Kruskal算法的C++语言程序

Kruskal算法是有关图的最小生成树的算法。Kruskal算法是两个经典的最小生成树算法之一，另外一个是Prim算法。

程序来源：Minimum Spanning Tree using Krushkal’s Algorithm。

百度百科：Kruskal算法。

维基百科：Kruskal's Algorithm。

C＋+语言程序：

/* Krushkal's Algorithm to find minimum spanning tree by TheCodersPortal */
#include <iostream>
#include <map>
using namespace std;/* Structure of a Disjoint-Set node */
typedef struct dset
{char data;int rank;struct dset* parent;
}dset;
/* To count the number of disjiont sets present at a time */
int count=0;/* Map is used to get the address of the node by its data */
map <char,dset*> mymap;/* MakeSet function is responsible for creating a disjoint-set whose only member is data,initially the rank is 0 and it is the representative of itself */
void MakeSet(char data)
{dset* node=new dset;node->data=data;mymap[data]=node;node->rank=0;node->parent=node;count++;
}/* FindSetUtil takes input to the pointer to the node and return the pointer tothe representative of that node. A Heuristic is used here, path compressionwhich means that all the nodes on the find path point directly to the root */
dset* FindSetUtil(dset* node)
{if(node!=node->parent)node->parent=FindSetUtil(node->parent);return node->parent;
}/*FindSet function is used to find the node using the data and pass this node to FindSetUtil*/
char FindSet(char x)
{dset* node=mymap[x];node=FindSetUtil(node);return node->data;
}/*isconnected checks whether the two elements of the set are connected or not */
bool isconnected(char x,char y)
{return (FindSet(x)==FindSet(y));
}/* LinkSet is responsible for union of two disjoint set according to a Heuristics, Union by Rank */
void LinkSet(char x,char y)
{if(isconnected(x,y))return;dset* node1=mymap[x];dset* node2=mymap[y];if(node1->rank>node2->rank)node2->parent=node1;elsenode1->parent=node2;if(node1->rank==node2->rank){node1->rank=node1->rank+1;}count--;
}/* UnionSet calls the LinkSet function with arguments as FindSet(x),FindSet(y) */
void UnionSet(char x,char y)
{LinkSet(FindSet(x),FindSet(y));
}/* freeset is used to free the memory allocated during the run-time */
void freeset(char arr[],int n)
{for(int i=0;i<n;i++){dset* node=mymap[arr[i]];delete node;}
}void QuickSort(int array[],int low,int high,char edgein[],char edgeout[])
{int i=low,j=high;/* Here we are taking pivot as mid element */int pivot=array[(low+high)/2];/* Partitioning the array */while(i<=j){while(array[i]<pivot)i++;while(array[j]>pivot)j--;if (i<=j){/* Swapping of elements at ith index and jth index */int temp = array[i];array[i] = array[j];array[j] = temp;char tmp=edgein[i];edgein[i]=edgein[j];edgein[j]=tmp;tmp=edgeout[i];edgeout[i]=edgeout[j];edgeout[j]=tmp;i++;j--;}}/* Recursion */if (i<high)QuickSort(array, i, high,edgein,edgeout);if (j>low)QuickSort(array, low, j,edgein, edgeout);}/* MSTKrushkal is the function which is used to find minimum spanning treeusing Krushkal'sAlgorithm */
void MSTKrushkal(char vertices[],char edgein[],char edgeout[],int weight[],int n,int m)
{//int n=sizeof(vertices)/sizeof(vertices[0]);for(int i=0;i<n;i++){MakeSet(vertices[i]);}/*Sorting of edges in non-decreasing order of their weights */QuickSort(weight,0,m-1,edgein,edgeout);int A=0;cout<<"Minimum spanning tree containing edges"<<endl;for(int i=0;i<9;i++){/* if adding the edge result in cycle, ignore the edge */if(isconnected(edgein[i],edgeout[i]))continue;/* Add the edge to the minimum spanning tree */UnionSet(edgein[i],edgeout[i]);A+=weight[i];cout<<edgein[i]<<"--"<<edgeout[i]<<endl;}cout<<"Total weight = "<<A<<endl;freeset(vertices,n);
}/* Driver program to test the above functions */
int main()
{/* vertices array contains all the vertices of the graph */char vertices[]={'A','B','C','D','E','F'};/* edgein,edgeout and weight array indicates that there is an edgebetween vertices edgein[i] and edgeout[i] having weight weight[i] */char edgein[]={'A','A','A','B','B','C','C','D','D'};char edgeout[]={'B','D','C','D','E','D','F','E','F'};int weight[]={6,5,3,8,2,2,6,5,3};int n=sizeof(vertices)/sizeof(vertices[0]);int m=sizeof(weight)/sizeof(weight[0]);MSTKrushkal(vertices,edgein,edgeout,weight,n,m);
}

程序运行结果：

Minimum spanning tree containing edges
B--E
C--D
D--F
A--C
D--E
Total weight = 15

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