图 - Java实现无向带权图的邻接矩阵表示法

1.图

1.1 图的介绍

• 图（Graph），是一种复杂的非线性表结构
• 图中的元素我们就叫做顶点（vertex）
• 图中的一个顶点可以与任意其他顶点建立连接关系。我们把这种建立的关系叫做边（edge），跟顶点相连接的边的条数叫做度（degree）
• 这是一个无向带权图：
  

1.2 邻接矩阵的介绍

• 图最直观的一种存储方法就是，邻接矩阵（Adjacency Matrix）

• 邻接矩阵的底层是一个二维数组
  

• 带权图：数组中就存储相应的权重
  

2.Java实现无向带权图邻接矩阵表示法的常见功能

package com.lagou;

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

/**
 * @author 云梦归遥
 * @date 2022/5/20 12:30
 * @description 无向带权图 - 邻接矩阵法
 */
public class NoDirectionWeightTuMethod {
    private List<Object> nodeList; // 存储所有节点的集合
    private int[][] adjacencyMatrix; // 邻接矩阵
    private int edge; // 边的数量

    public NoDirectionWeightTuMethod(int num){
        nodeList = new ArrayList<>(num);
        adjacencyMatrix = new int[num][num];
        edge = 0;
    }

    // 添加节点
    public NoDirectionWeightTuMethod insert(Object node){
        nodeList.add(node);
        return this;
    }

    // 查找节点
    public String select(Object node){
        StringBuilder stringBuilder = new StringBuilder();
        stringBuilder.append("【" + node + "】= ");
        int index = nodeList.indexOf(node); // 获取索引
        if (index >= 0){
            // 节点存在
            for (int i = 0; i < adjacencyMatrix.length; i++){
                if (adjacencyMatrix[index][i] > 0){
                    stringBuilder.append("【<" + node + ", " + nodeList.get(i) + "> - weight: " + adjacencyMatrix[index][i] + "】 => ");
                }
            }
        } else {
            stringBuilder.append("null");
        }
        String result = stringBuilder.toString();
        result = result.substring(0, result.lastIndexOf(" => "));
        return result;
    }

    // 获取节点的个数
    public int getNodeNum(){
        return nodeList.size();
    }

    // 添加边（权重）
    public NoDirectionWeightTuMethod addEdge(Object object1, Object object2, int weight){
        if (nodeList.contains(object1) && nodeList.contains(object2)){
            int index1 = nodeList.indexOf(object1);
            int index2 = nodeList.indexOf(object2);
            adjacencyMatrix[index1][index2] = weight;
            adjacencyMatrix[index2][index1] = weight;
        }
        return this;
    }

    // 获取权重
    public int getWeight(Object object1, Object object2){
        int result = Integer.MAX_VALUE; // 默认 int 最大值
        if (nodeList.contains(object1) && nodeList.contains(object2)){
            int index1 = nodeList.indexOf(object1);
            int index2 = nodeList.indexOf(object2);
            result = adjacencyMatrix[index1][index2];
        }
        return result;
    }

    // 判断边是否存在
    public boolean hasEdge(Object object1, Object object2){
        boolean result = false;
        if (nodeList.contains(object1) && nodeList.contains(object2)){
            int index1 = nodeList.indexOf(object1);
            int index2 = nodeList.indexOf(object2);
            if (adjacencyMatrix[index1][index2] > 0){
                result = true;
            }
        }
        return result;
    }

    // 获取边的数量
    public int getEdgeNum(Object object){
        int num = Integer.MAX_VALUE;
        if (nodeList.contains(object)){
            num = 0;
            int index = nodeList.indexOf(object);
            for (int i = 0; i < adjacencyMatrix.length; i++){
                if (adjacencyMatrix[index][i] > 0){
                    num++;
                }
            }
        }
        return num;
    }

    // 获取 邻接矩阵
    public String getAdjacencyMatrix(){
        StringBuilder stringBuilder = new StringBuilder();
        stringBuilder.append("  " + Arrays.toString(nodeList.toArray()) + "\n");
        for (int i = 0; i < adjacencyMatrix.length; i++){
            stringBuilder.append(nodeList.get(i) + " " + Arrays.toString(adjacencyMatrix[i]) + "\n");
        }
        return stringBuilder.toString();
    }
}

进行测试

package com.lagou.test;

import com.lagou.NoDirectionWeightTuMethod;

/**
 * @author 云梦归遥
 * @date 2022/5/20 13:05
 * @description
 */
public class NoDirectionWeightTuMethodTest {
    public static void main(String[] args) {
        NoDirectionWeightTuMethod weightTuMethod = new NoDirectionWeightTuMethod(5);
        weightTuMethod.insert("A").insert("B").insert("C").insert("D").insert("E"); // 链式调用
        weightTuMethod
                .addEdge("A", "B", 3) // 链式调用
                .addEdge("A", "D", 1)
                .addEdge("A", "E", 5)
                .addEdge("B", "C", 2)
                .addEdge("D", "E", 7)
                .addEdge("C", "D", 3);
        System.out.println("是否存在边：" + weightTuMethod.hasEdge("A", "D"));
        System.out.println("边的权重：" + weightTuMethod.getWeight("A", "D"));
        System.out.println("边的数量：" + weightTuMethod.getEdgeNum("A"));
        System.out.println("A 的所有关系：" + weightTuMethod.select("A"));
        System.out.println("图中节点个数：" + weightTuMethod.getNodeNum());
        System.out.println("整个图的邻接矩阵：");
        System.out.println(weightTuMethod.getAdjacencyMatrix());
    }
}

3.总结

• 无向带权图的邻接矩阵表示法主要是通过二维数组来实现的
• 每个行与列的交点存储的值其实是对应边上的权重