图、 prim 和 kruskal
数据结构笔记目录 栈 https://hubojing.github.io/2017/11/14/%E6%A0%88/ 队列 https://hubojing.github.io/2017/11/12/%E9%98%9F%E5%88%97/ 线性表 https://hubojing.github.io/2019/06/12/%E7%BA%BF%E6%80%A7%E8%A1%A8/ 树 https://hubojing.github.io/2017/07/23/%E6%A0%91/
图的基本操作和遍历 Node.h 1 2 3 4 5 6 7 8 9 10 11 12 #ifndef NODE_H #define NODE_H class Node { public : Node (char data = 0 ); char m_cData; bool m_bIsVisited; }; #endif
Node.cpp 1 2 3 4 5 6 7 #include "Node.h" Node::Node (char data) { m_cData = data; m_bIsVisited = false ; }
CMap.h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 #include "Node.h" #include <vector> using namespace std;class CMap { public : CMap (int capacity); ~CMap (); bool addNode (Node *pNode) ; void resetNode () ; bool setValueToMatrixForDirectedGraph (int row, int col, int val = 1 ) ; bool setValueToMatrixForUndirectedGraph (int row, int col, int val = 1 ) ; void printMatrix () ; void depthFirstTraverse (int nodeIndex) ; void breadthFirstTraverse (int nodeIndex) ; private : bool getValueFromMatrix (int row, int col, int &val) ; void breadthFirstTraverseImpl (vector<int > preVec) ; private : int m_iCapacity; int m_iNodeCount; Node *m_pNodeArray; int *m_pMatrix; };
CMap.cpp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 #include "CMap.h" #include <iostream> #include <vector> using namespace std;CMap::CMap (int capacity) { m_iCapacity = capacity; m_iNodeCount = 0 ; m_pNodeArray = new Node[m_iCapacity]; m_pMatrix = new int [m_iCapacity * m_iCapacity]; memset (m_pMatrix, 0 , m_iCapacity*m_iCapacity * sizeof (int )); } CMap::~CMap () { delete []m_pNodeArray; delete []m_pMatrix; } bool CMap::addNode (Node *pNode) { if (pNode == NULL ) { return false ; } m_pNodeArray[m_iNodeCount].m_cData = pNode->m_cData; m_iNodeCount++; return true ; } void CMap::resetNode () { for (int i = 0 ; i < m_iNodeCount; ++i) { m_pNodeArray[i].m_bIsVisited = false ; } } bool CMap::setValueToMatrixForDirectedGraph (int row, int col, int val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } m_pMatrix[row * m_iCapacity + col] = val; return true ; } bool CMap::setValueToMatrixForUndirectedGraph (int row, int col, int val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } m_pMatrix[row * m_iCapacity + col] = val; m_pMatrix[col * m_iCapacity + row] = val; return true ; } void CMap::printMatrix () { for (int i = 0 ; i < m_iCapacity; ++i) { for (int j = 0 ; j < m_iCapacity; ++j) { cout << m_pMatrix[i * m_iCapacity + j] << " " ; } cout << endl; } } bool CMap::getValueFromMatrix (int row, int col, int &val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } val = m_pMatrix[row * m_iCapacity + col]; return true ; } void CMap::depthFirstTraverse (int nodeIndex) { int value = 0 ; cout << m_pNodeArray[nodeIndex].m_cData << " " ; m_pNodeArray[nodeIndex].m_bIsVisited = true ; for (int i = 0 ; i < m_iCapacity; ++i) { getValueFromMatrix (nodeIndex, i, value); if (value == 1 ) { if (m_pNodeArray[i].m_bIsVisited) { continue ; } else { depthFirstTraverse (i); } } else { continue ; } } } void CMap::breadthFirstTraverse (int nodeIndex) { cout << m_pNodeArray[nodeIndex].m_cData << " " ; m_pNodeArray[nodeIndex].m_bIsVisited = true ; vector<int > curVec; curVec.push_back (nodeIndex); breadthFirstTraverseImpl (curVec); } void CMap::breadthFirstTraverseImpl (vector<int > preVec) { int value = 0 ; vector<int > curVec; for (int i = 0 ; (int )i < preVec.size (); ++i) { for (int j = 0 ; j < m_iCapacity; ++j) { getValueFromMatrix (preVec[i], j, value); if (value != 0 ) { if (m_pNodeArray[j].m_bIsVisited) { continue ; } else { cout << m_pNodeArray[j].m_cData << " " ; m_pNodeArray[j].m_bIsVisited = true ; curVec.push_back (j); } } } } if (curVec.size () == 0 ) { return ; } else { breadthFirstTraverseImpl (curVec); } }
demo.cpp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 #include <iostream> #include <stdlib.h> #include "CMap.h" using namespace std;int main () { CMap *pMap = new CMap (8 ); Node *pNodeA = new Node ('A' ); Node *pNodeB = new Node ('B' ); Node *pNodeC = new Node ('C' ); Node *pNodeD = new Node ('D' ); Node *pNodeE = new Node ('E' ); Node *pNodeF = new Node ('F' ); Node *pNodeG = new Node ('G' ); Node *pNodeH = new Node ('H' ); pMap->addNode (pNodeA); pMap->addNode (pNodeB); pMap->addNode (pNodeC); pMap->addNode (pNodeD); pMap->addNode (pNodeE); pMap->addNode (pNodeF); pMap->addNode (pNodeG); pMap->addNode (pNodeH); pMap->setValueToMatrixForUndirectedGraph (0 , 1 ); pMap->setValueToMatrixForUndirectedGraph (0 , 3 ); pMap->setValueToMatrixForUndirectedGraph (1 , 2 ); pMap->setValueToMatrixForUndirectedGraph (1 , 5 ); pMap->setValueToMatrixForUndirectedGraph (3 , 6 ); pMap->setValueToMatrixForUndirectedGraph (3 , 7 ); pMap->setValueToMatrixForUndirectedGraph (6 , 7 ); pMap->setValueToMatrixForUndirectedGraph (2 , 4 ); pMap->setValueToMatrixForUndirectedGraph (4 , 5 ); pMap->printMatrix (); cout << endl; pMap->depthFirstTraverse (0 ); cout << endl; pMap->resetNode (); pMap->breadthFirstTraverse (0 ); cout << endl; return 0 ; }
输出:1 2 3 4 5 6 7 8 9 10 11 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 A B C E F D G H A B D C F G H E
最小生成树算法 普利姆算法 Edge.h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #ifndef EDGE_H #define EDGE_H class Edge { public : Edge (int nodeIndexA = 0 , int nodeIndexB = 0 , int weightValue = 0 ); int m_iNodeIndexA; int m_iNodeIndexB; int m_iWeightValue; bool m_bSelected; }; #endif
Edge.cpp 1 2 3 4 5 6 7 8 9 #include "Edge.h" Edge::Edge (int nodeIndexA, int nodeIndexB, int weightValue) { m_iNodeIndexA = nodeIndexA; m_iNodeIndexB = nodeIndexB; m_iWeightValue = weightValue; m_bSelected = false ; }
Node.h 1 2 3 4 5 6 7 8 9 10 11 12 #ifndef NODE_H #define NODE_H class Node { public : Node (char data = 0 ); char m_cData; bool m_bIsVisited; }; #endif
Node.cpp 1 2 3 4 5 6 7 #include "Node.h" Node::Node (char data) { m_cData = data; m_bIsVisited = false ; }
