Topological Sorting（拓扑排序）
程序来源：Topological Sorting。
C++程序如下：
// A C++ program to print topological sorting of a DAG
#include<iostream>
#include <list>
#include <stack>
using namespace std;
// Class to represent a graph
class Graph
{
int V; // No. of vertices'
// Pointer to an array containing adjacency listsList
list<int> *adj;
// A function used by topologicalSort
void topologicalSortUtil(int v, bool visited[], stack<int> &Stack);
public:
Graph(int V); // Constructor
// function to add an edge to graph
void addEdge(int v, int w);
// prints a Topological Sort of the complete graph
void topologicalSort();
};
Graph::Graph(int V)
{
this->V = V;
adj = new list<int>[V];
}
void Graph::addEdge(int v, int w)
{
adj[v].push_back(w); // Add w to v’s list.
}
// A recursive function used by topologicalSort
void Graph::topologicalSortUtil(int v, bool visited[],
stack<int> &Stack)
{
// Mark the current node as visited.
visited[v] = true;
// Recur for all the vertices adjacent to this vertex
list<int>::iterator i;
for (i = adj[v].begin(); i != adj[v].end(); ++i)
if (!visited[*i])
topologicalSortUtil(*i, visited, Stack);
// Push current vertex to stack which stores result
Stack.push(v);
}
// The function to do Topological Sort. It uses recursive
// topologicalSortUtil()
void Graph::topologicalSort()
{
stack<int> Stack;
// Mark all the vertices as not visited
bool *visited = new bool[V];
for (int i = 0; i < V; i++)
visited[i] = false;
// Call the recursive helper function to store Topological
// Sort starting from all vertices one by one
for (int i = 0; i < V; i++)
if (visited[i] == false)
topologicalSortUtil(i, visited, Stack);
// Print contents of stack
while (Stack.empty() == false)
{
cout << Stack.top() << " ";
Stack.pop();
}
}
// Driver program to test above functions
int main()
{
// Create a graph given in the above diagram
Graph g(6);
g.addEdge(5, 2);
g.addEdge(5, 0);
g.addEdge(4, 0);
g.addEdge(4, 1);
g.addEdge(2, 3);
g.addEdge(3, 1);
cout << "Following is a Topological Sort of the given graph \n";
g.topologicalSort();
return 0;
}程序运行结果（下同）：
Following is a Topological Sort of the given graph 5 4 2 3 1 0
Java程序如下：
// A Java program to print topological sorting of a DAG
import java.io.*;
import java.util.*;
// This class represents a directed graph using adjacency
// list representation
class Graph
{
private int V; // No. of vertices
private LinkedList<Integer> adj[]; // Adjacency List
//Constructor
Graph(int v)
{
V = v;
adj = new LinkedList[v];
for (int i=0; i<v; ++i)
adj[i] = new LinkedList();
}
// Function to add an edge into the graph
void addEdge(int v,int w) { adj[v].add(w); }
// A recursive function used by topologicalSort
void topologicalSortUtil(int v, boolean visited[],
Stack stack)
{
// Mark the current node as visited.
visited[v] = true;
Integer i;
// Recur for all the vertices adjacent to this
// vertex
Iterator<Integer> it = adj[v].iterator();
while (it.hasNext())
{
i = it.next();
if (!visited[i])
topologicalSortUtil(i, visited, stack);
}
// Push current vertex to stack which stores result
stack.push(new Integer(v));
}
// The function to do Topological Sort. It uses
// recursive topologicalSortUtil()
void topologicalSort()
{
Stack stack = new Stack();
// Mark all the vertices as not visited
boolean visited[] = new boolean[V];
for (int i = 0; i < V; i++)
visited[i] = false;
// Call the recursive helper function to store
// Topological Sort starting from all vertices
// one by one
for (int i = 0; i < V; i++)
if (visited[i] == false)
topologicalSortUtil(i, visited, stack);
// Print contents of stack
while (stack.empty()==false)
System.out.print(stack.pop() + " ");
}
// Driver method
public static void main(String args[])
{
// Create a graph given in the above diagram
Graph g = new Graph(6);
g.addEdge(5, 2);
g.addEdge(5, 0);
g.addEdge(4, 0);
g.addEdge(4, 1);
g.addEdge(2, 3);
g.addEdge(3, 1);
System.out.println("Following is a Topological " +
"sort of the given graph");
g.topologicalSort();
}
}
// This code is contributed by Aakash HasijaPython程序如下：
#Python program to print topological sorting of a DAG
from collections import defaultdict
#Class to represent a graph
class Graph:
def __init__(self,vertices):
self.graph = defaultdict(list) #dictionary containing adjacency List
self.V = vertices #No. of vertices
# function to add an edge to graph
def addEdge(self,u,v):
self.graph[u].append(v)
# A recursive function used by topologicalSort
def topologicalSortUtil(self,v,visited,stack):
# Mark the current node as visited.
visited[v] = True
# Recur for all the vertices adjacent to this vertex
for i in self.graph[v]:
if visited[i] == False:
self.topologicalSortUtil(i,visited,stack)
# Push current vertex to stack which stores result
stack.insert(0,v)
# The function to do Topological Sort. It uses recursive
# topologicalSortUtil()
def topologicalSort(self):
# Mark all the vertices as not visited
visited = [False]*self.V
stack =[]
# Call the recursive helper function to store Topological
# Sort starting from all vertices one by one
for i in range(self.V):
if visited[i] == False:
self.topologicalSortUtil(i,visited,stack)
# Print contents of stack
print stack
g= Graph(6)
g.addEdge(5, 2);
g.addEdge(5, 0);
g.addEdge(4, 0);
g.addEdge(4, 1);
g.addEdge(2, 3);
g.addEdge(3, 1);
print "Following is a Topological Sort of the given graph"
g.topologicalSort()
#This code is contributed by Neelam Yadav
