資料結構圖之三（最短路徑--迪傑斯特拉演算法）
阿新 • • 發佈：2018-12-30
1 #include <iostream> 2 #include "SeqList.h" 3 #include "Stack.h" 4 #include <iomanip> 5 using namespace std; 6 7 #define INFINITY 65535 8 9 template<class NameType, class DistType> 10 class Graph 11 { 12 private: 13 SeqList<NameType> Vertices;14 DistType **Edges; 15 int nVer, nEdges; 16 17 public: 18 Graph() 19 : Edges(NULL) 20 , nEdges(0) 21 , nVer(0) 22 {} 23 ~Graph() 24 {} 25 26 public: 27 int GetVer() const 28 { 29 return nVer; 30 } 3132 istream & operator>>(istream &in) 33 { 34 int v, u, value; 35 int i, j; 36 NameType item; 37 cout << "請輸入頂點的個數: " << endl; 38 in >> nVer; 39 cout << "請輸入頂點的資料資訊: " << endl; 40 for(i = 0; i < nVer; ++i) 41 { 42 in >> item; 43 Vertices.push_back(item); // 儲存全部頂點 44 } 45 /////二維陣列的建立並初始化 46 Edges = new DistType*[nVer]; // DistType *ar[10]; 47 for (i = 0; i < nVer; ++i) 48 { 49 Edges[i] = new DistType[nVer]; 50 for (j = 0; j < nVer; ++j) 51 { 52 Edges[i][j] = 0; 53 } 54 } 55 cout << "請輸入邊的個數: " << endl; 56 in >> nEdges; 57 cout << "請輸入邊的資訊：" << endl; 58 for (i = 0; i < nEdges; ++i) 59 { 60 in >> v >> u >> value; 61 Edges[v][u] = value; 62 Edges[u][v] = value; 63 } 64 return in; 65 } 66 ostream & operator<<(ostream &out) const 67 { 68 int i, j; 69 out << "頂點資訊 " << endl; 70 for (i = 1; i <= nVer; ++i) 71 { 72 out << Vertices[i] << setw(5); 73 } 74 out << endl; 75 out << "矩陣資訊：" << endl; 76 out << setw(10); 77 for (i = 1; i <= nVer; ++i) 78 { 79 out << Vertices[i] << setw(5); 80 } 81 out << endl; 82 for (i = 0; i < nVer; ++i) 83 { 84 out << Vertices[i+1] << setw(5); 85 for (j = 0; j < nVer; ++j) 86 { 87 if (0 == Edges[i][j] && i != j) 88 Edges[i][j] = INFINITY; 89 cout << Edges[i][j] << setw(5); 90 } 91 out << endl; 92 } 93 out << endl; 94 95 return out; 96 } 97 // 迪傑斯特拉演算法實現 98 void ShortestPath_Dijkstra(int v0, int* final, int*p, int *D) 99 { 100 int v, w, k, min; 101 // 初始化資料 102 for (v = 0; v < nVer; ++v) 103 { 104 final[v] = 0; // 全部頂點初始化為未知對短路徑狀態 105 D[v] = Edges[v0][v]; //將與V0點有連線的頂點加上權值 106 p[v] = 0; // 初始化路徑陣列p為0 107 } 108 D[v0] = 0; // V0至V0路徑為0 109 final[v0] = 1; // final[W]=1表示V0至V0不需要求路徑 110 // 開始主迴圈，每次求得V0到某個V頂點的最短路徑 111 for (v = 1; v < nVer; ++v) 112 { 113 min = INFINITY; // 當前所知離V0頂點最近距離 114 for (w = 0; w < nVer; ++w) // 尋找離V0最近的頂點 115 { 116 if (!final[w] && D[w] < min) 117 { 118 min = D[w]; // w頂點離V0頂點更近 119 k = w; 120 } 121 } 122 123 final[k] = 1; // 將目前找到的最近的頂點置為1 124 for (w = 0; w < nVer; ++w) // 修正當前最短路徑距離 125 { 126 // 如果經過V頂點的路徑比現在這條路徑的長度短的話 127 if (!final[w] && (min + Edges[k][w] < D[w])) 128 { 129 // 說明找到了最短的路徑，修改D[w] 和 p[w] 130 D[w] = min + Edges[k][w]; // 修改當前路徑長度 131 p[w] = k; 132 } 133 } 134 } 135 } 136 }; 137 138 template<class NameType, class DistType> 139 istream & operator>>(istream &in, Graph<NameType,DistType> &g) 