CMap.h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 #include "Node.h" #include "Edge.h" #include <vector> using namespace std;class CMap { public : CMap (int capacity); ~CMap (); bool addNode (Node *pNode) ; void resetNode () ; bool setValueToMatrixForDirectedGraph (int row, int col, int val = 1 ) ; bool setValueToMatrixForUndirectedGraph (int row, int col, int val = 1 ) ; void printMatrix () ; void depthFirstTraverse (int nodeIndex) ; void breadthFirstTraverse (int nodeIndex) ; void primTree (int nodeIndex) ; private : bool getValueFromMatrix (int row, int col, int &val) ; void breadthFirstTraverseImpl (vector<int > preVec) ; int getMinEdge (vector<Edge> edgeVec) ; private : int m_iCapacity; int m_iNodeCount; Node *m_pNodeArray; int *m_pMatrix; Edge *m_pEdge; };
CMap.cpp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 #include "CMap.h" #include <iostream> #include <vector> using namespace std;CMap::CMap (int capacity) { m_iCapacity = capacity; m_iNodeCount = 0 ; m_pNodeArray = new Node[m_iCapacity]; m_pMatrix = new int [m_iCapacity * m_iCapacity]; memset (m_pMatrix, 0 , m_iCapacity*m_iCapacity * sizeof (int )); m_pEdge = new Edge[m_iCapacity - 1 ]; } CMap::~CMap () { delete []m_pNodeArray; delete []m_pMatrix; } bool CMap::addNode (Node *pNode) { if (pNode == NULL ) { return false ; } m_pNodeArray[m_iNodeCount].m_cData = pNode->m_cData; m_iNodeCount++; return true ; } void CMap::resetNode () { for (int i = 0 ; i < m_iNodeCount; ++i) { m_pNodeArray[i].m_bIsVisited = false ; } } bool CMap::setValueToMatrixForDirectedGraph (int row, int col, int val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } m_pMatrix[row * m_iCapacity + col] = val; return true ; } bool CMap::setValueToMatrixForUndirectedGraph (int row, int col, int val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } m_pMatrix[row * m_iCapacity + col] = val; m_pMatrix[col * m_iCapacity + row] = val; return true ; } void CMap::printMatrix () { for (int i = 0 ; i < m_iCapacity; ++i) { for (int j = 0 ; j < m_iCapacity; ++j) { cout << m_pMatrix[i * m_iCapacity + j] << " " ; } cout << endl; } } bool CMap::getValueFromMatrix (int row, int col, int &val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } val = m_pMatrix[row * m_iCapacity + col]; return true ; } void CMap::depthFirstTraverse (int nodeIndex) { int value = 0 ; cout << m_pNodeArray[nodeIndex].m_cData << " " ; m_pNodeArray[nodeIndex].m_bIsVisited = true ; for (int i = 0 ; i < m_iCapacity; ++i) { getValueFromMatrix (nodeIndex, i, value); if (value == 1 ) { if (m_pNodeArray[i].m_bIsVisited) { continue ; } else { depthFirstTraverse (i); } } else { continue ; } } } void CMap::breadthFirstTraverse (int nodeIndex) { cout << m_pNodeArray[nodeIndex].m_cData << " " ; m_pNodeArray[nodeIndex].m_bIsVisited = true ; vector<int > curVec; curVec.push_back (nodeIndex); breadthFirstTraverseImpl (curVec); } void CMap::breadthFirstTraverseImpl (vector<int > preVec) { int value = 0 ; vector<int > curVec; for (int i = 0 ; (int )i < preVec.size (); ++i) { for (int j = 0 ; j < m_iCapacity; ++j) { getValueFromMatrix (preVec[i], j, value); if (value != 0 ) { if (m_pNodeArray[j].m_bIsVisited) { continue ; } else { cout << m_pNodeArray[j].m_cData << " " ; m_pNodeArray[j].m_bIsVisited = true ; curVec.push_back (j); } } } } if (curVec.size () == 0 ) { return ; } else { breadthFirstTraverseImpl (curVec); } } void CMap::primTree (int nodeIndex) { int value = 0 ; int edgeCount = 0 ; vector<int > nodeVec; vector<Edge> edgeVec; cout << m_pNodeArray[nodeIndex].m_cData << endl; nodeVec.push_back (nodeIndex); m_pNodeArray[nodeIndex].m_bIsVisited = true ; while (edgeCount < m_iCapacity - 1 ) { int temp = nodeVec.back (); for (int i = 0 ; i < m_iCapacity; ++i) { getValueFromMatrix (temp, i, value); if (value != 0 ) { if (m_pNodeArray[i].m_bIsVisited) { continue ; } else { Edge edge (temp, i, value); edgeVec.push_back (edge); } } } int edgeIndex = getMinEdge (edgeVec); edgeVec[edgeIndex].m_bSelected = true ; cout << edgeVec[edgeIndex].m_iNodeIndexA << "---" << edgeVec[edgeIndex].m_iNodeIndexB << " " ; cout << edgeVec[edgeIndex].m_iWeightValue << endl; m_pEdge[edgeCount] = edgeVec[edgeIndex]; edgeCount++; int nextNodeIndex = edgeVec[edgeIndex].m_iNodeIndexB; nodeVec.push_back (nextNodeIndex); m_pNodeArray[nextNodeIndex].m_bIsVisited = true ; cout << m_pNodeArray[nextNodeIndex].m_cData << endl; } } int CMap::getMinEdge (vector<Edge> edgeVec) { int minWeight = 0 ; int edgeIndex = 0 ; int i = 0 ; for (; i < edgeVec.size (); ++i) { if (!edgeVec[i].m_bSelected) { minWeight = edgeVec[i].m_iWeightValue; edgeIndex = i; break ; } } if (minWeight == 0 ) { return -1 ; } for (; i < edgeVec.size (); ++i) { if (edgeVec[i].m_bSelected) { continue ; } else { if (minWeight > edgeVec[i].m_iWeightValue) { minWeight = edgeVec[i].m_iWeightValue; edgeIndex = i; } } } return edgeIndex; }
demo.cpp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 #include <iostream> #include <stdlib.h> #include "CMap.h" using namespace std;int main () { CMap *pMap = new CMap (6 ); Node *pNodeA = new Node ('A' ); Node *pNodeB = new Node ('B' ); Node *pNodeC = new Node ('C' ); Node *pNodeD = new Node ('D' ); Node *pNodeE = new Node ('E' ); Node *pNodeF = new Node ('F' ); pMap->addNode (pNodeA); pMap->addNode (pNodeB); pMap->addNode (pNodeC); pMap->addNode (pNodeD); pMap->addNode (pNodeE); pMap->addNode (pNodeF); pMap->setValueToMatrixForUndirectedGraph (0 , 1 , 6 ); pMap->setValueToMatrixForUndirectedGraph (0 , 4 , 5 ); pMap->setValueToMatrixForUndirectedGraph (0 , 5 , 1 ); pMap->setValueToMatrixForUndirectedGraph (1 , 2 , 3 ); pMap->setValueToMatrixForUndirectedGraph (1 , 5 , 2 ); pMap->setValueToMatrixForUndirectedGraph (2 , 5 , 8 ); pMap->setValueToMatrixForUndirectedGraph (2 , 3 , 7 ); pMap->setValueToMatrixForUndirectedGraph (3 , 5 , 4 ); pMap->setValueToMatrixForUndirectedGraph (3 , 4 , 2 ); pMap->setValueToMatrixForUndirectedGraph (4 , 5 , 9 ); pMap->primTree (0 ); return 0 ; }
输出:1 2 3 4 5 6 7 8 9 10 11 A 0---5 1 F 5---1 2 B 1---2 3 C 5---3 4 D 3---4 2 E
克鲁斯卡尔算法 Node.h 1 2 3 4 5 6 7 8 9 10 11 12 #ifndef NODE_H #define NODE_H class Node { public : Node (char data = 0 ); char m_cData; bool m_bIsVisited; }; #endif
