数据结构——数据结构算法之《图》

图的定义和术语

完全图：任意两个点都有一条边相连

连通图（强连通图）

连通分量（强连通分量）

有向图和无向图的工程案例

#include "pch.h"
#include <iostream>
using namespace std;

//有向图 无向图 有向网 无向网
enum GraphKing { DG, DN, UDG, UDN };

//定义图
typedef struct Node
{
	int *vex;		//顶点个数
	int vexnum;		//顶点数
	int edge;		//图的边数
	int **adjmatrix;//图的邻接矩阵
	GraphKing kind;	//图的类型
}Mygraph;

//创建图
void CreateGraph(Mygraph &g,GraphKing king)
{
	cout << "请输入图的顶点个数：";
	cin >> g.vexnum;
	cout << "请输入图的边的条数：";
	cin >> g.edge;

	g.kind = king;//确认创建图的类型
	//开辟空间
	g.vex = new int[g.vexnum];
	g.adjmatrix = new int*[g.vexnum];

	cout << "输出顶点个数：" << g.vexnum << endl;
	//给邻接矩阵申请空间
	for (int i = 0; i < g.vexnum; i++)
	{
		g.adjmatrix[i] = new int[g.vexnum];
	}
	//给邻接矩阵初始化
	for (int j = 0; j < g.vexnum; j++)
	{
		for (int k = 0; k < g.vexnum; k++)
		{
			if (g.kind==DG||g.kind==DN)
			{
				g.adjmatrix[j][k] = 0;
			}
			else
			{
				g.adjmatrix[j][k] = INT_MAX;
			}
		}
	}

	//输入图的顶点
	cout << "请输入两个顶点的序号（1，2分别代表1号顶点和2号顶点）：" << endl;;
	for (int i = 0; i < g.edge; i++)
	{
		int a, b;
		cout << "请依次输入图(vi, vj)的vi和vj：";
		cin >> a >> b;
		//无向图
		if (g.kind==DN)
		{
			g.adjmatrix[b - 1][a - 1] = 1;
			g.adjmatrix[a - 1][b - 1] = 1;
		}
		//有向图
		else if (g.kind==DG)
		{
			g.adjmatrix[a - 1][b - 1] = 1;
		}
		//有向网
		else if (g.kind==UDG)
		{
			int weight;
			cout << "请输入该边的权：";
			cin >> weight;
			g.adjmatrix[a - 1][b - 1] = weight;
		}
		else if (g.kind == UDN)
		{
			int weight;
			cout << "请输入该边的权：";
			cin >> weight;
			g.adjmatrix[a - 1][b - 1] = weight;
			g.adjmatrix[a - 1][b - 1] = weight;
		}
	}
}

//输出图
void PrintGraph(Mygraph g)
{
	for (int i = 0; i <g.vexnum; i++)
	{
		for (int j = 0; j < g.vexnum; j++)
		{
			//有/无向网
			if (g.adjmatrix[i][j]==INT_MAX)
			{
				cout << "∞" << endl;
			}
			else
			{
				cout << g.adjmatrix[i][j] << " ";
			}
		}
		cout << endl;
	}
}

//清除图
void ClearGraph(Mygraph g)
{
	delete g.vex;
	g.vex = NULL;
	for (int i = 0; i < g.vexnum; i++)
	{
		delete g.adjmatrix[i];
		g.adjmatrix[i] = NULL;
	}
	delete g.adjmatrix;
}
int main()
{
	Mygraph g;
	cout << "有向图案例：" << endl;
	CreateGraph(g, DG);
	PrintGraph(g);
	ClearGraph(g);
	cout << endl;

	cout << "无向图案例：" << endl;
	CreateGraph(g, DN);
	PrintGraph(g);
	ClearGraph(g);
	cout << endl;
	return 0;
}

结果为：