数据结构：点对之间最短距离--Floyd算法

#include<iostream>  
#include<iomanip>
#include<stack>
using namespace std;
#define MAXWEIGHT 100
#undef INFINITY
#define INFINITY 1000
class Graph
{
private:
	//顶点数  
	int numV;
	//边数  
	int numE;
	//邻接矩阵  
	int **matrix;
public:
	Graph(int numV);
	//建图  
	void createGraph(int numE);
	//析构方法  
	~Graph();
	//Floyd算法
	void Floyd();
	//打印邻接矩阵  
	void printAdjacentMatrix();
	//检查输入  
	bool check(int, 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];
	for (i = 0; i < numV; i++)
	for (j = 0; j < numV; j++)
	{
		if (i == j)
			matrix[i][i] = 0;
		else
			matrix[i][j] = INFINITY;
	}
}
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, weight, i;
	i = 0;
	cout << "输入每条边的起点(弧尾)、终点(弧头)和权值" << endl;
	while (i < numE)
	{
		cin >> tail >> head >> weight;
		while (!check(tail, head, weight))
		{
			cout << "输入的边不正确！请重新输入 " << endl;
			cin >> tail >> head >> weight;
		}
		matrix[tail][head] = weight;
		i++;
	}
}
Graph::~Graph()
{
	int i;
	for (i = 0; i < numV; i++)
		delete[] matrix[i];
	delete[]matrix;
}
/*
弗洛伊德算法
求各顶点对之间的最短距离
及其路径
*/
void Graph::Floyd()
{
	//为了不修改邻接矩阵，多用一个二维数组
	int **Distance = new int*[numV];
	int i, j;
	for (i = 0; i < numV; i++)
		Distance[i] = new int[numV];
	//初始化
	for (i = 0; i < numV; i++)
	for (j = 0; j < numV; j++)
		Distance[i][j] = matrix[i][j];

	//prev数组
	int **prev = new int*[numV];
	for (i = 0; i < numV; i++)
		prev[i] = new int[numV];
	//初始化prev
	for (i = 0; i < numV; i++)
	for (j = 0; j < numV; j++)
	{
		if (matrix[i][j] == INFINITY)
			prev[i][j] = -1;
		else
			prev[i][j] = i;
	}
	
	int d, v;
	for (v = 0; v < numV; v++)
	for (i = 0; i < numV; i++)
	for (j = 0; j < numV; j++)
	{
		d = Distance[i][v] + Distance[v][j];
		if (d < Distance[i][j])
		{
			Distance[i][j] = d;
			prev[i][j] = v;
		}
	}
	//打印Distance和prev数组
	cout << "Distance..." << endl;
	for (i = 0; i < numV; i++)
	{
		for (j = 0; j < numV; j++)
			cout << setw(3) << Distance[i][j];
		cout << endl;
	}
	cout << endl << "prev..." << endl;
	for (i = 0; i < numV; i++)
	{
		for (j = 0; j < numV; j++)
			cout << setw(3) << prev[i][j];
		cout << endl;
	}
	cout << endl;
	//打印顶点对最短路径
	stack<int> s;
	for (i = 0; i < numV; i++)
	{
		for (j = 0; j < numV; j++)
		{
			if (Distance[i][j] == 0);
			else if (Distance[i][j] == INFINITY)
				cout << "顶点 " << i << " 到顶点 " << j << " 无路径！" << endl;
			else
			{
				s.push(j);
				v = j;
				do{
					v = prev[i][v];
					s.push(v);
				} while (v != i);
				//打印路径
				cout << "顶点 " << i << " 到顶点 " << j << " 的最短路径长度是 "
					<< Distance[i][j] << " ，其路径序列是...";
				while (!s.empty())
				{
					cout << setw(3) << s.top();
					s.pop();
				}
				cout << endl;
			}
		}
		cout << endl;
	}
	//释放空间
	for (i = 0; i < numV; i++)
	{
		delete[] Distance[i];
		delete[] prev[i];
	}
	delete[]Distance;
	delete[]prev;
}
//打印邻接矩阵  
void Graph::printAdjacentMatrix()
{
	int i, j;
	cout.setf(ios::left);
	cout << setw(7) << " ";
	for (i = 0; i < numV; i++)
		cout << setw(7) << i;
	cout << endl;
	for (i = 0; i < numV; i++)
	{
		cout << setw(7) << i;
		for (j = 0; j < numV; j++)
			cout << setw(7) << matrix[i][j];
		cout << endl;
	}
}
bool Graph::check(int tail, int head, int weight)
{
	if (tail < 0 || tail >= numV || head < 0 || head >= numV
		|| weight <= 0 || weight >= MAXWEIGHT)
		return false;
	return true;
}

int main()
{
	cout << "******Floyd***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 << endl << "Floyd..." << endl;
	graph.Floyd();
	system("pause");
	return 0;
}

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