Non recursive Depth first search

深度优先非递归实现算法：

1 递归算法:

//初始化相关数据结构
DFS(G)
-----------------------------------------------------------------------------------
1  for each vertex u ∈ G.V
2      u.color ← WHITE       // paint all vertices white; undiscovered
3      u.π ← NIL
4      time ← 0              // global variable, timestamps
5  for each vertex u ∈ G.V
6      if u.color = WHITE
7          DFS-VISIT(G,u)

DFS-VISIT(G, u)
-----------------------------------------------------------------------------------
1  u.color ← GRAY          // grey u; it is discovered
2  time ← time + 1
3  u.d ← time
4  for each v ∈ G.Adj[u]   // explore edge (u,v)
5      if v.color == WHITE
6          v.π ← u
7          DFS-VISIT(G,v)
8  u.color ← BLACK         // blacken u; it is finished
9  time ← time + 1
10 u.f ← time

#ifndef GCC_LINUX_
#include <stdlib.h>
#include <iostream>
using namespace std;
#endif
#include "Graph.h"

enum color{WHITE, GRAY, BLACK};
int colour[MAX_VERTEX_NUM];
int time[MAX_VERTEX_NUM];
int curTime;

void DFSRec(LGraph graph, int u){
    cout<<"for debug"<<endl;
    cout<<"u: "<<u<<endl;
    colour[u] = GRAY;
    time[u] = ++curTime;
    //DFS adj node
    adjnode *temp;
    temp = graph.vertices[u].firstadj;

    while(temp){
        int v = temp->index;
        //for debug
        cout<<"for debug"<<endl;
        cout<<"v: "<<v<<" line: "<<__LINE__<<endl;
        if(colour[v] == WHITE)
            DFSRec(graph, v);
        else if(colour[v] == GRAY)
            cout<<"back edge between "<<u<<" and "<<v<<endl;
        else
            cout<<"cross edge between "<<u<<" and "<<v<<endl;
        temp = temp->adjnext;
    }
    colour[u] = BLACK;
}

void DFSTraverse(LGraph graph){
    for(int k = 1; k < graph.vexnum + 1; k++){
        if(colour[k] == WHITE) DFSRec(graph, k);
        cout<<__LINE__<<" for debug: "<<k<<endl;
    }
}

int main()
{
    LGraph* graph;
    graph = CreateGraph(graph);
    cout<<graph->edgenum<<endl;
    cout<<graph->vexnum<<endl;
    print(*graph);
    DFSTraverse(*graph);
    //print time visit
    cout<<"print the visit array:"<<endl;
    for(int i = 1; i < graph->vexnum + 1; i++)
        cout<<time[i]<<" ";
    cout<<endl;

    int ch;
    cout<<"enter integer for terminating:"<<endl;
    cin>>ch;
    return 0;
}

2 非递归算法

1   for each vertex u ∈ G.V //initialize colour array and time
2       u.color ← WHITE
3       u.π ← NIL
4   time = 0
5   for each vertex u ∈ G.V
6       if u.color = WHITE
7           u.color ← GRAY
8           time ← time + 1
9           u.d ← time
7           push(u, S)
8           while stack S not empty
9               u ← pop(S)
10              for each vertex v ∈ G.Adj[u]
11                  if v.color = WHITE
12                      v.color = GRAY
13                      time ← time + 1
14                      v.d ← time
15                      v.π ← u
16                      push(v, S)
17              u.color ← BLACK
18              time ← time + 1
19              u.f ← time

具体实现代码如下：

栈采用数组实现：

#ifndef GCC_LINUX_
#include <stdlib.h>
#include <iostream>
using namespace std;
#endif
#include "Graph.h"

int myStack[MAX_VERTEX_NUM];
int top = 0; //we not use array[0]
bool visited[MAX_VERTEX_NUM];
int timeSec[MAX_VERTEX_NUM];
int curTimeSec;