Node.cpp 1 2 3 4 5 6 7 #include "Node.h" Node::Node (char data) { m_cData = data; m_bIsVisited = false ; }
Edge.h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #ifndef EDGE_H #define EDGE_H class Edge { public : Edge (int nodeIndexA = 0 , int nodeIndexB = 0 , int weightValue = 0 ); int m_iNodeIndexA; int m_iNodeIndexB; int m_iWeightValue; bool m_bSelected; }; #endif
Edge.cpp 1 2 3 4 5 6 7 8 9 #include "Edge.h" Edge::Edge (int nodeIndexA, int nodeIndexB, int weightValue) { m_iNodeIndexA = nodeIndexA; m_iNodeIndexB = nodeIndexB; m_iWeightValue = weightValue; m_bSelected = false ; }
CMap.h 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 #include "Node.h" #include "Edge.h" #include <vector> using namespace std;class CMap { public : CMap (int capacity); ~CMap (); bool addNode (Node *pNode) ; void resetNode () ; bool setValueToMatrixForDirectedGraph (int row, int col, int val = 1 ) ; bool setValueToMatrixForUndirectedGraph (int row, int col, int val = 1 ) ; void printMatrix () ; void depthFirstTraverse (int nodeIndex) ; void breadthFirstTraverse (int nodeIndex) ; void primTree (int nodeIndex) ; void kruskalTree () ; private : bool getValueFromMatrix (int row, int col, int &val) ; void breadthFirstTraverseImpl (vector<int > preVec) ; int getMinEdge (vector<Edge> edgeVec) ; bool isInSet (vector<int > nodeSet, int target) ; void mergeNodeSet (vector<int > &nodeSetA, vector<int > nodeSetB) ; private : int m_iCapacity; int m_iNodeCount; Node *m_pNodeArray; int *m_pMatrix; Edge *m_pEdge; };
CMap.cpp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 #include "CMap.h" #include <iostream> #include <vector> using namespace std;CMap::CMap (int capacity) { m_iCapacity = capacity; m_iNodeCount = 0 ; m_pNodeArray = new Node[m_iCapacity]; m_pMatrix = new int [m_iCapacity * m_iCapacity]; memset (m_pMatrix, 0 , m_iCapacity*m_iCapacity * sizeof (int )); m_pEdge = new Edge[m_iCapacity - 1 ]; } CMap::~CMap () { delete []m_pNodeArray; delete []m_pMatrix; delete []m_pEdge; } bool CMap::addNode (Node *pNode) { if (pNode == NULL ) { return false ; } m_pNodeArray[m_iNodeCount].m_cData = pNode->m_cData; m_iNodeCount++; return true ; } void CMap::resetNode () { for (int i = 0 ; i < m_iNodeCount; ++i) { m_pNodeArray[i].m_bIsVisited = false ; } } bool CMap::setValueToMatrixForDirectedGraph (int row, int col, int val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } m_pMatrix[row * m_iCapacity + col] = val; return true ; } bool CMap::setValueToMatrixForUndirectedGraph (int row, int col, int val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } m_pMatrix[row * m_iCapacity + col] = val; m_pMatrix[col * m_iCapacity + row] = val; return true ; } void CMap::printMatrix () { for (int i = 0 ; i < m_iCapacity; ++i) { for (int j = 0 ; j < m_iCapacity; ++j) { cout << m_pMatrix[i * m_iCapacity + j] << " " ; } cout << endl; } } bool CMap::getValueFromMatrix (int row, int col, int &val) { if (row < 0 || row >= m_iCapacity) { return false ; } if (col < 0 || col >= m_iCapacity) { return