图（有向图，无向图）的邻接矩阵表示C++实现(遍历，拓扑排序，最短路径，最小生成树) Implement of digraph and undigraph using adjacency matrix

本文实现了有向图，无向图的邻接矩阵表示，并且实现了从创建到销毁图的各种操作。

以及两种图的深度优先遍历，广度优先遍历，Dijkstra最短路径算法，Prim最小生成树算法，有向图的拓扑排序算法。

 

通过一个全局变量控制当前图为有向图还是无向图。

若为无向图，则生成的邻接矩阵是对称的，有向图则不对称。

可结合我的另一篇文章（图的邻接表表示）看。

PS: 等有时间了作详细的讲解。

#include <iostream>#include <climits>#include <sstream> #include <queue>using namespace std;const bool UNDIGRAPH = 0;struct Graph{string *vertexLabel;//the number of the labels is equal to vertexesint vertexes;int edges;int **AdjMat;bool *visited;//only for DFS,BFS,Dijkstraint *distance; //only for Dijkstraint *path;//only for Dijkstra};void BuildGraph(Graph *&graph, int n){if (graph == NULL){graph = new Graph;graph->vertexes = n;graph->edges = 0;graph->AdjMat = new int *[n];graph->vertexLabel = new string[n];graph->visited = new bool[n];graph->distance = new int[n];graph->path = new int[n];for (int i = 0; i < graph->vertexes; i++){stringstream ss;  ss<<"v" << i+1;  ss >> graph->vertexLabel[i];graph->visited[i] = false;graph->distance[i] = INT_MAX;graph->path[i] = -1;graph->AdjMat[i] = new int[n];if(UNDIGRAPH)memset(graph->AdjMat[i],0, n * sizeof(int));elsefor (int j = 0; j < graph->vertexes; j++){if(i == j)graph->AdjMat[i][j] = 0;elsegraph->AdjMat[i][j] = INT_MAX;}}}}void MakeEmpty(Graph *&graph){if(graph == NULL)return;delete []graph->vertexLabel;delete []graph->visited;delete []graph->distance;delete []graph->path;for (int i = 0; i < graph->vertexes; i++){delete []graph->AdjMat[i];}delete []graph->AdjMat;delete graph;}void AddEdge(Graph *graph,int v1, int v2, int weight){if (graph == NULL) return;if (v1 < 0 || v1 > graph->vertexes-1) return;if (v2 < 0 || v2 > graph->vertexes-1) return;if (v1 == v2) return; //no loop is allowedif(UNDIGRAPH){if (graph->AdjMat[v1][v2] == 0)//not exist,edges plus 1  graph->edges++;graph->AdjMat[v1][v2] = graph->AdjMat[v2][v1] = weight;}else{if (graph->AdjMat[v1][v2] == 0 || graph->AdjMat[v1][v2] == INT_MAX)//not exist,edges plus 1graph->edges++;graph->AdjMat[v1][v2] = weight;}}void RemoveEdge(Graph *graph, int v1, int v2){if (graph == NULL) return;if (v1 < 0 || v1 > graph->vertexes-1) return;if (v2 < 0 || v2 > graph->vertexes-1) return;if (v1 == v2) return; //no loop is allowedif (UNDIGRAPH){if (graph->AdjMat[v1][v2] == 0)//not exists,return  return;graph->AdjMat[v1][v2] = graph->AdjMat[v2][v1] = 0;  graph->edges--;  }else{if (graph->AdjMat[v1][v2] == 0 || graph->AdjMat[v1][v2] == INT_MAX)//not exists,returnreturn;graph->AdjMat[v1][v2] = INT_MAX;graph->edges--;}}int GetIndegree(Graph *graph, int v){if(graph == NULL) return -1;if(v < 0 || v > graph->vertexes -1) return -2;if(UNDIGRAPH) return -3;int degree = 0;for (int i = 0; i < graph->vertexes; i++){if(graph->AdjMat[i][v] != 0 && graph->AdjMat[i][v] != INT_MAX)degree++;}return degree;}int GetOutdegree(Graph *graph, int v){if(graph == NULL) return -1;if(v < 0 || v > graph->vertexes -1) return -2;if(UNDIGRAPH) return -3;int degree = 0;for (int i = 0; i < graph->vertexes; i++){if(graph->AdjMat[v][i] != 0 && graph->AdjMat[v][i] != INT_MAX)degree++;}return degree;}int GetDegree(Graph *graph, int v){if(graph == NULL) return -1;if(v < 0 || v > graph->vertexes -1) return -2;if(UNDIGRAPH){int degree = 0;  