数据结构之拓扑排序

Posted 2020-11-03 迷途纸鸢

算法解析(图片内容来自《大话数据结构》这本书不错哦):

 

代码如下:

  1 #include "stdafx.h"
  2 #include<iostream>
  3 #include<string>
  4 using namespace std;
  5 #define MAXSIZE 100
  6 #define ERROR 0
  7 #define OK 1
  8 #define INFINITY 65535
  9 typedef int Status;
 10 typedef struct ArcNode                 //边表结点
 11 {
 12     int adjvex;                        //改变所指向的顶点的位置
 13     struct ArcNode *nextarc;           //指向下一条边的指针    
 14 }ArcNode;
 15 typedef struct VNode                   //顶点表结点
 16 {
 17     int in;
 18     char data;                         //顶点域，存储顶点信息
 19     ArcNode *firstarc;                 //指向第一条依附该顶点的边的指针
 20 }VNode, AdjList[MAXSIZE];              //AdList表示邻接表类型
 21 typedef struct                         //邻接表
 22 {
 23     AdjList vertices;
 24     int vexnum, arcnum;                //图的当前顶点数和边数
 25 }ALGraph;
 26 
 27 typedef struct
 28 {
 29     char vexs[MAXSIZE];                //顶点表
 30     int arcs[MAXSIZE][MAXSIZE];        //邻接矩阵
 31     int vexnum, arcnum;                //图的当前点数和边数
 32 }AMGraph;
 33 
 34 void CreateUDN(AMGraph &G)             //采用邻接矩阵表示法，创建无向网&G
 35 {
 36     int i, j, w;
 37     cout << "请输入总顶点数、总边数(空格隔开):" << endl;
 38     cin >> G.vexnum >> G.arcnum;       //输入总顶点数、总边数
 39     cout << "请输入顶点信息(空格隔开):" << endl;
 40     for (i = 0; i < G.vexnum; i++)     //依次输入点的信息
 41     {
 42         cin >> G.vexs[i];
 43     }
 44     for (i = 0; i < G.vexnum; i++)     //初始化邻接矩阵，编的权值均为极大值MaxInt
 45         for (j = 0; j < G.vexnum; j++)
 46             G.arcs[i][j] = 0;
 47     cout << "请输入边的信息(输入顺序：连接点1编号，连接点2编号):" << endl;
 48     for (int k = 0; k < G.arcnum; k++) //构造邻接矩阵
 49     {
 50         cin >> i >> j;                 //输入一条边依附的顶点
 51         G.arcs[i-1][j-1] = 1;
 52     }
 53 }
 54 
 55 void CreateALGraph(AMGraph G, ALGraph &GL)
 56 {
 57     int i, j;
 58     ArcNode *e;
 59     GL.vexnum = G.vexnum;
 60     GL.arcnum = G.arcnum;
 61     for (i = 0; i <G.vexnum; i++)      //读入顶点信息，建立顶点表
 62     {
 63         GL.vertices[i].in = 0;
 64         GL.vertices[i].data = G.vexs[i];
 65         GL.vertices[i].firstarc = NULL;//将边表置为空表
 66     }
 67 
 68     for (i = 0; i<G.vexnum; i++)       //建立边表
 69     {
 70         for (j = 0; j<G.vexnum; j++)
 71         {
 72             if (G.arcs[i][j] == 1)
 73             {
 74                 e = new ArcNode;
 75                 e->adjvex = j;           //邻接序号为j
 76                 e->nextarc = GL.vertices[i].firstarc;//将当前顶点上的指向的结点指针赋值给e
 77                 GL.vertices[i].firstarc = e;//将当前顶点的指针指向e
 78                 GL.vertices[j].in++;
 79             }
 80         }
 81     }
 82 }
 83 
 84 Status TopologicalSort(ALGraph GL)
 85 {
 86     ArcNode *e;
 87     int i, k, gettop;
 88     int top = 0;                       //用于栈指针下标
 89     int count = 0;                     // 用于统计输出顶点的个数
 90     int *stack;                        //建栈将入度为0的顶点入栈
 91     stack = new int[GL.vexnum];
 92     for (i = 0; i<GL.vexnum; i++)
 93         if (0 == GL.vertices[i].in)    //将入度为0的顶点入栈
 94             stack[++top] = i;
 95     while (top != 0)
 96     {
 97         gettop = stack[top--];
 98         cout << GL.vertices[gettop].data<<"->"; 
 99         count++;                       //输出i号顶点，并计数
100         for (e = GL.vertices[gettop].firstarc; e; e = e->nextarc)
101         {
102             k = e->adjvex;
103             if (!(--GL.vertices[k].in)) //将i号顶点的邻接点的入度减1，如果减1后为0，则入栈
104                 stack[++top] = k;
105         }
106     }
107     cout << endl;
108     if (count <GL.vexnum)
109         return ERROR;
110     else
111         return OK;
112 }
113 
114 int main()
115 {
116     AMGraph G;
117     ALGraph GL;
118     int result;
119     CreateUDN(G);
120     CreateALGraph(G,GL);
121     result = TopologicalSort(GL);
122     cout << "result:" << result << endl;
123     return 0;
124 }

 

 

示例结果(就是上面那几张图片的示例):