数据结构：图的实现--邻接矩阵

                         图的实现：邻接矩阵

为了表现图中顶点之间的关联，我们能够使用邻接矩阵来实现图结构。

所谓的邻接矩阵。就是一个反应边与边之间联系的二维数组。这个二维数组我们用matrix[numV][numV]表示。当中numV是顶点数。

对于无权图

若顶点Vi和Vj之间有边，则matrix[Vi][Vj]=1;否则matrix[Vi][Vj]=0。

对于有权图

若顶点Vi和Vj之间有边，且权值为weight，则matrix[Vi][Vj]=weight;否则matrix[Vi][Vj]=0或MAXWEIGHT(取最小权值或最大权值)。

以下给出一个实例

类定义

#include<iostream>
#include<iomanip>
using namespace std;
//最大权值
#define MAXWEIGHT 100
//用邻接矩阵实现图
class Graph
{
private:
	//是否带权
	bool isWeighted;
	//是否有向
	bool isDirected;
	//顶点数
	int numV;
	//边数
	int numE;
	//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, bool isWeighted = false, bool isDirected = false);
	//建图
	void createGraph();
	//析构方法
	~Graph();
	//获取顶点数
	int getVerNums()
	{return numV;}
	//获取边数
	int getEdgeNums()
	{return numE;}
	//设置指定边的权值
	void setEdgeWeight(int tail, int head, int weight);
	//打印邻接矩阵
	void printAdjacentMatrix();
	//检查输入
	bool check(int i, int j, int w = 1);
};

/*
构造方法
numV是顶点数，isWeighted是否带权值，isDirected是否有方向
*/
Graph::Graph(int numV, bool isWeighted, bool isDirected)
{
	while (numV <= 0)
	{
		cout << "输入的顶点数不正确。，又一次输入 ";
		cin >> numV;
	}
	this->numV = numV;
	this->isWeighted = isWeighted;
	this->isDirected = isDirected;
	matrix = new int*[numV];  //指针数组
	int i, j;
	for (i = 0; i < numV; i++)
		matrix[i] = new int[numV];
	//对图进行初始化
	if (!isWeighted)  //无权图
	{
		//全部权值初始化为0
		for (i = 0; i < numV; i++)
		for (j = 0; j < numV; j++)
			matrix[i][j] = 0;
	}
	else  //有权图
	{
		//全部权值初始化为最大权值
		for (i = 0; i < numV; i++)
		for (j = 0; j < numV; j++)
			matrix[i][j] = MAXWEIGHT;
	}
}
//建图
void Graph::createGraph()
{
	cout << "输入边数 ";
	while (cin >> numE && numE < 0)
		cout << "输入有误！，又一次输入 ";

	int i, j, w;
	if (!isWeighted)  //无权图
	{
		if (!isDirected)  //无向图
		{
			cout << "输入每条边的起点和终点：\n";
			for (int k = 0; k < numE; k++)
			{
				cin >> i >> j;
				while (!check(i, j))
				{
					cout << "输入的边不正确！又一次输入\n";
					cin >> i >> j;
				}
				matrix[i][j] = matrix[j][i] = 1;
			}
		}
		else  //有向图
		{
			cout << "输入每条边的起点和终点：\n";
			for (int k = 0; k < numE; k++)
			{
				cin >> i >> j;
				while (!check(i, j))
				{
					cout << "输入的边不正确！
又一次输入\n";
					cin >> i >> j;
				}
				matrix[i][j] = 1;
			}
		}
	}
	else  //有权图
	{
		if (!isDirected)   //无向图
		{
			cout << "输入每条边的起点、终点和权值：\n";
			for (int k = 0; k < numE; k++)
			{
				cin >> i >> j >> w;
				while (!check(i, j, w))
				{
					cout << "输入的边不正确。又一次输入\n";
					cin >> i >> j >> w;
				}
				matrix[i][j] = matrix[j][i] = w;
			}
		}
		else  //有向图
		{
			cout << "输入每条边的起点、终点和权值：\n";
			for (int k = 0; k < numE; k++)
			{
				cin >> i >> j >> w;
				while (!check(i, j, w))
				{
					cout << "输入的边不正确！
又一次输入\n";
					cin >> i >> j >> w;
				}
				matrix[i][j] = w;
			}
		}
	}
}
//析构方法
Graph::~Graph()
{
	int i = 0;
	for (i = 0; i < numV; i++)
		delete[] matrix[i];
	delete[]matrix;
}
//设置指定边的权值
void Graph::setEdgeWeight(int tail, int head, int weight)
{
	if (isWeighted)
	{
		while (!check(tail, head, weight))
		{
			cout << "输入不正确。又一次输入边的起点、终点和权值 ";
			cin >> tail >> head >> weight;
		}
		if (isDirected)
			matrix[tail][head] = weight;
		else
			matrix[tail][head] = matrix[head][tail] = weight;
	}
	else
	{
		while (!check(tail, head, 1))
		{
			cout << "输入不正确。又一次输入边的起点、终点 ";
			cin >> tail >> head;
		}
		if (isDirected)
			matrix[tail][head] = 1-matrix[tail][head];
		else
			matrix[tail][head] = matrix[head][tail] = 1 - matrix[tail][head];
	}
}
//输入检查
bool Graph::check(int i, int j, int w)
{
	if (i >= 0 && i < numV && j >= 0 && j < numV && w > 0 && w <= MAXWEIGHT)
		return true;
	else
		return false;
}
//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;
	}
}

int main()
{
	cout << "******使用邻接矩阵实现图结构***by David***" << endl;
	bool isDirected, isWeighted;
	int numV;
	cout << "建图" << endl;
	cout << "输入顶点数 ";
	cin >> numV;
	cout << "边是否带权值，0(不带) or 1(带) ";
	cin >> isWeighted;
	cout << "是否是有向图，0(无向) or 1(有向) ";
	cin >> isDirected;
	Graph graph(numV, isWeighted, isDirected);
	cout << "这是一个";
	isDirected ?
 cout << "有向、" : cout << "无向、";
	isWeighted ? cout << "有权图" << endl : cout << "无权图" << endl;
	graph.createGraph();
	cout << "打印邻接矩阵" << endl;
	graph.printAdjacentMatrix();
	cout << endl;
	int tail, head, weight;
	cout << "改动指定边的权值" << endl;
	if (isWeighted)  //针对有权图
	{
		cout << "输入边的起点、终点和权值 ";
		cin >> tail >> head >> weight;
		graph.setEdgeWeight(tail, head, weight);
	}
	else  //针对无权图
	{
		cout << "输入边的起点、终点 ";
		cin >> tail >> head;
		graph.setEdgeWeight(tail, head, 1);
	}
	cout << "改动成功！
" << endl;
	cout << "打印邻接矩阵" << endl;
	graph.printAdjacentMatrix();
	system("pause");
	return 0;
}

实例一

实例二

完整代码下载：图的实现：邻接矩阵

转载请注明出处，本文地址：http://blog.csdn.net/zhangxiangdavaid/article/details/38321327

若有所帮助。顶一个哦。

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