		graph2.addEdge(0, 1);
		graph2.addEdge(0, 2);
		graph2.addEdge(0, 3);
		graph2.addEdge(0, 4);
		
		graph2.addEdge(1, 2);
		graph2.addEdge(1, 3);
		graph2.addEdge(1, 4);
		
		graph2.addEdge(2, 3);
		graph2.addEdge(2, 4);
		
		graph2.addEdge(3, 4);
		
		graph2.printGraph();
		
	}
}