Kruskal算法：使用并查集求最小生成树，引入parent数组
1 #include <iostream> 2 #include <vector> 3 #include <queue> 4 #include <string> 5 #include <climits> 6 7 using namespace std; 8 9 struct EdgeNode 10 { 11 int src; 12 int dest; 13 int weight; 14 //自定义优先级：weight小的优先 15 friend bool operator<(EdgeNode a, EdgeNode b) { 16 return a.weight > b.weight; 17 } 18 }; 19 20 template<class T> 21 class Graph 22 { 23 public: 24 Graph(){} 25 Graph(int * vertexArray, T * nameOfVertex, int numberOfVertex); 26 void KruskalMST(); 27 int FindSet(int index); //查找集 28 void UnionSet(int vertexFrom,int vertexTo); //合并集 29 private: 30 int vertexNum, arcNum; 31 vector<vector<int>>adjacencyMatrix; //邻接矩阵.大小不一定够 32 vector<EdgeNode>MSTArray; //存放最小生成树的边集 33 vector<int>parent; 34 priority_queue<EdgeNode>queue; //优先级队列，对边集按边上权值排序 35 vector<string>vertexName; //顶点名字 36 }; 37 38 39 int main() 40 { 41 const int numofVertex = 7; 42 int cost[numofVertex][numofVertex] = { 43 { INT_MAX, 12 , 5 , 11 ,INT_MAX , INT_MAX ,INT_MAX }, 44 { 12, INT_MAX , INT_MAX ,INT_MAX , 33 , INT_MAX ,INT_MAX }, 45 { 5, INT_MAX , INT_MAX , 21 ,INT_MAX , 19 ,INT_MAX }, 46 { 11, INT_MAX , 21 ,INT_MAX , 28 , 8 ,INT_MAX }, 47 { INT_MAX, 33, INT_MAX , 28 ,INT_MAX , INT_MAX , 6 }, 48 { INT_MAX, INT_MAX , 19 , 8 ,INT_MAX , INT_MAX , 16 }, 49 { INT_MAX, INT_MAX , INT_MAX ,INT_MAX , 6 , 16 ,INT_MAX } 50 }; 51 //初始化各顶点 52 string verName[numofVertex] = { "A","B","C","D","E","F","G" }; 53 Graph<string>g(*cost, verName, numofVertex); 54 55 cout << "Kruskal算法执行结果：" << endl; 56 try { 57 g.KruskalMST(); 58 } 59 catch (...) { 60 cout << "算法执行失败" << endl; 61 } 62 system("pause"); 63 return 0; 64 } 65 66 template<class T> 67 Graph<T>::Graph(int * vertexArray, T * nameOfVertex, int numberOfVertex) 68 { 69 vertexNum = numberOfVertex; //顶点数 70 arcNum = 0; 71 for (int i = 0; i < vertexNum; i++) 72 { 73 parent.push_back(i); //将每个数组元素设置为顶点的编号，表示每一个顶点自成一个连通分支 74 vertexName.push_back(nameOfVertex[i]); 75 } 76 //分配所需空间 77 adjacencyMatrix.resize(vertexNum, vector<int>(vertexNum)); 78 for (int i = 0; i < vertexNum; i++) 79 for (int j = 0; j < vertexNum; j++) 80 adjacencyMatrix[i][j] = *(vertexArray + i*vertexNum + j); 81 //初始化邻接矩阵 82 EdgeNode tempEdgeNode; 83 for(int i=0; i<vertexNum; i++) 84 for (int j = 0; j < vertexNum; j++) 85 { 86 if (adjacencyMatrix[i][j] < INT_MAX) 87 { 88 tempEdgeNode.src = i; 89 tempEdgeNode.dest = j; 90 tempEdgeNode.weight = adjacencyMatrix[i][j]; 91 queue.push(tempEdgeNode); //按权值排序的边集 92 arcNum++; 93 } 94 } 95 } 96 97 template<class T> 98 void Graph<T>::KruskalMST() 99 { 100 EdgeNode tempEdgeNode; 101 while (!queue.empty()) { 102 tempEdgeNode = queue.top(); 103 queue.pop(); 104 //边的两个端点不是来自同一连通分量，加入待求集合 105 if (FindSet(tempEdgeNode.src) != FindSet(tempEdgeNode.dest)) 106 { 107 MSTArray.push_back(tempEdgeNode); 108 UnionSet(tempEdgeNode.src, tempEdgeNode.dest); 109 } 110 } 111 for (int i = 0; i < MSTArray.size(); i++) 112 cout << vertexName[MSTArray[i].src] << "----" << vertexName[MSTArray[i].dest] << " "; 113 cout << endl; 114 } 115 116 template<class T> 117 int Graph<T>::FindSet(int index) 118 { 119 if (index == parent[index]) 120 return index; 121 else 122 return FindSet(parent[index]); 123 } 124 125 template<class T> 126 void Graph<T>::UnionSet(int vertexFrom, int vertexTo) 127 { 128 vertexFrom = FindSet(vertexFrom); 129 vertexTo = FindSet(vertexTo); 130 if (vertexFrom != vertexTo) 131 parent[vertexFrom] = vertexTo; //顶点合并到同一连通分量 132 }
parent数组：
1，FindSet函数中判断一个元素所属集合
2，UnionSet函数中合并两个元素各自所属的集合