for (int i = 0; i < graph->vertexes; i++)  {  if(graph->AdjMat[v][i] != 0)  degree++;  }  return degree;  }elsereturn GetIndegree(graph,v) + GetOutdegree(graph,v);}void PrintGraph(Graph *graph){if(graph == NULL)return;cout << "Vertex: " << graph->vertexes <<"\n";cout << "Edge: " << graph->edges << "\n";for (int i = 0; i < graph->vertexes; i++){cout << "  "<< graph->vertexLabel[i];}cout << "\n";for (int i = 0; i < graph->vertexes; i++){for (int j = 0; j < graph->vertexes; j++){if(j == 0)cout << graph->vertexLabel[i] << " ";if(graph->AdjMat[i][j] == INT_MAX)cout << "~" << "   ";elsecout << graph->AdjMat[i][j] << "   ";}cout << "\n";}cout << "\n";}//depth first search (use stack or recursion)//DFS is similar to preorder traversal of treesvoid DFS(Graph *graph, int i){if (!graph->visited[i]){cout << graph->vertexLabel[i] << " ";graph->visited[i] = true;}for (int j = 0; j < graph->vertexes; j++){if (UNDIGRAPH){if (graph->AdjMat[i][j] != 0 && !graph->visited[j])DFS(graph,j);}else{if (graph->AdjMat[i][j] != INT_MAX && !graph->visited[j])DFS(graph,j);}}}void BeginDFS(Graph *graph){if(graph == NULL) return;cout << "DFS\n";for (int i = 0; i < graph->vertexes; i++)graph->visited[i] = false;for (int i = 0; i < graph->vertexes; i++)DFS(graph,i);}//breadth first search(use queue)//BFS is similar to leverorder traversal of trees//all of the vertexes will be searched once no matter how the digraph is constructedvoid BFS(Graph *graph){if(graph == NULL)return;cout << "BFS\n";memset(graph->visited,false,graph->vertexes * sizeof(bool));queue<int> QVertex;for (int i = 0; i < graph->vertexes; i++){if (!graph->visited[i]){QVertex.push(i);cout << graph->vertexLabel[i] << " ";graph->visited[i] = true;while(!QVertex.empty()){int vtxNO = QVertex.front();QVertex.pop();for (int j = 0; j < graph->vertexes; j++){if (UNDIGRAPH){if(!graph->visited[j] && graph->AdjMat[vtxNO][j]!=0){cout << graph->vertexLabel[j] << " ";graph->visited[j] = true;QVertex.push(j);}}else{if(!graph->visited[j] && graph->AdjMat[vtxNO][j]!=INT_MAX){cout << graph->vertexLabel[j] << " ";graph->visited[j] = true;QVertex.push(j);}}}}}}cout << "\n";}//after executing this function,the value of AdjMat changedvoid TopologicalSort(Graph *graph){if(UNDIGRAPH) return;if(graph == NULL) return;cout << "TopologicalSort"<<"\n";int counter = 0;queue <int> qVertex;for (int i = 0; i < graph->vertexes; i++){if(GetIndegree(graph,i) == 0)qVertex.push(i);}while (!qVertex.empty()){int vertexNO = qVertex.front();counter++;cout << graph->vertexLabel[vertexNO];if(counter != graph->vertexes)cout << " > ";qVertex.pop();for (int i = 0; i < graph->vertexes; i++){if(i == vertexNO) continue;if (GetIndegree(graph,i) != 0){graph->AdjMat[vertexNO][i] = INT_MAX;//indegree--if(GetIndegree(graph,i) == 0)qVertex.push(i);}}}cout << "\n";}void Dijkstra(Graph *graph, int v){if(graph == NULL) return;if(v < 0 || v > graph->vertexes-1) return;for (int i = 0; i < graph->vertexes; i++){graph->visited[i] = false;graph->distance[i] = INT_MAX;//can delete this line,as initialized in BuildGraphgraph->path[i] = -1;}graph->distance[v] = 0;//the rest are all INT_MAXwhile(1){int minDisInx = -1;int minDis = INT_MAX;for (int i = 0; i < graph->vertexes; i++){if(!graph->visited[i]){if(graph->distance[i] < minDis){minDis = graph->distance[i];minDisInx = i;}}}if(minDisInx == -1)//all visitedbreak;graph->visited[minDisInx] = true;for (int i = 0; i < graph->vertexes; i++){//unvisited and adjacent to current vertex//&& graph->AdjMat[minDisInx][i]!