最短路径

  1 #include "iostream"
  2 #include "vector"
  3 #include "stack"
  4 using namespace std;
  5 
  6 const int MaxNumVertex  = 20; //最大顶点数
  7 const int infinity = 65535;//无穷大
  8 typedef int elementtype;       //elementtype 为int 型
  9 class graph{
 10 public:
 11     graph();
 12     ~graph();
 13     elementtype insertvertex(elementtype v); //在图中增加一个顶点
 14     elementtype insertedge(elementtype v,elementtype u,elementtype weight);//在图中增加一条从v顶点到u顶点的弧
 15     elementtype firstadj(elementtype v);//求图g中顶点v的第一个邻接点
 16     elementtype nextadj(elementtype v,elementtype m);//求图中顶点v的m邻接点之后的邻接点
 17     elementtype Dijkstra(elementtype v0);//求解从v0到各顶点的最短路径
 18     elementtype create();//创建图
 19     int  CurrentVertex;//当前顶点数
 20 
 21 private:
 22     elementtype vertex[MaxNumVertex];//顶点表
 23     elementtype edge[MaxNumVertex][MaxNumVertex];//图中弧的类型
 24     
 25 };
 26 
 27 /*
 28 *初始化
 29 */
 30 graph::graph()
 31 {
 32     CurrentVertex = 0; 
 33     int i,j;
 34     for (i=MaxNumVertex-1;i>=1;i--)
 35     {
 36         for (j=MaxNumVertex-1;j>=1;j--)
 37         {
 38             edge[i][j] = infinity;
 39 
 40         }
 41     }
 42     
 43 }
 44 
 45 /*
 46 *在图中增加一个顶点
 47 */
 48 elementtype graph::insertvertex(elementtype v)
 49 {
 50     //判断这个顶点是否已经存在
 51     int i;
 52     bool flags = true;
 53     for(i=1; i<=CurrentVertex; i++)
 54     {
 55         if(vertex[i]==v)
 56         {
 57             flags = false;
 58             break;
 59         }
 60     }
 61     
 62     if(flags)
 63     {
 64         CurrentVertex++;
 65         vertex[CurrentVertex] = v;
 66     }else{
 67         cout<<v<<"顶点已经存在!"<<endl;
 68     }
 69     return 0;
 70 }
 71 
 72 /*
 73 *在图中增加一条从v顶点到u顶点的弧
 74 */
 75 elementtype graph::insertedge(elementtype v,elementtype u,elementtype weight)
 76 {
 77     if(edge[v][u]!=infinity)
 78     {
 79         cout<<v<<"->"<<u<<"这条弧弧已经存在!"<<endl;
 80     }else{
 81         edge[v][u] = weight;
 82     }
 83     return 0;
 84 }
 85 
 86 
 87 /*
 88 *求图中顶点v的第一个邻接点
 89 */
 90 elementtype graph::firstadj(elementtype v)
 91 {
 92     int u,i;
 93     bool flags = true;//用于判断是否存在邻接点
 94     for(i=1;i<=CurrentVertex;i++)
 95     {
 96         if(edge[v][i]!=0){
 97             u = i;
 98             flags = false;
 99             break;
100         }
101     }
102     if(flags) u = 0;//邻接点不存在
103     return u;
104 }
105 
106 /*
107 *求图中顶点v的m邻接点以后的邻接点
108 */
109 elementtype graph::nextadj(elementtype v,elementtype m)
110 {
111     int i,u;
112     bool flags = true;
113     for(i=m+1;i<=CurrentVertex;i++)
114     {
115         if(edge[v][i]!=0)
116         {
117             u = i;
118             flags = false;
119             break;
120         }
121     }
122     if(flags) u = 0;//邻接点不存在
123     return u;
124 }
125 
126 /*
127 *求解v0到各顶点的最短路径
128 */
129 elementtype graph::Dijkstra(elementtype v0)
130 {
131     int i,j,k,w,v;
132     bool solved[20];
133     int dist[20];
134     vector<vector<int>>path(MaxNumVertex);//存储v0到各顶点的路径
135     for(i=1;i<=CurrentVertex;i++)
136     {
137         solved[i] = false;
138     }
139 
140     solved[v0] = true;//将v0设置为已解顶点
141     for(i=1;i<=CurrentVertex;i++)
142     {
143         if(edge[v0][i]!=infinity)
144         {
145             dist[i] = edge[v0][i];
146             path[i].push_back(v0);
147             path[i].push_back(i);
148         }else{
149             dist[i] = infinity;
150         }
151     }
152 
153     for(i=1;i<CurrentVertex;i++)
154     {
155         int min = infinity;
156         for(j=1;j<=CurrentVertex;j++)//在未解顶点中搜索最近的顶点v
157         {
158             if((solved[j]==false)&&(dist[j]<min))
159             {
160                 min = dist[j];
161                 v = j;
162             }
163         }
164 
165         solved[v] = true;//所搜索到的当前最短的未解顶点为已解顶点
166         for(w=firstadj(v);w!=0;w=nextadj(v,w))//修改v的后继路径以及长度
167         {
168             if(dist[v]+edge[v][w]<dist[w])
169             {
170                 dist[w] = dist[v]+edge[v][w];//修改w的dist值
171                 path[w].clear();//清空w的path
172                 //重新形成w的path
173                 for(k=0;k<path[v].size();k++)
174                 {
175                     path[w].push_back(path[v][k]);
176                 }
177                 path[w].push_back(w);
178             }
179         }
180     }
181     for(i=1;i<=CurrentVertex;i++)
182     {
183         if(v0!=i)
184         {
185             cout<<"dist["<<v0<<"->"<<i<<"]:"<<dist[i]<<endl;
186             cout<<"path["<<v0<<"->"<<i<<"]:";
187             for(j=0;j<path[i].size();j++)
188             {
189                 if(j<path[i].size()-1)cout<<path[i][j]<<",";
190                 else cout<<path[i][j]<<endl;
191             }
192             cout<<endl;
193         }
194     }
195     return 0;
196 }
197 /*
198 *创建图
199 */
200 elementtype graph::create()
201 {
202     int i,numv,v,u,weight;
203     cout<<"please create graph"<<endl;
204     cout<<"input numvertex(顶点数):";
205     cin>>numv;
206     cout<<"input vertex(顶点):";
207     for(i=1;i<=numv;i++)
208     {
209         cin>>v;
210         insertvertex(v);
211     }
212     cout<<"input num(u,v,weight)(弧的数目):";
213     cin>>numv;
214     for(i=1;i<=numv;i++)
215     {
216         cout<<"u->v,weight:";
217         cin>>u>>v>>weight;
218         insertedge(u,v,weight);
219     }
220     cout<<"graph create finish！"<<endl<<endl;
221     return 0;
222 }
223 graph::~graph()
224 {
225 }
226 
227 int main()
228 {
229     graph g;
230     g.create();
231     int v0;
232     cout<<"please input start(起点):";
233     cin>>v0;
234     g.Dijkstra(v0);
235     return 0;
236 }