图处理算法-Kosaraju's-算法

1.写了算法课关于有向图的作业。

用c++开辟大数组容易出segment fault,后来改用堆开辟。图的邻接表用了链表表示。 

long int numVertexes = 875714;
long int numEdges;
VertexNode* adjList = new VertexNode[875714];

2.关于图的存储,用了邻接链表存储(用链表比vector数组存取速度快多了)。

2.1 边表

/********边表***********/
class EdgeNode
{
public:
    long int adjvex; //边表数据
    EdgeNode *next; //边表指向的下一个节点
    EdgeNode(long int adj, EdgeNode *n = NULL): adjvex(adj), next(n){}
    
};

2.2 顶点表

/*********顶点表**********/
class VertexNode
{
public:
    long int data;    //当前顶点数据
    EdgeNode *firstEdge; //顶点第一条边
//    VertexNode(long int d, EdgeNode *fir = NULL) : data(d), firstedge(fir) {}
};

2.3 初始化图边时用了头插法

/*************头插法*************************/
    void addEdge(long int a, long int b)
    {
        EdgeNode *enode = new EdgeNode(b,NULL);
        enode->next = (adjList+a)->firstEdge;
        (adjList+a)->firstEdge = enode; 
    }

3.深度优先搜索

3.1 递归实现

伪代码如下: 

输入:有向图G和某个顶点i

1.将该顶点i标记为已访问。

2.对边(i,j),即顶点i的邻接点j遍历:

3.if 存在某个顶点j未被访问,则对顶点j进行访问:

DFS(G,j)

c++代码如下:

/*---------------------第一次dfs-------------------*/
void DFS(Graph graph, long int i) 
    {
        marked[i] = true;
        
        list<long int>::iterator iter;
        for(iter = graph._storage[i].begin(); iter != graph._storage[i].end(); iter++)
        {
            long int temp = *iter;
            if(!marked[temp])
            {
                DFS(graph, temp);
            }
        }
        time++;
        ff[time-1] = i;
    }
/*---------------第二次dfs---------------*/
void DFS2(Graph graph, long int i)
    {
        marked[i] = true;
        leader[i] = s;

        list<long int>::iterator iter;
        for(iter = graph._storage[i].begin(); iter != graph._storage[i].end(); iter++)
        {
            long int temp = *iter;
            if(!marked[temp])
            {
                DFS2(graph, temp);
            }
        }
    }

 

3.2 非递归实现

伪代码如下: 

输入:有向图G,顶点i。

1.栈初始化,将顶点i入栈,将i标记为已访问。

2.while(栈非空)

x = 栈顶元素

3. 对边(x,j)进行遍历:

if:存在某个顶点j未被访问:

  将j标记为已访问

  将j入栈

  break

else:

  x出栈

c++代码:

/*================第一次dfs================*/
    void dfsLoop1(Graph graph)
    {
        markedInit();
        time = 0; 
        for(long int i = length-1; i >= 0; i--)
        {
            if(!marked[i])
            {
                DFS1(graph, i);
            }
        }
    }
    void DFS1(Graph graph, long int i)
    {
        stack< VertexNode* > stack;
        stack.push(graph.adjList+i);
        marked[i] = true;
        while(!stack.empty())
        {
            VertexNode *temp = new VertexNode;
            temp = stack.top();
            EdgeNode *p = new EdgeNode(0, NULL);
            p = temp->firstEdge;
            int flag = 0;
            while(p)
            {
                if(!marked[p->adjvex])
                {
                    marked[p->adjvex] = true;
                    stack.push(graph.adjList + (p->adjvex));        
                    flag = 1;
                    break;
                }
                p = p->next;
            }
            if(!flag)
            {
                ff[time] = temp->data;
                time++;
                stack.pop();
            }
        }
    }
/*================第二次dfs================*/
    void dfsLoop2(Graph graph)
    {
        markedInit();
        time = 0;
        for(long int i = length-1; i >=0 ; i--)
        {
            if(!marked[ff[i]])
            {
                s = ff[i];
                DFS2(graph, ff[i]);
            }
        }
    }
void DFS2(Graph graph, long int i)
    {
        stack < VertexNode* > stack;
        stack.push(graph.adjList+i);
        leader[i] = s;
        marked[i] = true;
        while(!stack.empty())
        {
            VertexNode *temp = new VertexNode;
            temp = stack.top();
            marked[temp->data] = true;
            EdgeNode *p = new EdgeNode(0,NULL);
            p = temp->firstEdge;
            int flag = 0;
            while(p)
            {
                if(!marked[p->adjvex])
                {
                    marked[p->adjvex] = true;
                    stack.push(graph.adjList + p->adjvex);
                    flag = 1;
                    break;
                }
                p = p->next;
            }
            if(!flag)
            {
                leader[temp->data] = s;
                stack.pop();
            }


        }
    }

完整代码: 
https://github.com/Shinered/Kosaraju/blob/master/dfs3.cpp

 

转载于:https://www.cnblogs.com/Shinered/p/8999688.html

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