void DFSNoRecur(LGraph graph, int u){
    cout<<u;
    myStack[top++] = u;
    cout<<" top:"<<top<<endl;
    adjnode* temp;
    //for test
    int test = 1;
    while(top){
        int v = myStack[top - 1];
        cout<<test++<<" for test top: "<<top;
        cout<<" stack elem: "<<v<<endl;
        visited[v] = true;
        timeSec[v] = ++curTimeSec;
        temp = graph.vertices[v].firstadj;
        cout<<"pointer temp: "<<temp<<endl;
        top--; //Pop
    cout<<top;
        while(temp != NULL){
           if(visited[temp->index] == false){
             myStack[top++] = temp->index;
             cout<<test++<<" for test top: "<<top;
             cout<<" stack elem: "<<myStack[top - 1]<<endl;
           }
           else{
             cout<<"back edge between "<<temp->index;
             cout<<" and "<<v<<endl;
           }
        temp = temp->adjnext;
        }//while
    }//while(top)
}

void DFSTravNRecur(LGraph graph){
    cout<<"No recursive DFS starting"<<endl;
    for(int v = 1; v < graph.vexnum + 1; v++)
        if(visited[v] == false) DFSNoRecur(graph, v);
    cout<<"No recursive DFS terminating"<<endl;
}

int main()
{
    LGraph* graph;
    graph = CreateGraph(graph);
    cout<<graph->edgenum<<endl;
    cout<<graph->vexnum<<endl;
    print(*graph);
    DFSTraverse(*graph);
    //print time visit
    cout<<"print the time array:"<<endl;
    for(int i = 1; i < graph->vexnum + 1; i++)
        cout<<time[i]<<" ";
    cout<<endl;

    DFSTravNRecur(*graph);
    cout<<"print the visit array:"<<endl;
    for(int i = 1; i < graph->vexnum + 1; i++)
        cout<<time[i]<<" ";
    cout<<endl;

    int ch;
    cout<<"enter integer for terminating:"<<endl;
    cin>>ch;
    return 0;
}

"Graph.h"文件代码定义：

#ifndef GCC_LINUX_
#include <stdlib.h>
#include <iostream>
using namespace std;
#endif
#define MAX_VERTEX_NUM 128

struct adjnode{
    int index;
    struct adjnode* adjnext;
};

typedef struct vexnode{
    struct adjnode* firstadj;
}VertexLink[MAX_VERTEX_NUM];

typedef struct LGraph{
    VertexLink vertices;
    int vexnum, edgenum;

};

void AddEdge(LGraph *graph, int head, int tail){
    //new a adj node
   adjnode *newadjnode = (adjnode*)malloc(sizeof(struct adjnode));
   if(!newadjnode)
     exit(EXIT_FAILURE);
   newadjnode->index = tail;
   newadjnode->adjnext = NULL;
   adjnode *temp;

   temp = graph->vertices[head].firstadj;
   cout<<"this edge: "<<head<<"->"<<newadjnode->index<<endl;
   newadjnode->adjnext =temp;
   graph->vertices[head].firstadj = newadjnode;
   //debug
cout<<"line: "<<__LINE__;
cout<<" first adj index: "<<graph->vertices[head].firstadj->index<<endl;

}

LGraph* CreateGraph(LGraph *graph){
    graph = (LGraph*)malloc(sizeof(struct LGraph));
    if(!graph)
       exit(EXIT_FAILURE);
    cout<<"enter the vertex number and edge number:"<<endl;
    cin>>graph->vexnum>>graph->edgenum;

    //initialize the vertexes
    for(int v = 0; v < graph->vexnum + 1; v++){
        graph->vertices[v].firstadj = NULL;
    }

    //initialize the edge
    int i, j;
    for(int e = 0; e < graph->edgenum; e++){
        cout<<"enter edge of graph:"<<endl;
        cin>>i>>j;
        AddEdge(graph, i, j);
    }
    cout<<"graph.vertex number: "<<graph->vexnum<<endl;
    return graph;
}

void print(LGraph graph){
    adjnode *temp = NULL;
    for(int i = 1; i < graph.vexnum + 1; i++){
        cout<<"vertex: "<<i;
        temp = graph.vertices[i].firstadj;
       // cout<<"temp"<<temp<<endl;
        while(temp){
            cout<<" adj vertex: "<<temp->index<<endl;
            temp = temp->adjnext;
        }
    }
    cout<<endl;
}

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