[数据结构与算法]深度优先搜索dfs和广度优先搜索bfs

　第一步，构造一个图，图的结构如下

   

 这个图构造方式有二种，一种二维数组，一种Map + 链表，因为图比较稀疏，使用Map加链表来构建，代码如下所示

private static Map<Character,List<Character>> buildGraph(){
        Map<Character, List<Character>> graph = new HashMap<>();
        List<Character> aList = new LinkedList<>(Arrays.asList('B','C'));
        List<Character> bList = new LinkedList<>(Arrays.asList('A','C','D'));
        List<Character> cList = new LinkedList<>(Arrays.asList('A','B','D','E'));
        List<Character> dList = new LinkedList<>(Arrays.asList('B','F','E','C'));
        List<Character> eList = new LinkedList<>(Arrays.asList('C','D'));
        List<Character> fList = new LinkedList<>(Arrays.asList('D'));
        graph.put('A',aList);
        graph.put('B',bList);
        graph.put('C',cList);
        graph.put('D',dList);
        graph.put('E',eList);
        graph.put('F',fList);
        return graph;
    }

　　Map的key表示节点，Value是邻接节点组成的链表。

广度优先搜索 bfs：思想就是先访问当前节点，然后访问当前节点的邻接节点，依次类推。使用队列的先进先出特性，可以按层遍历。

深度优先搜索 bfs：思想就是先访问当前节点，然后一直访问走，直到路不通，然后往回走。

public static void main(String[] args) {

        Map<Character, List<Character>> graph = buildGraph();

        dfs(graph, 'C');

        bfs(graph, 'D');
    }

    private static Map<Character,List<Character>> buildGraph(){
        Map<Character, List<Character>> graph = new HashMap<>();
        List<Character> aList = new LinkedList<>(Arrays.asList('B','C'));
        List<Character> bList = new LinkedList<>(Arrays.asList('A','C','D'));
        List<Character> cList = new LinkedList<>(Arrays.asList('A','B','D','E'));
        List<Character> dList = new LinkedList<>(Arrays.asList('B','F','E','C'));
        List<Character> eList = new LinkedList<>(Arrays.asList('C','D'));
        List<Character> fList = new LinkedList<>(Arrays.asList('D'));
        graph.put('A',aList);
        graph.put('B',bList);
        graph.put('C',cList);
        graph.put('D',dList);
        graph.put('E',eList);
        graph.put('F',fList);
        return graph;
    }

    /**
     * 深度优先搜索
     * @param graph 要遍历的图
     * @param s 起始点
     */
    public static void dfs(Map<Character,List<Character>> graph, Character s){
        //走过的节点
        Set<Character> visited = new HashSet<>();
        Stack<Character> stack = new Stack<>();
        stack.push(s);

        while(!stack.empty()){
            Character accessC = stack.pop();
            if(!visited.contains(accessC)){
                System.out.print("->"+accessC);
                visited.add(accessC);
            }
            graph.get(accessC).forEach(c ->{
                if(!visited.contains(c)){
                    stack.push(c);
                }
            });
        }
    }

    public static void bfs(Map<Character,List<Character>> graph, Character s){
        //走过的节点
        Set<Character> visited = new HashSet<>();
        Queue<Character> queue = new LinkedList<>();

        queue.offer(s);

        while (!queue.isEmpty()){
            Character accessC = queue.poll();
            if(!visited.contains(accessC)){
                System.out.print("->"+accessC);
                visited.add(accessC);
            }
            graph.get(accessC).forEach(c ->{
                if(!visited.contains(c)){
                    queue.offer(c);
                }
            });
        }
    }