无向图中寻找指定路径：深度优先遍历算法

刷题记录

1. 节点依赖

背景: 类似于无向图中, 寻找从起始节点 --> 目标节点的线路.

需求: 现在需要从起始节点 A, 找到所有到终点 H 的所有路径

A – B ：路径由一个对象构成

public class NodeAssociation {

    private String leftNodeName;

    private String rightNodeName;
}

A – B 可以是：

{ leftNodeName = A ， rightNodeName = B }

或者

{ leftNodeName = B ， rightNodeName = A }

在这里插入图片描述

找到 A --> E 的所有路径：

以及

找到 A --> D 的所有路径：

【注意】

可能存在 A --B ， B – A 这种干扰项
可能存在 A – A 这种干扰项

【思路】

深度优先遍历算法解决

这个就是一个典型的无向图中求 路径的问题; 

从A 开始找到 A的邻接点列表, 然后选择其中一个结点, 再依次选择其下一个结点, 再找到其邻接点列表,再从列表中选择一个访问, 再访问其下一个结点, 直到找到E为止.

具体: 
从 A 开始, 
	A 的邻接列表 [B, C, D]
访问 B , B不是目标节点,继续向下~  
	B 的邻接列表 [E]
访问 E, E是目标, 存储路径 (A-B-E)

然后回退到A, 访问 A的邻接列表的第2个节点 C .....

具体代码实现

@Data
public class Solution {

    // 原始数据
    private List<NodeAssociation> rawData;

    // 测试
        public static void main(String[] args) {
        Solution solution = new Solution();
        NodeAssociation nodeAssociation1 = new NodeAssociation("A",  "B");
        NodeAssociation nodeAssociation2 = new NodeAssociation("A",  "C" );
        NodeAssociation nodeAssociation3 = new NodeAssociation("A",  "D" );
        NodeAssociation nodeAssociation4 = new NodeAssociation("B",  "E" );
        NodeAssociation nodeAssociation5 = new NodeAssociation("E",  "C" );
        NodeAssociation nodeAssociation6 = new NodeAssociation("E",  "H" );
        NodeAssociation nodeAssociation7 = new NodeAssociation("D",  "F" );
        NodeAssociation nodeAssociation8 = new NodeAssociation("H",  "F" );
        NodeAssociation nodeAssociation9 = new NodeAssociation("D",  "A" ); // 干扰项
        NodeAssociation nodeAssociation10 = new NodeAssociation("C",  "F" );

        ArrayList<NodeAssociation> list = new ArrayList<>();
        list.add(nodeAssociation1);
        list.add(nodeAssociation2);
        list.add(nodeAssociation3);
        list.add(nodeAssociation4);
        list.add(nodeAssociation5);
        list.add(nodeAssociation6);
        list.add(nodeAssociation7);
        list.add(nodeAssociation8);
        list.add(nodeAssociation9);
        list.add(nodeAssociation10);

        solution.setRawData(list);
        System.out.println("打印原始数据");
        for (NodeAssociation rawDatum : solution.rawData) {
            System.out.println(rawDatum);
        }
        solution.find("A", "E", "D");
    }

    public void find(String rootNodeName, String target1, String target2) {
        // 1. 对模型对去重 (A-B) (B-A) --> (A-B);  (A-A)无效节点直接删除
        List<String> tempList = new ArrayList<>();
        for (int i = rawData.size() - 1; i >= 0; i--) {
            NodeAssociation nodeAssociation = rawData.get(i);
            String leftNodeName = nodeAssociation.getLeftNodeName();
            String rightNodeName = nodeAssociation.getRightNodeName();
            // 若有重复,则去重 (A-B) (B-A) --> (A-B)
            if (tempList.contains(leftNodeName + rightNodeName) || tempList.contains(rightNodeName + leftNodeName)) {
                rawData.remove(i);
                continue;
            }
            // (A-A) 直接删除
            if (leftNodeName.equals(rightNodeName)){
                rawData.remove(i);
                continue;
            }
            tempList.add(leftNodeName + rightNodeName);
        }

        // 2. 从索引模型开始遍历
        List<String> roadList = new ArrayList<>();
        roadList.add(rootNodeName);
        List<NodeAssociation> roadNodeList = new ArrayList<>();
        // 2.1 找到 target1
        List<List<NodeAssociation>> result1 = new ArrayList<>();
        dfs(result1, roadList, roadNodeList, rootNodeName, target1);
        System.out.println("打印  "+rootNodeName+"  -->  "+target1+"结果集:" );
        for (int i = 0; i < result1.size(); i++) {
            System.out.println("打印第"+(i+1)+"条路:");
            for (NodeAssociation nodeAssociation : result1.get(i)) {
                System.out.println(nodeAssociation);
            }
        }

        // 2.2 找到 target2
        List<List<NodeAssociation>> result2 = new ArrayList<>();
        dfs(result2, roadList, roadNodeList, rootNodeName, target2);
        System.out.println("打印  "+rootNodeName+"  -->  "+target2+"结果集:" );
        for (int i = 0; i < result2.size(); i++) {
            System.out.println("打印第"+(i+1)+"条路:");
            for (NodeAssociation nodeAssociation : result2.get(i)) {
                System.out.println(nodeAssociation);
            }
        }
    }


    // 1. 当前走过的路
    public void dfs(List<List<NodeAssociation>> finalList, List<String> roadList, List<NodeAssociation> roadNodeList, String startName, String targetName) {
        // 0. 对数据处理 - 放在上一层方法中.