=0 is for undigraphif (!graph->visited[i] && graph->AdjMat[minDisInx][i]!=INT_MAX && graph->AdjMat[minDisInx][i]!=0){if (graph->distance[minDisInx] + graph->AdjMat[minDisInx][i] < graph->distance[i]){graph->distance[i] = graph->distance[minDisInx] + graph->AdjMat[minDisInx][i];graph->path[i] = minDisInx;cout << graph->vertexLabel[i] << " Updated to " << graph->distance[i] <<"\n";}}}}cout << "Vertex  Visited  Distance  Path\n";for (int i = 0; i < graph->vertexes; i++){cout << graph->vertexLabel[i]<< "";cout << graph->visited[i]<< "";cout << graph->distance[i]<< "";if(graph->path[i] == -1)cout << "NONE\n";elsecout << graph->vertexLabel[graph->path[i]]<< "\n";}}//almost for undigraphvoid Prim(Graph *graph, int v){if(graph == NULL) return;if(v < 0 || v > graph->vertexes-1) return;for (int i = 0; i < graph->vertexes; i++){graph->visited[i] = false;graph->distance[i] = INT_MAX;//can delete this line,as initialized in BuildGraphgraph->path[i] = -1;}graph->distance[v] = 0;//the rest are all INT_MAXwhile(1){int minDisInx = -1;int minDis = INT_MAX;for (int i = 0; i < graph->vertexes; i++){if(!graph->visited[i]){if(graph->distance[i] < minDis){minDis = graph->distance[i];minDisInx = i;}}}if(minDisInx == -1)//all visitedbreak;graph->visited[minDisInx] = true;for (int i = 0; i < graph->vertexes; i++){//unvisited and adjacent to current vertex//&& graph->AdjMat[minDisInx][i]!=0 is for undigraphif (!graph->visited[i] && graph->AdjMat[minDisInx][i]!=INT_MAX && graph->AdjMat[minDisInx][i]!=0){if (graph->AdjMat[minDisInx][i] < graph->distance[i]){graph->distance[i] = graph->AdjMat[minDisInx][i];graph->path[i] = minDisInx;cout << graph->vertexLabel[i] << " Updated to " << graph->distance[i] <<"\n";}}}}cout << "Vertex  Visited  Distance  Path\n";for (int i = 0; i < graph->vertexes; i++){cout << graph->vertexLabel[i]<< "";cout << graph->visited[i]<< "";cout << graph->distance[i]<< "";if(graph->path[i] == -1)cout << "NONE\n";elsecout << graph->vertexLabel[graph->path[i]]<< "\n";}}int main(){Graph *graph = NULL;BuildGraph(graph,7);PrintGraph(graph);//for simple test, 0 indexed/*AddEdge(graph,0,1,1);AddEdge(graph,0,2,1);AddEdge(graph,1,3,1);*///for TopologicalSort//0 indexed/*AddEdge(graph,0,1,1);AddEdge(graph,0,2,1);AddEdge(graph,0,3,1);AddEdge(graph,1,3,1);AddEdge(graph,1,4,1);AddEdge(graph,2,5,1);AddEdge(graph,3,2,1);AddEdge(graph,3,5,1);AddEdge(graph,3,6,1);AddEdge(graph,4,3,1);AddEdge(graph,4,6,1);AddEdge(graph,6,5,1);*///for Dijkstra(shortest path),Prim(minimum spanning tree)//0 indexedAddEdge(graph,0,1,2);  AddEdge(graph,0,3,1);  AddEdge(graph,1,3,3);  AddEdge(graph,1,4,10);  AddEdge(graph,2,0,4);  AddEdge(graph,2,5,5);  AddEdge(graph,3,2,2);AddEdge(graph,3,4,2);AddEdge(graph,3,5,8);  AddEdge(graph,3,6,4);  AddEdge(graph,4,6,6);  AddEdge(graph,6,5,1);PrintGraph(graph);BeginDFS(graph);cout << "\n";BFS(graph);for (int i = 0; i < graph->vertexes; i++){cout << "\n";Dijkstra(graph,i);}Prim(graph,0);TopologicalSort(graph);MakeEmpty(graph);return 0;}