[图] 7.1 拓扑排序|拓扑序列 - C实现

拓扑排序原理：https://blog.csdn.net/summer_dew/article/details/81604206

【测试数据】

【结果】
在这里插入图片描述

【数据结构】邻接表为例
需要将邻接表的数据结构加上一个count，表示入度

typedef struct VNode{
	char data;
	int count; //入度
	ArcNode *firstarc; //第一条边
}VNode, AdjList[MAX_VERTEX_NUM];

【代码】

//计算每个顶点的入度
void CntGraphIndegree(ALGraph *pG) {
	ArcNode *p;
	int i;
	for (i=0; i<pG->vernum; i++) {
		for (p=pG->vers[i].firstarc; p; p=p->next) {
			pG->vers[p->adjV].count++;
		}
	}
}
// 拓扑排序，并打印拓扑序列
int TopSort(ALGraph *pG) {
	int i,j;
	int n=0;
	int stack[maxSize],top=-1; //保存当前所有入度为0的顶点
	ArcNode *p;

	CntGraphIndegree(pG); //计算入度
	//将入度为0的顶点压入栈中
	for (i=0; i<pG->vernum; i++) {
		if (pG->vers[i].count==0)
			stack[++top]=i; 
	}

	while (top!=-1) {
		i = stack[top--]; //顶点出栈，等效于在图中删掉
		++n;
		printf("%c ", pG->vers[i].data);

		p=pG->vers[i].firstarc;
		while (p!=NULL) {
			j = p->adjV;
			--(pG->vers[j].count);
			if (pG->vers[j].count==0)
				stack[++top]=j;
			p=p->next;
		}
	}

	if (n==pG->vernum) //拓扑排序后没有剩余顶点
		return 1;
	else //拓扑排序后还有剩余顶点
		return 0;
}

【完整代码】

#include<stdio.h>
#include<stdlib.h>

#define maxSize 50
#define MAX_VERTEX_NUM 20

#ifndef BASE
#define BASE
#define TRUE 1
#define FALSE 0
#define OK 1
#define ERROR 0
#define INFEASIBLE -1
#define OVERFLOW -2
typedef int Status;
typedef int bool;
#endif

typedef struct ArcNode{
	int adjV;
	struct ArcNode *next;
}ArcNode;
typedef struct VNode{
	char data;
	int count; //入度
	ArcNode *firstarc; //第一条边
}VNode, AdjList[MAX_VERTEX_NUM];
typedef struct{
	int vernum,arcnum;
	AdjList vers;
}ALGraph;

/*------------------------
 |创建有向图的邻接表     |
 ------------------------*/
Status InitGraph_AL(ALGraph *pG) { //初始化
	int i;
	pG->arcnum = 0;
	pG->vernum = 0;
	for (i=0; i<MAX_VERTEX_NUM; ++i)
		pG->vers[i].firstarc = NULL; //VC++6.0中指针初始化为0xcccccccc
	return OK;
}
int LocateVex_AL(ALGraph G, char e) { //定位值为e的元素下标
	int i;
	for (i=0; i<G.vernum; ++i) {
		if (G.vers[i].data == e) {
			return i;
		}
	}
	return -1;
}
Status CreateDG_AL(ALGraph *pG) { //创建有向图的邻接表--不带权
	//输入规则：顶点数目->弧的数目->各顶点的信息->各条弧的信息
	int i,a,b;
	char tmp[MAX_VERTEX_NUM];
	char h,t;
	ArcNode *p, *q;

	InitGraph_AL(pG); //VC++6.0中指针初始化为0xcccccccc，如果不将指针初始化为NULL，会出错
	//顶点数目
	scanf("%d", &i); if (i<0) return ERROR;
	pG->vernum = i;
	//弧的数目
	scanf("%d", &i); if (i<0) return ERROR;
	pG->arcnum = i;
	//各顶点信息
	scanf("%s", tmp);
	for (i=0; i<pG->vernum; ++i) {
		pG->vers[i].data=tmp[i];
		pG->vers[i].count=0;
	}
	//弧的信息
	for (i=0; i<pG->arcnum; ++i) {
		scanf("%s", tmp);
		h = tmp[0]; t = tmp[2];
		a = LocateVex_AL(*pG, h);
		b = LocateVex_AL(*pG, t);
		if (a<0 || b<0) return ERROR;
		p = (ArcNode *)malloc(sizeof(ArcNode)); if (!p) exit(OVERFLOW);
		p->adjV=b;p->next=NULL;
		if (pG->vers[a].firstarc) { //已经有边了
			for (q = pG->vers[a].firstarc; q->next; q=q->next) ; //找到最后一条
			q->next = p;
		} else { //第一条边
			pG->vers[a].firstarc = p;
		}
	}
	return OK;
}

//计算每个顶点的入度
void CntGraphIndegree(ALGraph *pG) {
	ArcNode *p;
	int i;
	for (i=0; i<pG->vernum; i++) {
		for (p=pG->vers[i].firstarc; p; p=p->next) {
			pG->vers[p->adjV].count++;
		}
	}
}
// 拓扑排序，并打印拓扑序列
int TopSort(ALGraph *pG) {
	int i,j;
	int n=0;
	int stack[maxSize],top=-1; //保存当前所有入度为0的顶点
	ArcNode *p;

	CntGraphIndegree(pG); //计算入度
	//将入度为0的顶点压入栈中
	for (i=0; i<pG->vernum; i++) {
		if (pG->vers[i].count==0)
			stack[++top]=i; 
	}

	while (top!=-1) {
		i = stack[top--]; //顶点出栈，等效于在图中删掉
		++n;
		printf("%c ", pG->vers[i].data);

		p=pG->vers[i].firstarc;
		while (p!=NULL) {
			j = p->adjV;
			--(pG->vers[j].count);
			if (pG->vers[j].count==0)
				stack[++top]=j;
			p=p->next;
		}
	}

	if (n==pG->vernum) //拓扑排序后没有剩余顶点
		return 1;
	else //拓扑排序后还有剩余顶点
		return 0;
}

int main() {
/*
测试数据：没有回路
9
11
ABCDEFGHI
A,D
B,D
B,E
C,E
D,F
D,G
E,H
F,I
G,E
G,I
H,I
测试数据二：有回路
9
11
ABCDEFGHI
A,D
B,D
C,E
D,F
D,G
E,B
E,H
F,I
G,E
G,I
H,I
*/
	ALGraph G;
	int ret;

	CreateDG_AL(&G);

	ret = TopSort(&G);
	printf("\n该有向图是否有回路：%d\n", !ret);
	
	return 0;
}

[图] 7.1 拓扑排序|拓扑序列 - C实现

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