数据结构：图--拓扑排序

#include<iostream>  
#include<iomanip>
#include<queue>
using namespace std;
/*
用邻接矩阵实现图  
拓扑排序必须是有向图
*/
class Graph
{
private:
	//顶点数  
	int numV;
	//边数  
	int numE;
	//顶点的入度
	int *indegree;
	//邻接矩阵  
	int **matrix;
public:
	/*
	构造方法
	numV是顶点数，isWeighted是否带权值，isDirected是否有方向
	*/
	Graph(int numV);
	//建图  
	void createGraph(int numE);
	//析构方法  
	~Graph();
	//获取顶点数  
	int getVerNums()
	{
		return numV;
	}
	//获取边数  
	int getEdgeNums()
	{
		return numE;
	}
	//拓扑排序
	void topologicalSort();
	//打印邻接矩阵  
	void printAdjacentMatrix();
	//检查输入  
	bool check(int, int);
};

//构造函数，指定顶点数目
Graph::Graph(int numV)
{
	//对输入的顶点数进行检测
	while (numV <= 0)
	{
		cout << "顶点数有误！重新输入 ";
		cin >> numV;
	}
	this->numV = numV;
	//构建邻接矩阵，并初始化
	matrix = new int*[numV];
	int i, j;
	for (i = 0; i < numV; i++)
		matrix[i] = new int[numV];
	//由于权值对于拓扑排序并无作用，故采取无权图的做法
	for (i = 0; i < numV; i++)
	for (j = 0; j < numV; j++)
		matrix[i][j] = 0;
	//构建顶点的入度数组，并初始化
	indegree = new int[numV];
	for (i = 0; i < numV; i++)
		indegree[i] = 0;
}
void Graph::createGraph(int numE)
{
	/*
	对输入的边数做检测
	一个numV个顶点的有向图，最多有numV*(numV - 1)条边
	*/
	while (numE < 0 || numE > numV*(numV - 1))
	{
		cout << "边数有问题！重新输入 ";
		cin >> numE;
	}
	this->numE = numE;
	int tail, head, i;
	i = 0;
	cout << "输入每条边的起点(弧尾)、终点(弧头)" << endl;
	while (i < numE)
	{
		cin >> tail >> head;
		while (!check(tail, head))
		{
			cout << "输入的边不正确！请重新输入 " << endl;
			cin >> tail >> head;
		}
		matrix[tail][head] = 1;
		indegree[head]++;
		i++;
	}
}
Graph::~Graph()
{
	int i;
	for (i = 0; i < numV; i++)
		delete[] matrix[i];
	delete[]matrix;
	delete[]indegree;
}
//拓扑排序
void Graph::topologicalSort()
{
	int i, vertex;
	queue<int> q;
	//入度为零的顶点入队
	for (i = 0; i < numV; i++)
	if (indegree[i] == 0)
		q.push(i);
	bool *visited = new bool[numV];
	for (i = 0; i < numV; i++)
		visited[i] = false;
	while (!q.empty())
	{
		vertex = q.front();
		q.pop();
		cout << setw(4) << vertex;
		visited[vertex] = true;
		for (i = 0; i < numV; i++)
		if (matrix[vertex][i] == 1)
		{
			//调整入度，入度为0则需入队
			if (!(--indegree[i]))
				q.push(i);
		}
	}
	cout << endl;
	for (i = 0; i < numV; i++)
	if (!visited[i])
		cout << "该有向图有环！";
	cout << endl;
	delete[]visited;
}
//打印邻接矩阵  
void Graph::printAdjacentMatrix()
{
	int i, j;
	cout.setf(ios::left);
	cout << setw(4) << " ";
	for (i = 0; i < numV; i++)
		cout << setw(4) << i;
	cout << endl;
	for (i = 0; i < numV; i++)
	{
		cout << setw(4) << i;
		for (j = 0; j < numV; j++)
			cout << setw(4) << matrix[i][j];
		cout << endl;
	}
}
bool Graph::check(int tail, int head)
{
	if (tail < 0 || tail >= numV || head < 0 || head >= numV)
		return false;
	return true;
}

int main()
{
	cout << "******拓扑排序***by David***" << endl;
	int numV, numE;
	cout << "建图..." << endl;
	cout << "输入顶点数 ";
	cin >> numV;
	Graph graph(numV);
	cout << "输入边数 ";
	cin >> numE;
	graph.createGraph(numE);
	cout << "打印邻接矩阵..." << endl;
	graph.printAdjacentMatrix();
	cout << "拓扑排序..."<<endl;
	graph.topologicalSort();
	system("pause");
	return 0;
}

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