学校数据结构的课程实验之一。
用到的数据结构：无向带权图
用到的算法：Floyd最短路径算法，深度优先搜索（递归实现）
需求分析：
设计一个校园导航程序，为访客提供各种信息查询服务：
1. 以图中各顶点表示校内各单位地点，存放单位名称，代号，简介等信息；以边表示路径，存放路径长度等相关信息。
2. 图中任意单位地点相关信息的查询。
3. 图中任意单位的问路查询，即查询任意两个单位之间的一条最短的路径。
2. 从图中任意单位地点出发的一条深度优先遍历路径。
主函数：
1 #include <iostream>
2 #include "School.h"
3 using namespace std;
4
5 int main()
6 {
7 School mySchool=School("School.txt");
8 char choice=‘y‘;
9 while(choice==‘y‘)
10 {
11 cout << "请选择操作"<<endl;
12 cout << "--------------------------------" << endl;
13 cout << "1----查看地点列表" << endl;
14 cout << "2----查看地点简介" << endl;
15 cout << "3----查询最短路径" << endl;
16 cout << "4----从一点出发遍历" << endl;
17 cout << "5----任意一点的可直达地点" << endl;
18 cout << "--------------------------------" << endl;
19 int option;
20 cin >> option;
21 switch (option)
22 {
23 case 1: mySchool.display(); break;
24 case 2: mySchool.search(); break;
25 case 3: mySchool.path(); break;
26 case 4: mySchool.traverse(); break;
27 case 5: mySchool.reachable(); break;
28 }
29 cout << "继续吗?[y/n]";
30 cin >> choice;
31 }
32 return 0;
33 }
图类（邻接矩阵存储，因有向图是无向图的超集，所以可以定义为有向图，邻接矩阵为对称阵）
1 #include <fstream>
2 #include <string>
3
4 template <class Vertex,int graph_size>
5 class Digraph
6 {
7 public:
8 Digraph()
9 {
10 count=0;
11 for (int i = 0; i < graph_size; i++)
12 adjacency[i][i] = 0;
13 }
14 void insert(Vertex &new_entry)
15 {
16 nodes[count++]=new_entry;
17 }
18 void distance_set(int i, int j, int dis)
19 {
20 adjacency[i][j] = adjacency[j][i] = dis;
21 }
22 void traverse(void (*visit)(Vertex &))//遍历整个图（逐个访问各结点）
23 {
24 for(int i=0;i<graph_size;i++)
25 (*visit)(nodes[i]);
26 }
27 void search_vertex(int num,Vertex &target)
28 {
29 target=nodes[num];
30 }
31 void calculate_path()//计算最短路径并将结果更新到以上两个二维数组里
32 {
33 for (int i = 0; i < graph_size; i++)
34 {
35 for (int j = 0; j < graph_size; j++)
36 {//初始化路径长度数组，结点跟踪数组
37 shortest_dis[i][j] = adjacency[i][j];
38 trace_node[i][j] = j;
39 }
40 }
41 cout << "这是邻接矩阵：" << endl;
42 for (int i = 0; i < graph_size; i++)
43 {
44 for (int j = 0; j < graph_size; j++)
45 cout << adjacency[i][j] << " ";
46 cout << endl;
47 }
48 //Floyd算法计算任意两点之间的最短路径
49 for (int k = 0; k < graph_size; k++)
50 for (int v = 0; v < graph_size; v++)
51 for (int w = 0; w < graph_size; w++)
52 if (shortest_dis[v][k] + shortest_dis[k][w] < shortest_dis[v][w])
53 {
54 shortest_dis[v][w] = shortest_dis[v][k] + shortest_dis[k][w];
55 trace_node[v][w] = trace_node[v][k];
56 }
57 cout << "这是最短路径数组：" << endl;
58 for (int i = 0; i < graph_size; i++)
59 {
60 for (int j = 0; j < graph_size; j++)
61 cout << shortest_dis[i][j] << " ";
62 cout << endl;
63 }
64 cout << "这是结点跟踪数组：" << endl;
