有向图—拓扑排序，Kosaraju算法

有向图基本算法

对于有向图的结构，和无向图类似，甚至更简单，有疑问请留言。

1>有向图的数据结构

package graphTheory;
/**
* @author luoz
* @date 2016年9月19日 下午9:26:21
**/
public class Digraph {

private final int V;
private int E;
private Bag<Integer>[] adj;

public Digraph(int V)
{
this.V = V;
this.E = 0;
adj = (Bag<Integer>[])new Bag[V];
for(int i = 0;i<V;i++)
adj[i] = new Bag<>();
}

public int V()
{
return V;
}
public int E()
{
return E;
}

public void addEdge(int v,int w)
{
adj[v].add(w);
E++;
}

public Iterable<Integer> adj(int v)
{
return adj[v];
}

public Digraph reverse()
{
Digraph g = new Digraph(V);
for(int j = 0; j<V;j++)
for(int w : adj[j])
g.addEdge(w,j);
return g;
}
}

基于深度优先遍历的顶点排序

1>前序：在递归调用之前将顶点加入队列；

2>后序：在递归调用之后将顶点加入队列；

3>逆后序：在递归调用之后将顶点压入栈；

package graphTheory;

import java.util.*;
import javax.management.Query;

/**
* @author luoz
* @date 2016年9月19日 下午10:11:48
**/
public class DepthFirstOrder {

private boolean[] marked;
//pre order
private Queue<Integer> pre;
//postorder
private Queue<Integer> post;
//reverse postorder
private Stack<Integer> repost;

public DepthFirstOrder(Digraph g)
{
marked = new boolean[g.V()];
pre = new LinkedList<>();
post =  new LinkedList<>();
repost = new Stack<>();
for(int i = 0;i<g.V();i++)
if(!marked[i])
dfs(g,i);
}

private void dfs(Digraph g,int v)
{
pre.add(v);
marked[v] = true;
for(int w : g.adj(v))
if(!marked[w])
dfs(g,w);
post.add(v);
repost.add(v);
}

public Iterable<Integer> pre()
{
return pre;
}

public Iterable<Integer> post()
{
return post;
}

public Iterable<Integer> reversepost() {
return repost;
}
}

检测有无环

package graphTheory;

import java.io.File;
import java.util.Stack;

/**
* @author  luoz
* @date 2016年9月19日 下午9:48:41
**/
public class DirectedCycle {

private boolean[] marked;
private int[] edgeTo;

//All vertices of a directed loop
private Stack<Integer> cycle;
//resursion all vertices of the cycle
private boolean[] onStack;

private boolean marked(int v)
{
return marked[v];
}

public boolean hasCycle()
{
return cycle != null;
}

public DirectedCycle(Digraph g)
{
marked = new boolean[g.V()];
edgeTo = new int[g.V()];
onStack = new boolean[g.V()];
for(int i = 0;i<g.V();i++)
if(!marked[i])
dfs(g,i);
}

private void dfs(Digraph g,int v)
{
marked[v] = true;
onStack[v] = true;
for(int w : g.adj(v))
{
if(this.hasCycle())
return;
else if(!marked[w])
{
edgeTo[w] = v;
dfs(g,w);
}
else if(onStack[w])
{
cycle = new Stack<Integer>();
for(int i = v; i != w; i = edgeTo[i])
cycle.push(i);
cycle.push(w);
cycle.push(v);
}
onStack[v] = false;
}
}

public Iterable<Integer> cycle()
{
return cycle;
}
/*测试代码,从文件中读取的,可以自己写测试代码*/
public static void main(String[] args) {
FileIo fileio = new FileIo();
String s = fileio.characterReader(new File("cycle.txt"));
String[] st = s.split(",");

Digraph g = new Digraph(13);

int E = st.length;
for(int i = 0;i<E;i++)
{
String[] str = st[i].split(" ");
g.addEdge(Integer.parseInt(str[0]),Integer.parseInt(str[1]));
}
DirectedCycle cc = new DirectedCycle(g);
System.out.println(cc.hasCycle());
System.out.println(cc.cycle);
}

}

拓扑排序

拓扑排序只针对有向无环图。

一幅有向无环图的拓扑排序，也就是所有顶点的逆后序排列。

package graphTheory;

/**
* @author  luoz
* @date 2016年9月20日 上午8:30:05
**/
public class Topological {

private Iterable<Integer> order;

public Topological(Digraph g)
{
DirectedCycle hascycle = new DirectedCycle(g);
if(!hascycle.hasCycle())
{
DepthFirstOrder df = new DepthFirstOrder(g);
order = df.reversepost();
}
}

public Iterable<Integer> order()
{
return order;
}
}

Kosaraju算法

计算强连通分量的算法。

主要运用了图G的反转和顶点排序的逆后序。

package graphTheory;
/**
* @author  luoz
* @date 2016年9月20日 上午9:08:53
**/
public class KosarajuSCC {

private boolean[] marked;
private int[] id;
private int count;

public KosarajuSCC(Digraph g)
{
marked = new boolean[g.V()];
id = new int[g.V()];
//
DepthFirstOrder df = new DepthFirstOrder(g.reverse());
for(int i : df.reversepost())
if(!marked[i])
{
dfs(g,i);
count++;
}
}
private void dfs(Digraph g,int v)
{
marked[v] = true;
id[v] = count;
for(int w :g.adj(v))
if(!marked[w])
dfs(g,w);
}
public int count()
{
return count;
}

public boolean connected(int v,int w)
{
return id[v] == id[w];
}
}

算法第四版