        // 1. 边界条件: ① 如果 开始节点没有子节点 可以结束 ② 该节点为 目标节点, 则对list进行结果的收取 并返回
        // 1.1 判断该节点是否为目标节点:
        if (startName.equals(targetName)) {
            // 拷贝
            List<NodeAssociation> result = new ArrayList<>(roadNodeList);
            // 结果收割
            finalList.add(result);
            return;
        }
        // 1.2 如果不是目标节点,则需要判断有没有子节点, 从原始数据中
        List<NodeAssociation> sonNodeList = findSonNodeList(rawData, startName);
        // 对子节点list进行过滤,过滤掉已经走过的路的结点
        List<NodeAssociation> collect = sonNodeList.stream().filter((item) -> {
            String leftNodeName = item.getLeftNodeName();
            String rightNodeName = item.getRightNodeName();
            String nextNode = startName.equals(leftNodeName) ? rightNodeName : leftNodeName;
            return !roadList.contains(nextNode);
        }).collect(Collectors.toList());

        if (collect.size() == 0) {
            return;
        }

        // 3. 开始遍历--> 横向遍历
        for (int i = 0; i < collect.size(); i++) {
            // 3.1 把当前遍历节点加入路径
            NodeAssociation curNode = collect.get(i);
            String leftNodeName = curNode.getLeftNodeName();
            String rightNodeName = curNode.getRightNodeName();
            String nextNode = startName.equals(leftNodeName) ? rightNodeName : leftNodeName;
            roadList.add(nextNode);
            roadNodeList.add(curNode);

            // 3.2 开始遍历递归
            dfs(finalList, roadList, roadNodeList, nextNode, targetName);

            // 3.3 回溯
            roadList.remove(roadList.size() - 1);
            roadNodeList.remove(roadNodeList.size() - 1);
        }
    }

    // 找到子节点list
    private List<NodeAssociation> findSonNodeList(List<NodeAssociation> data, String startName) {
        return data.stream().filter((item) -> startName.equals(item.getLeftNodeName()) || startName.equals(item.getRightNodeName())).collect(Collectors.toList());
    }
}

最后的结果：

打印原始数据
NodeAssociation{leftNodeName='A', rightNodeName='B'}
NodeAssociation{leftNodeName='A', rightNodeName='C'}
NodeAssociation{leftNodeName='A', rightNodeName='D'}
NodeAssociation{leftNodeName='B', rightNodeName='E'}
NodeAssociation{leftNodeName='E', rightNodeName='C'}
NodeAssociation{leftNodeName='E', rightNodeName='H'}
NodeAssociation{leftNodeName='D', rightNodeName='F'}
NodeAssociation{leftNodeName='H', rightNodeName='F'}
NodeAssociation{leftNodeName='D', rightNodeName='A'}
NodeAssociation{leftNodeName='C', rightNodeName='F'}
打印  A  -->  E结果集:
打印第1条路:
NodeAssociation{leftNodeName='A', rightNodeName='B'}
NodeAssociation{leftNodeName='B', rightNodeName='E'}
打印第2条路:
NodeAssociation{leftNodeName='A', rightNodeName='C'}
NodeAssociation{leftNodeName='E', rightNodeName='C'}
打印第3条路:
NodeAssociation{leftNodeName='A', rightNodeName='C'}
NodeAssociation{leftNodeName='C', rightNodeName='F'}
NodeAssociation{leftNodeName='H', rightNodeName='F'}
NodeAssociation{leftNodeName='E', rightNodeName='H'}
打印第4条路:
NodeAssociation{leftNodeName='D', rightNodeName='A'}
NodeAssociation{leftNodeName='D', rightNodeName='F'}
NodeAssociation{leftNodeName='H', rightNodeName='F'}
NodeAssociation{leftNodeName='E', rightNodeName='H'}
打印第5条路:
NodeAssociation{leftNodeName='D', rightNodeName='A'}
NodeAssociation{leftNodeName='D', rightNodeName='F'}
NodeAssociation{leftNodeName='C', rightNodeName='F'}
NodeAssociation{leftNodeName='E', rightNodeName='C'}

打印  A  -->  D结果集:
打印第1条路:
NodeAssociation{leftNodeName='A', rightNodeName='B'}
NodeAssociation{leftNodeName='B', rightNodeName='E'}
NodeAssociation{leftNodeName='E', rightNodeName='C'}
NodeAssociation{leftNodeName='C', rightNodeName='F'}
NodeAssociation{leftNodeName='D', rightNodeName='F'}
打印第2条路:
NodeAssociation{leftNodeName='A', rightNodeName='B'}
NodeAssociation{leftNodeName='B', rightNodeName='E'}
NodeAssociation{leftNodeName='E', rightNodeName='H'}
NodeAssociation{leftNodeName='H', rightNodeName='F'}
NodeAssociation{leftNodeName='D', rightNodeName='F'}
打印第3条路:
NodeAssociation{leftNodeName='A', rightNodeName='C'}
NodeAssociation{leftNodeName='E', rightNodeName='C'}
NodeAssociation{leftNodeName='E', rightNodeName='H'}
NodeAssociation{leftNodeName='H', rightNodeName='F'}
NodeAssociation{leftNodeName='D', rightNodeName='F'}
打印第4条路:
NodeAssociation{leftNodeName='A', rightNodeName='C'}
NodeAssociation{leftNodeName='C', rightNodeName='F'}
NodeAssociation{leftNodeName='D', rightNodeName='F'}
打印第5条路:
NodeAssociation{leftNodeName='D', rightNodeName='A'}

如果想要得到最短路径，那么也很简单，在每次收割结果时，对list做一下判断即可，每次取最小的list，便可得到最短路径。

欢迎讨论~~~