false ; } val = m_pMatrix[row * m_iCapacity + col]; return true ; } void CMap::depthFirstTraverse (int nodeIndex) { int value = 0 ; cout << m_pNodeArray[nodeIndex].m_cData << " " ; m_pNodeArray[nodeIndex].m_bIsVisited = true ; for (int i = 0 ; i < m_iCapacity; ++i) { getValueFromMatrix (nodeIndex, i, value); if (value == 1 ) { if (m_pNodeArray[i].m_bIsVisited) { continue ; } else { depthFirstTraverse (i); } } else { continue ; } } } void CMap::breadthFirstTraverse (int nodeIndex) { cout << m_pNodeArray[nodeIndex].m_cData << " " ; m_pNodeArray[nodeIndex].m_bIsVisited = true ; vector<int > curVec; curVec.push_back (nodeIndex); breadthFirstTraverseImpl (curVec); } void CMap::breadthFirstTraverseImpl (vector<int > preVec) { int value = 0 ; vector<int > curVec; for (int i = 0 ; (int )i < preVec.size (); ++i) { for (int j = 0 ; j < m_iCapacity; ++j) { getValueFromMatrix (preVec[i], j, value); if (value != 0 ) { if (m_pNodeArray[j].m_bIsVisited) { continue ; } else { cout << m_pNodeArray[j].m_cData << " " ; m_pNodeArray[j].m_bIsVisited = true ; curVec.push_back (j); } } } } if (curVec.size () == 0 ) { return ; } else { breadthFirstTraverseImpl (curVec); } } void CMap::primTree (int nodeIndex) { int value = 0 ; int edgeCount = 0 ; vector<int > nodeVec; vector<Edge> edgeVec; cout << m_pNodeArray[nodeIndex].m_cData << endl; nodeVec.push_back (nodeIndex); m_pNodeArray[nodeIndex].m_bIsVisited = true ; while (edgeCount < m_iCapacity - 1 ) { int temp = nodeVec.back (); for (int i = 0 ; i < m_iCapacity; ++i) { getValueFromMatrix (temp, i, value); if (value != 0 ) { if (m_pNodeArray[i].m_bIsVisited) { continue ; } else { Edge edge (temp, i, value); edgeVec.push_back (edge); } } } int edgeIndex = getMinEdge (edgeVec); edgeVec[edgeIndex].m_bSelected = true ; cout << edgeVec[edgeIndex].m_iNodeIndexA << "---" << edgeVec[edgeIndex].m_iNodeIndexB << " " ; cout << edgeVec[edgeIndex].m_iWeightValue << endl; m_pEdge[edgeCount] = edgeVec[edgeIndex]; edgeCount++; int nextNodeIndex = edgeVec[edgeIndex].m_iNodeIndexB; nodeVec.push_back (nextNodeIndex); m_pNodeArray[nextNodeIndex].m_bIsVisited = true ; cout << m_pNodeArray[nextNodeIndex].m_cData << endl; } } int CMap::getMinEdge (vector<Edge> edgeVec) { int minWeight = 0 ; int edgeIndex = 0 ; int i = 0 ; for (; i < edgeVec.size (); ++i) { if (!edgeVec[i].m_bSelected) { minWeight = edgeVec[i].m_iWeightValue; edgeIndex = i; break ; } } if (minWeight == 0 ) { return -1 ; } for (; i < edgeVec.size (); ++i) { if (edgeVec[i].m_bSelected) { continue ; } else { if (minWeight > edgeVec[i].m_iWeightValue) { minWeight = edgeVec[i].m_iWeightValue; edgeIndex = i; } } } return edgeIndex; } void CMap::kruskalTree () { int value = 0 ; int edgeCount = 0 ; vector<vector<int >> nodeSets; vector<Edge> edgeVec; for (int i = 0 ; i < m_iCapacity; ++i) { for (int j = i + 1 ; j < m_iCapacity; ++j) { getValueFromMatrix (i, j, value); if (value != 0 ) { Edge edge (i, j, value) ; edgeVec.push_back (edge); } } } while (edgeCount < m_iCapacity - 1 ) { int