拓扑排序

拓扑排序是针对有向无环图。
拓扑排序算法主要是循环执行以下两步，直到不存在入度为0的顶点为止。

(1) 选择一个入度为0的顶点并输出之；

(2) 从网中删除此顶点及所有出边。

循环结束后，若输出的顶点数小于网中的顶点数，则输出“有回路”信息，否则输出的顶点序列就是一种拓扑序列。

简单实现：

#include<iostream>
#define MVNum 100//表示最大顶点数
using namespace std;

typedef struct ArcNode//边结点
{
	int adjvex;//该边所指向顶点的位置 下标
	struct ArcNode *nextarc;//指向下一条边的指针
}ArcNode;

typedef struct VNode//顶点信息
{
	int data;
	ArcNode *firstarc;//指向第一条依附于该顶点的边的指针
}VNode, AdjList[MVNum];

typedef struct//邻接表
{
	AdjList vertices;
	int vexnum, arcnum;//图的当前顶点数和边数
}DAGraph;

typedef struct StackNode
{
	int data;
	struct StackNode *next;
}StackNode,*LinkStack;

void InitStack(LinkStack &S)
{
	S = NULL;
}

int Pop(LinkStack &S,int &e)
{
	StackNode *p;
	e = S->data;
	p = S;
	S = S->next;
	delete p;
	return e;
}

void Push(LinkStack &S, int e)
{
//	cout << "b" << endl;
	StackNode *p;
	p = new StackNode;
	p->data = e;
	p->next = S;
	S = p;
}

int StackEmpty(LinkStack S)
{
	if (S == NULL)
		return 1;
	else
		return 0;
}

int Get_Position(DAGraph G, int ch)
{
	int i;
	for (i = 0; i<G.vexnum; i++)
	if (G.vertices[i].data == ch)
		return i;
	return -1;
}

DAGraph *Create_Graph()
{
	DAGraph *G1;
	int i, s, d, a, b;
	ArcNode *p1;
	G1 = new DAGraph;
	cout << "请输入总顶点数：" << endl;
	cin >> G1->vexnum;
	cout << "请输入总边数：" << endl;
	cin >> G1->arcnum;
	cout << "输入顶点：" << endl;
	for (i = 0; i < G1->vexnum; ++i)
	{
		cin >> G1->vertices[i].data;
		G1->vertices[i].firstarc = NULL;
	}
//   for (i = 0; i < G1->vexnum; ++i)
//	{
//		cout << G1->vertices[i].data << " ";
//		G1->vertices[i].firstarc = NULL;
//	}
//	cout<<endl;
	for (i = 0; i < G1->arcnum; ++i)
	{
		cout << "输入一条边的起点和终点：" << endl;
		cin >> s >> d;
		a = Get_Position(*G1, s);
		b = Get_Position(*G1, d);
		p1 = new ArcNode;
		p1->adjvex = b;
		p1->nextarc = G1->vertices[a].firstarc;
		G1->vertices[a].firstarc = p1;
		cout << "e" << endl;//tiaoshi
	}

//   for (int i = 0; i < G1->arcnum; ++i){
//       cout << "Node:" <<i<<"->";
//       ArcNode *p1 = G1->vertices[i].firstarc;
//       while(p1){
//         cout << p1->adjvex <<" ";
//         p1 = p1->nextarc;
//       }
//       cout<<endl;
//   }
	return G1;
}


void TopologicalSort(DAGraph G)
{
	int i, m, k;
	int topo[100] = {0};
	int indegree[100] = {0};
	ArcNode *p,*q;
	LinkStack S;
	InitStack(S);
	for (i = 0; i < G.vexnum; i++)//统计每一个结点的入度
	{
		q = G.vertices[i].firstarc;
		while (q != NULL)
		{
         int index = q->adjvex;
			indegree[index]++;
			q = q->nextarc;
		}
	}
	for (i = 0; i < G.vexnum; ++i)
	if (!indegree[i])
		Push(S, i);
	m = 0;
//	cout << "a" << endl;//tioaoshi
	while (StackEmpty(S) == 0)
	{
		Pop(S, i);
		topo[m] = i;
//		cout << "i" << i << endl;//tiaoshi
		++m;
//		cout << "a" << endl;//tioaoshi
		p = G.vertices[i].firstarc;
//		cout << "d" << endl;//tiaoshi
		while (p != NULL)
		{
//			cout << "c" << endl;
			k = p->adjvex;
			--indegree[k];
			if (indegree[k] == 0)
				Push(S, k);
			p = p->nextarc;
		}
	}
	if (m < G.vexnum)
		cout << "该有向图有回路" << endl;
	else
	{
		cout << "拓扑排序为：" << endl;
		for (i = 0; i < m; i++)
		{
			cout << topo[i]+1 << " ";
		}
	}
}
int main()
{
	DAGraph *G;
	G=Create_Graph();
	TopologicalSort(*G);
	return 0;
}