图的实现：邻接表
当图中的边数较少时，用邻接表来实现图结构，则会浪费非常多内存空间。因此，考虑还有一种实现图结构的方法：邻接表。在邻接表中主要有两种节点结构体：
顶点节点
边节点
直接看代码
类定义
#include<iostream>
#include<iomanip>
using namespace std;
//最大权值
#define MAXWEIGHT 100
//边节点
typedef struct edgenode_tag
{
int adjvex; //邻接点
int weight; //边的权值
struct edgenode_tag *next;
}EdgeNode;
//顶点节点
typedef struct vertex_tag
{
int vertex; //顶点
EdgeNode *next;
}Vertex;
class Graph
{
private:
//是否带权
bool isWeighted;
//是否有向
bool isDirected;
//顶点数
int numV;
//边数
int numE;
//邻接表
Vertex *adjList;
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;}
//插入边
void insertEdge(int tail, int head, int weight = 1);
void insertedge(int tail, int head, int weight);
//设置指定边的权值
void setEdgeWeight(int tail, int head, int weight);
//打印邻接表
void printAdjacentList();
//检查输入
bool check(int tail, int head, int weight = 1);
};
类实现
/*
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;
//边数初始化为0
numE = 0;
adjList = new Vertex[numV]; //指针数组
for (int i = 0; i < numV; i++)
{
adjList[i].vertex = i;
adjList[i].next = NULL;
}
}
//建图
void Graph::createGraph()
{
//用一个新的变量表示边数，numE的改动则留到insertedge()中
int numEdge = 0;
cout << "输入边数 ";
while (cin >> numEdge && numEdge < 0)
cout << "输入有误！，又一次输入 ";
int i, j, w;
if (!isWeighted) //无权图
{
cout << "输入每条边的起点和终点：
";
for (int k = 0; k < numEdge; k++)
{
cin >> i >> j;
while (!check(i, j))
{
cout << "输入的边不正确！又一次输入
";
cin >> i >> j;
}
insertEdge(i, j);
}
}
else //有权图
{
cout << "输入每条边的起点、终点和权值：
";
for (int k = 0; k < numEdge; k++)
{
cin >> i >> j >> w;
while (!check(i, j, w))
{
cout << "输入的边不正确！又一次输入
";
cin >> i >> j >> w;
}
insertEdge(i, j, w);
}
}
}
//析构方法
Graph::~Graph()
{
int i;
EdgeNode *p, *q;
for (i = 0; i < numV; i++)
{
if (adjList[i].next)
{
p = adjList[i].next;
while (p)
{
q = p->next;
delete p;
p = q;
}
}
}
delete[]adjList;
}
//设置指定边的权值
void Graph::setEdgeWeight(int tail, int head, int weight)
{
if (!isWeighted) //无权图
{
while (!check(tail, head))
{
cout << "输入的边不正确！又一次输入
";
cin >> tail >> head;
}
insertEdge(tail, head);
}
else //有权图
{
while (!check(tail, head, weight))
{
cout << "输入的边不正确！又一次输入
";
cin >> tail >> head >> weight;
}
insertEdge(tail, head, weight);
}
}
//插入边
void Graph::insertEdge(int vertex, int adjvex, int weight)
{
insertedge(vertex, adjvex, weight);
if (!isDirected) //无向图
insertedge(adjvex, vertex, weight);
}
void Graph::insertedge(int vertex, int adjvex, int weight)
{
EdgeNode *p, *q, *r;
p = q = r = NULL;
if (adjList[vertex].next) //非第一个节点
{
p = adjList[vertex].next;
//移动p到合适位置
while (p && (p->adjvex < adjvex))
{
q = p;
p = p->next;
}
if (p && (p->adjvex == adjvex)) //改动已有边权值
p->weight = weight;
else
{
r = new EdgeNode;
r->adjvex = adjvex;
r->weight = weight;
r->next = p;
//当增加的新节点位于表的第一个位置
if (adjList[vertex].next == p)
adjList[vertex].next = r;
else
q->next = r;
numE++;
}
}
else
{
p = new EdgeNode;
p->adjvex = adjvex;
p->weight = weight;
p->next = NULL;
adjList[vertex].next = p;
numE++;
}
}
//输入检查
bool Graph::check(int tail, int head, int weight)
{
if (tail >= 0 && tail < numV && head >= 0 && head < numV
&& weight > 0 && weight <= MAXWEIGHT)
return true;
else
return false;
}
//打印邻接表
void Graph::printAdjacentList()
{
int i;
EdgeNode *edge = NULL;
for (i = 0; i < numV; i++)
{
edge = adjList[i].next;
if (edge) //为什么加一个if推断？跟后面的换行有关。若某顶点无邻接点(无边)，则会空出一行
{
while (edge)
{
cout << "w(" << i << "," << edge->adjvex << ")=" << edge->weight << " ";
edge = edge->next;
}
cout << endl;
}
}
}主函数
int main(void)
{
cout << "******使用邻接表实现图结构***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 << "打印邻接表" << endl;
graph.printAdjacentList();
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.printAdjacentList();
system("pause");
return 0;
}执行
邻接表
完整代码下载：图的实现：邻接表
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