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，我们可以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，其中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)。
下面给出一个实例
类定义
#include
#include
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！，重新输入 ";
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
{
//所有权值初始化为0
for (i = 0; i < numV; i++)
for (j = 0; j < numV; j++)
matrix[i][j] = 0;
}
else //有权图
{
//所有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！，重新输入 ";
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 << "输入的边不对！重新输入\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 << "输入的边不对！重新输入\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 << "输入的边不对！重新输入\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 << "输入的边不对！重新输入\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，重新输入边的起点、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，重新输入边的起点、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 << "修改指定边的权值" << 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 << "修改成功！" << 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
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