minEdgeIndex = getMinEdge (edgeVec); edgeVec[minEdgeIndex].m_bSelected = true ; int nodeAIndex = edgeVec[minEdgeIndex].m_iNodeIndexA; int nodeBIndex = edgeVec[minEdgeIndex].m_iNodeIndexB; bool nodeAIsInSet = false ; bool nodeBIsInSet = false ; int nodeAInSetLabel = -1 ; int nodeBInSetLabel = -1 ; for (int i = 0 ; i < nodeSets.size (); ++i) { nodeAIsInSet = isInSet (nodeSets[i], nodeAIndex); if (nodeAIsInSet) { nodeAIsInSet = i; } } for (int i = 0 ; i < nodeSets.size (); ++i) { nodeBIsInSet = isInSet (nodeSets[i], nodeBIndex); if (nodeBIsInSet) { nodeBIsInSet = i; } } if (nodeAInSetLabel == -1 && nodeBInSetLabel == -1 ) { vector<int > vec; vec.push_back (nodeAIndex); vec.push_back (nodeBIndex); nodeSets.push_back (vec); } else if (nodeAInSetLabel == -1 && nodeBInSetLabel != -1 ) { nodeSets[nodeBInSetLabel].push_back (nodeAIndex); } else if (nodeAInSetLabel != -1 && nodeBInSetLabel == -1 ) { nodeSets[nodeBInSetLabel].push_back (nodeBIndex); } else if (nodeAInSetLabel != -1 && nodeBInSetLabel != -1 && nodeAInSetLabel != nodeBInSetLabel) { mergeNodeSet (nodeSets[nodeAInSetLabel], nodeSets[nodeBInSetLabel]); for (int i = 0 ; i < (int )nodeSets.size () - 1 ; ++i) { nodeSets[i] = nodeSets[i + 1 ]; } } else if (nodeAInSetLabel != -1 && nodeBInSetLabel != -1 && nodeAInSetLabel == nodeBInSetLabel) { continue ; } m_pEdge[edgeCount] = edgeVec[minEdgeIndex]; edgeCount++; cout << edgeVec[minEdgeIndex].m_iNodeIndexA << "---" << edgeVec[minEdgeIndex].m_iNodeIndexB << " " ; cout << edgeVec[minEdgeIndex].m_iWeightValue << endl; } } bool CMap::isInSet (vector<int > nodeSet, int target) { for (int i = 0 ; i < nodeSet.size (); ++i) { if (nodeSet[i] == target) { return true ; } } return false ; } void CMap::mergeNodeSet (vector<int > &nodeSetA, vector<int > nodeSetB) { for (int i = 0 ; i < nodeSetB.size (); ++i) { nodeSetA.push_back (nodeSetB[i]); } }
demo.cpp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 #include <iostream> #include <stdlib.h> #include "CMap.h" using namespace std;int main () { CMap *pMap = new CMap (6 ); Node *pNodeA = new Node ('A' ); Node *pNodeB = new Node ('B' ); Node *pNodeC = new Node ('C' ); Node *pNodeD = new Node ('D' ); Node *pNodeE = new Node ('E' ); Node *pNodeF = new Node ('F' ); pMap->addNode (pNodeA); pMap->addNode (pNodeB); pMap->addNode (pNodeC); pMap->addNode (pNodeD); pMap->addNode (pNodeE); pMap->addNode (pNodeF); pMap->setValueToMatrixForUndirectedGraph (0 , 1 , 6 ); pMap->setValueToMatrixForUndirectedGraph (0 , 4 , 5 ); pMap->setValueToMatrixForUndirectedGraph (0 , 5 , 1 ); pMap->setValueToMatrixForUndirectedGraph (1 , 2 , 3 ); pMap->setValueToMatrixForUndirectedGraph (1 , 5 , 2 ); pMap->setValueToMatrixForUndirectedGraph (2 , 5 , 8 ); pMap->setValueToMatrixForUndirectedGraph (2 , 3 , 7 ); pMap->setValueToMatrixForUndirectedGraph (3 , 5 , 4 ); pMap->setValueToMatrixForUndirectedGraph (3 , 4 , 2 ); pMap->setValueToMatrixForUndirectedGraph (4 , 5 , 9 ); pMap->kruskalTree (); return 0 ; }
输出:1 2 3 4 5 0---5 1 1---5 2 3---4 2 1---2 3 3---5 4