140 { 141 g >> in; 142 return in; 143 } 144 145 template<class NameType, class DistType> 146 ostream & operator<<(ostream &out, const Graph<NameType,DistType> &g) 147 { 148 g << out; 149 return out; 150 } 151 152 void main() 153 { 154 Graph<char, int> myg; 155 cin >> myg; 156 cout << "列印所有輸入資訊：" << endl; 157 cout << myg << endl; 158 cout << "求最短路徑....." << endl; 159 int numVer = myg.GetVer(); 160 int* pFinal = new int[numVer]; 161 int* pPathmatirx = new int[numVer]; 162 int* pShortPath = new int[numVer]; 163 myg.ShortestPath_Dijkstra(0, pFinal, pPathmatirx, pShortPath); 164 cout << "列印各頂點最短路徑標記陣列值：" << " "; 165 for (int i = 0; i < numVer; ++i) 166 { 167 cout << pFinal[i] << " "; 168 } 169 cout << endl; 170 cout << "列印最短路徑陣列值：" << " "; 171 for (int i = 0; i < numVer; ++i) 172 { 173 cout << pShortPath[i] << " "; 174 } 175 cout << endl; 176 cout << "列印最短路徑前驅陣列值：" << " "; 177 for (int i = 0; i < numVer; ++i) 178 { 179 cout << pPathmatirx[i] << " "; 180 } 181 cout << endl; 182 cout << "列印V0到各個頂點最短路徑值以及路徑資訊：" << endl; 183 SeqStack<int> sQ; 184 for (int i = 1; i < numVer; ++i) 185 { 186 cout << "V0~V" << i << ": " << pShortPath[i] << endl; 187 188 sQ.Push(pPathmatirx[i]); 189 int n = 0; 190 while (sQ.GetTop(n) && n != 0) 191 { 192 sQ.Push(pPathmatirx[n]); 193 } 194 195 while (!sQ.IsEmpty()) 196 { 197 int m = 0; 198 sQ.Pop(m); 199 cout << "V" << m << "->"; 200 } 201 cout << "V" << i << endl; 202 } 203 delete []pFinal; 204 delete []pPathmatirx; 205 delete []pShortPath; 206 pFinal = NULL; 207 pPathmatirx = NULL; 208 pShortPath = NULL; 209 } 210 // 備註： 211 // 最短路徑迪傑斯特拉演算法實現 212 // 整理於2013-12-04 213 // 測試輸入程式為： 214 /* 215 請輸入頂點的個數: 216 9 217 請輸入頂點的資料資訊: 218 A B C D E F G H I 219 請輸入邊的個數: 220 16 221 請輸入邊的資訊： 222 0 1 1 223 0 2 5 224 1 2 3 225 1 3 7 226 1 4 5 227 2 4 1 228 2 5 7 229 3 4 2 230 3 6 3 231 4 5 3 232 4 6 6 233 4 7 9 234 5 7 5 235 6 7 2 236 6 8 7 237 7 8 4 238 列印所有輸入資訊： 239 頂點資訊 240 A B C D E F G H I 241 矩陣資訊： 242 A B C D E F G H I 243 A 0 1 5655356553565535655356553565535 244 B 1 0 3 7 565535655356553565535 245 C 5 3 065535 1 7655356553565535 246 D65535 765535 0 265535 36553565535 247 E65535 5 1 2 0 3 6 965535 248 F6553565535 765535 3 065535 565535 249 G655356553565535 3 665535 0 2 7 250 H65535655356553565535 9 5 2 0 4 251 I655356553565535655356553565535 7 4 0 252 253 254 求最短路徑..... 255 列印各頂點最短路徑標記陣列值： 1 1 1 1 1 1 1 1 1 256 列印最短路徑陣列值： 0 1 4 7 5 8 10 12 16 257 列印最短路徑前驅陣列值： 0 0 1 4 2 4 3 6 7 258 列印V0到各個頂點最短路徑值以及路徑資訊： 259 V0~V1: 1 260 V0->V1 261 V0~V2: 4 262 V0->V1->V2 263 V0~V3: 7 264 V0->V1->V2->V4->V3 265 V0~V4: 5 266 V0->V1->V2->V4 267 V0~V5: 8 268 V0->V1->V2->V4->V5 269 V0~V6: 10 270 V0->V1->V2->V4->V3->V6 271 V0~V7: 12 272 V0->V1->V2->V4->V3->V6->V7 273 V0~V8: 16 274 V0->V1->V2->V4->V3->V6->V7->V8 275 */