图的遍历,深度优先与广度优先详解

图采用邻接矩阵实现,深度优先搜索采用栈来实现,广度优先遍历采用队列来实现.附上代码详解.

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图的实现

1.邻接矩阵实现

简单来说就是用一个二维数组来存储图之间的联通情况,比如有5个点,就可以用一个 5*5的 矩阵来存储 两点间是否联通.

比如上图 false 表示不连通, true表示连通.

public class Graph {
    private boolean[][] map ;
    private int length;
    public Graph(int length)//生成图
    {
        this.length = length;
        map = new boolean[length][length];
    }
    public void addEdge(int i,int j)//加边
    {
        if (map == null)
        {
            if (i>j)
            {
                map = new boolean[i][i];
                length = i;
            }
            else
            {
                map = new boolean[j][j];
                length = j;
            }
        }
        map[i][j]  = true;
        map[j][i]  = true;
    }

    public void removeEdge(int i,int j)//去边
    {
        if (map == null || j>=length||i>=length)
            return;
        else {
            map[i][j] = false;
            map[j][i] = false;
        }
    }
    public boolean isEdge(int i,int j)//判断是否联通
    {
        if (map==null||i>=length||j>=length)
            return false;
        else
            return true;
    }
}

这个为无向图,若为有向图,则生成的边只有一个就好,即只有A到B.

2.邻接链表实现

采用一个一维链表数组用来存储每个点.若这个节点与其他节点有联通,则与它相连通的子节点构成一个链表.

import java.util.ArrayList;

/**
 * Created by max on 17-5-9.
 */
public class ListGraph {
    ListNode[] listNodes;
    int length ;
    ArrayList<Integer> vertices;

    public ListGraph(int lenght)
    {
        this.length = lenght;
        listNodes = new ListNode[length];
        vertices = new ArrayList<>();
        for (int i=0;i<length;i++)
        {
            listNodes[i] = new ListNode();
            vertices.add(i);
        }
    }
    public void addEdge(int start,int end)
    {
        int i = vertices.indexOf(start);
        int j = vertices.indexOf(end);
        if (j!=-1&&i!=-1)
        {
            listNodes[i].insertAtBeginning(j);
            listNodes[j].insertAtBeginning(i);
        }
    }

}

DFS深度优先搜索

思路是采用栈的用来存储访问的节点,而先进后出的机制刚好满足深度搜索的需求.给每个节点添加一个boolean属性,用于判断是否被访问过.

import java.util.ArrayList;
import java.util.Stack;

/**
 * Created by max on 17-5-9.
 */
public class DFS {
    private class Vertics
    {
        public char label;
        public boolean visited;
        public Vertics(char label)
        {
            this.label  = label;
            visited = false;
        }
    }
    private class Graph
    {
        private boolean[][] map;
        private ArrayList<Vertics> vertices;
        private  int countVertices;
        private Stack<Integer> stack;
        public Graph(int length)
        {
            stack = new Stack<>();
            countVertices = 0;
            vertices = new ArrayList<>();
            map = new boolean[length][length];
        }
        public Graph()
        {
            stack = new Stack<>();
            int length =20;
            countVertices = 0;
            vertices = new ArrayList<>();
            map = new boolean[length][length];
        }

        public void addVertice(char label)
        {
            vertices.add(new Vertics(label));
            countVertices++;
        }

        public void addEdge(int i,int j)
        {
            map[i][j] = true;
            map[j][i] = true;
        }
        public void removeEdge(int i ,int j)
        {
            map[i][j] = false;
            map[j][i] = false;
        }

        public void showLabel(int i)
        {
            System.out.print(" "+vertices.get(i).label);
        }
        public void dfs()
        {
            showLabel(0);
            vertices.get(0).visited = true;
            stack.push(0);
            while(!stack.isEmpty())
            {
                int v =getNextNode(stack.peek());
                if (v==-1)
                {
                    stack.pop();
                }
                else
                {
                    vertices.get(v).visited=true;
                    showLabel(v);
                    stack.push(v);
                }
            }
            for (int i = 0 ;i<countVertices;i++)
                vertices.get(i).visited=false;
        }
        private int getNextNode(int peek) {
            for (int i = 0; i < countVertices; i++)
            {
                if (map[peek][i]==true&&vertices.get(i).visited==false)
                    return i;
            }
            return -1;

        }
    }
}

BFS广度优先搜索

广度优先搜索主要是通过队列的先进先出的机制来实现. 以JAVA中的ArrayQueue实现.

       public void bfs()
        {
            showLabel(0);
            vertices.get(0).visited = false;
            queue.add(0);
            int ans;
            int deal;
            while(!queue.isEmpty())
            {
                deal = (int) queue.remove();
                while ((ans = getNextNode(deal))!=-1)
                {
                    vertices.get(ans).visited=true;
                    showLabel(ans);
                    queue.add(ans);
                }
            }
            for (int i = 0 ;i<countVertices;i++)
                vertices.get(i).visited=false;
        }

以上是笔主自己对 深搜广搜的理解与笔记,欢迎交流撕逼.