65 for (int i = 0; i < graph_size; i++)
66 {
67 for (int j = 0; j < graph_size; j++)
68 cout << trace_node[i][j] << " ";
69 cout << endl;
70 }
71 }
72 void shortest_path(int i, int j)
73 {
74 cout << "从" << i << "到" << j << "的最短路径长度为" << shortest_dis[i][j] << endl;
75 cout << "路径为：" << endl;
76 int k = trace_node[i][j];
77 cout << i ;
78 while (k != j)
79 {
80 cout << "->" << k;
81 k = trace_node[k][j];//从起点出发，找到途经结点
82 }
83 cout << "->" << j << endl;
84 }
85 void connected(int v)//输出所有和v直达的结点
86 {
87 for (int i = 0; i < graph_size; i++)
88 {
89 if (adjacency[v][i] != 100 && adjacency[v][i] != 0)
90 cout << nodes[i] << " 距离为：" << adjacency[v][i] << ";" << endl;
91 }
92 }
93 int BFS(int v,void (*visit)(Vertex &))
94 {
95 distance = 0;
96 bool visited[graph_size] = { false };
97 Vertex src = nodes[v];//找到选定的源点
98 visited[v] = true;
99 (*visit)(src);
100 for (int i = 0; i < graph_size; i++)
101 {
102 if (adjacency[v][i] != 100 && adjacency[v][i] != 0)//对相邻点进行深度优先遍历
103 traverse(i, visited, visit);
104 }
105 return distance;
106 }
107 private:
108 int count;//结点数
109 int distance;//一条遍历路径总长
110 int adjacency[graph_size][graph_size];//存储权的邻接矩阵
111 Vertex nodes[graph_size];//存储结点内容的一维数组
112 int shortest_dis[graph_size][graph_size];//保存最短路径长度
113 int trace_node[graph_size][graph_size];//保存结点跟踪路径
114 void traverse(int v, bool visited[], void (*visit)(Vertex &))//辅助遍历函数
115 {
116 if (visited[v] == false)
117 {
118 (*visit)(nodes[v]);
119 visited[v] = true;
120 for (int i = 0; i < graph_size; i++)
121 if (adjacency[v][i] != 100 && adjacency[v][i] != 0 && visited[i] == false)
122 {
123 traverse(i, visited, visit);//递归地进行深度优先遍历
124 distance += adjacency[v][i];
125 }
126
127 }
128 }
129 };
Digraph.h
学校类
1 #include <fstream>
2 #include <string>
3 #include "Digraph.h"
4 using namespace std;
5
6 struct Place//地点定义
7 {
8 int number;
9 string name;
10 string introduction;
11
12 Place(){}
13 Place(int num,string nam,string intro):number(num),name(nam),introduction(intro){}
14 void print()//显示此地点的信息
15 {
16 cout<<"---------------------------"<<endl;
17 cout<<"编号："<<number<<endl;
18 cout<<"地点名："<<name<<endl;
19 cout<<"简介："<<introduction<<endl;
20 cout<<"---------------------------"<<endl;
21 }
22 };
23 ostream& operator<<(ostream &os, Place &aPlace)//重载输出运算符
24 {
25 os << aPlace.number << ":" << aPlace.name;
26 return os;
27 }
28 ofstream outFile;//输出流
29
30 class School
31 {
32 private:
33 int total;//总的地点数
34 Digraph<Place,13> places_graph;
35 void readFile(const char filename[20])//读文件
36 {
37 total = 0;
38 ifstream inFile;
39 inFile.open(filename);
40 char trying;
41 while(inFile.is_open() && !inFile.eof())
42 {
43 //先试探是否为结束符
44 inFile >> trying;
45 if (trying == ‘#‘) break;
46 else
47 {
48 inFile.putback(trying);
49 int number;
50 inFile>>number;
51 string name;
52 inFile>>name;
53 string introduction;
54 inFile>>introduction;
55 Place aPlace=Place(number,name,introduction);
56 //aPlace.print();//显示这个地点的信息
57 places_graph.insert(aPlace);
58 total++;
59 }
60 }
61 for (int i = 0; i < 13; i++)//读入距离内容
62 for (int j = 0; j < 13; j++)
63 {
64 int dis;
65 inFile >> dis;
66 places_graph.distance_set(i, j, dis);
67 }
68 inFile.close();
69 places_graph.calculate_path();//计算所有最短路径并存入数组
70 cout << "学校共有" << total << "个地方"<<endl;
71 }
72 static void readPlace(Place &aPlace)
73 {
74 outFile<<aPlace.number<<endl;
75 outFile<<aPlace.name<<endl;
76 outFile<<aPlace.introduction<<endl;
77 }
78 static void print(Place &aPlace)//显示此地点的信息编号、名称
79 {
80 cout<<aPlace.number<<": "<<aPlace.name<<endl;
81 }
82 static void visit(Place &aPlace)
83 {
84 cout << "->" << aPlace.number << ":" << aPlace.name << endl;
85 }
86 public:
87 School(const char filename[20])
88 {
89 readFile(filename);
90 }
91 void display()
92 {
93 cout<<"以下为学校的所有地点："<<endl;
94 places_graph.traverse(print);
95 }
96 void search()
97 {
98 cout<<"请输入要查询的地点编号：";
99 int num;
100 cin>>num;
101 Place aPlace;
102 places_graph.search_vertex(num,aPlace);//查到要查的地点
103 cout<<"以下是这一地点的信息："<<endl;
104 aPlace.print();
105 }
106 void path()
107 {
108 cout << "请输入想查询最短路径的两个地点的编号（如：5 7）：";
109 int i, j;
110 cin >> i >> j;
111 places_graph.shortest_path(i, j);
112 }
113 void traverse()//深度优先遍历，输出路线
114 {
115 cout << "请输入源点的编号：";
116 int v;
117 cin >> v;
118 int distance;
119 distance = places_graph.BFS(v, visit);
120 cout << endl << "路径总长为：" << distance<<endl;
121 }
122 void reachable()
123 {
124 cout << "请输入源点的编号：";
125 int v;
126 cin >> v;
127 cout << "和地点" << v << "有直达路径的地点如下：" << endl;
128 places_graph.connected(v);
129 }
130 };
主函数流程图：
运行截图：
附：测试用的文件School.txt内容
0 前门 南门；车辆进出 1 教一楼 阶梯教室；英语教室 2 教二楼 普通教室 3 教三楼 实验室；办公室；阶梯教室 4 学一公寓 男生宿舍 5 学二公寓 男生宿舍 6 学三公寓 女生宿舍 7 学四公寓 男生宿舍 8 食堂 一层；二层；清真 9 水房 在食堂旁边 10 操场 300米一圈的跑道 11 图书馆 借阅部；自习室 12 后门 北门；取快递 # 0 1 4 8 6 100 100 10 100 1 100 10 100 1 0 3 4 5 100 10 100 1 100 1 100 100 4 3 0 10 1 7 100 6 100 10 100 100 8 8 4 10 0 2 100 3 100 100 6 5 9 7 6 5 1 2 0 3 6 9 100 7 9 8 5 100 100 7 100 3 0 100 5 100 6 7 8 4 100 10 100 3 6 100 0 2 7 2 9 10 2 10 100 6 100 9 5 2 0 4 100 2 3 7 100 1 100 100 100 100 7 4 0 10 4 5 1 1 100 10 6 7 6 2 100 10 0 8 5 7 100 1 100 5 9 7 9 2 4 8 0 2 9 10 100 100 9 8 8 10 3 5 5 2 0 100 100 100 8 7 5 4 2 7 1 7 9 100 0
School.txt
时间： 2024-10-11 19:45:18