最小生成树kruskal算法适合稀疏图（网络整理）8.1.3

来源：互联网发布：淘宝上小提琴教学视频编辑：程序博客网时间：2024/06/07 03:04
上一篇实现了prim算法，适合稠密图，这次来实现另一种算法KRUSKAL算法
#include<stdio.h>#include<stdlib.h>#include<stdbool.h>#define MAXSIZE 100typedef int Weight;typedef char Datatype; typedef struct AdjVNode{Weight weight;int adjv;struct AdjVNode *Next;}*PtrToAdjVNode;typedef struct Vnode{Datatype data;PtrToAdjVNode FirstEdge;/* 边表头指针 */  }AdjList[MAXSIZE];typedef struct Lnode{int Nv;int Ne;AdjList G;}*LGraph;typedef struct Enode{int v1;int v2;Weight weight;//bool flag;//true -> false ->}Edge;LGraph  CreateGraph(int n){LGraph Graph=(LGraph)malloc(sizeof(struct Lnode));Graph->Nv=n;Graph->Ne=0;for(int i=0;i<n;i++){Graph->G[i].FirstEdge=NULL;}return Graph;}void InsertEdge(LGraph Graph,const Edge *ptre){PtrToAdjVNode Newnode=(PtrToAdjVNode)malloc(sizeof(struct AdjVNode));Newnode->weight=ptre->weight;Newnode->adjv=ptre->v2;Newnode->Next=Graph->G[ptre->v1].FirstEdge;Graph->G[ptre->v1].FirstEdge=Newnode;//若是无向边Newnode=(PtrToAdjVNode)malloc(sizeof(struct AdjVNode));Newnode->weight=ptre->weight;Newnode->adjv=ptre->v1;Newnode->Next=Graph->G[ptre->v2].FirstEdge;Graph->G[ptre->v2].FirstEdge=Newnode;}LGraph  buildGraph(){LGraph Graph;      Edge E;      int V;      int Nv, i;             scanf("%d", &Nv);   /* 读入顶点个数 */      Graph = CreateGraph(Nv); /* 初始化有Nv个顶点但没有边的图 */              scanf("%d", &(Graph->Ne));   /* 读入边数 */      if ( Graph->Ne != 0 ) { /* 如果有边 */                    /* 读入边，格式为"起点 终点 权重"，插入邻接矩阵 */          for (i=0; i<Graph->Ne; i++) {              scanf("%d %d %d", &E.v1, &E.v2, &E.weight);               /* 注意：如果权重不是整型，Weight的读入格式要改 */              InsertEdge( Graph, &E );          }     } /* 如果顶点有数据的话，读入数据 */      for (V=0; V<Graph->Nv; V++)           scanf(" %c", &(Graph->G[V].data));         return Graph;  }/*-------------------- 边的最小堆定义 --------------------*/typedef Edge Ele;const Ele ERROR={-1,-1,-1};typedef struct heap{Ele *data;int size;int maxsize;}*MinHeap;MinHeap createMinHeap(int n){MinHeap minheap=(MinHeap)malloc(sizeof(struct heap));minheap->data=(Ele*)malloc(sizeof(Ele)*(n+1));minheap->size=0;minheap->maxsize=n;return minheap;}bool isfull(MinHeap heap){    return heap->size>=heap->maxsize;}bool isempty(MinHeap heap){if(heap==NULL)heap->size =5;    return heap->size<=0;}void InsertMinHeap(MinHeap heap,Ele e){if(isfull(heap))    return;heap->size++;int i;for(i=heap->size;i>1&&e.weight<heap->data[i/2].weight;i/=2)heap->data[i]=heap->data[i/2];heap->data[i]=e;}Ele DelMinHeap(MinHeap heap){if(isempty(heap))return ERROR;Ele min=heap->data[1];Ele tmp=heap->data[heap->size--];int i=0,childmin;for(i=1;2*i<=heap->size;i=childmin){childmin=2*i;if(childmin!=heap->size&&heap->data[childmin].weight>heap->data[childmin+1].weight)childmin++;if(tmp.weight<=heap->data[childmin].weight)break; heap->data[i]=heap->data[childmin];   }heap->data[i]=tmp;return min;}void PercDown(MinHeap heap, int p){  Ele tmp = heap->data[p]; /* 取出根结点存放的值 */    int i=p,childmin;for(;2*i<=heap->size;i=childmin){childmin=2*i;if(childmin!=heap->size&&heap->data[childmin].weight>heap->data[childmin+1].weight)childmin++;if(tmp.weight<=heap->data[childmin].weight)break; heap->data[i]=heap->data[childmin];   }heap->data[i]=tmp;}MinHeap buildMinHeap(Ele e[],int n){MinHeap heap=createMinHeap(n);heap->size=n;for(int i=0;i<n;i++)heap->data[i]=e[i];for(int i=n/2;i>0;i--)    PercDown(heap,i);return heap;}/*-------------------- 边的最小堆定义end --------------------*//*-------------------- 顶点并查集定义 --------------------*/typedef int ElementType; /* 默认元素可以用非负整数表示 */typedef int SetName;     /* 默认用根结点的下标作为集合名称 */typedef ElementType SetType[MAXSIZE]; /* 假设集合元素下标从0开始 */ void InitializeVSet( SetType S, int N ){ /* 初始化并查集 */    int X;     for ( X=0; X<N; X++ ) S[X] = -1;} void Union( SetType S, SetName Root1, SetName Root2 ){ /* 这里默认Root1和Root2是不同集合的根结点 */    /* 保证小集合并入大集合 */    //if ( S[Root2] < S[Root1] ) { /* 如果集合2比较大 */      //  S[Root2] += S[Root1];     /* 集合1并入集合2  */        //S[Root1] = Root2;    //}    //else {                         /* 如果集合1比较大 */      //  S[Root1] += S[Root2];     /* 集合2并入集合1  */        //S[Root2] = Root1;    //}S[Root2]=Root1;} SetName Find( SetType S, ElementType X ){ /* 默认集合元素全部初始化为-1 */    if ( S[X] < 0 ) /* 找到集合的根 */        return X;    else        return Find( S, S[X] ); /* 路径压缩 */} bool CheckCycle( SetType VSet, int V1, int V2 ){ /* 检查连接V1和V2的边是否在现有的最小生成树子集中构成回路 */    int Root1, Root2;     Root1 = Find( VSet, V1 ); /* 得到V1所属的连通集名称 */    Root2 = Find( VSet, V2 ); /* 得到V2所属的连通集名称 */     if( Root1==Root2 ) /* 若V1和V2已经连通，则该边不能要 */        return false;    else { /* 否则该边可以被收集，同时将V1和V2并入同一连通集 */        Union( VSet, Root1, Root2 );        return true;    }}MinHeap InitializeESet(LGraph Graph){    PtrToAdjVNode W;    Edge edge;MinHeap edgeheap=createMinHeap(Graph->Ne);for (int V=0; V<Graph->Nv; V++ )        for ( W=Graph->G[V].FirstEdge; W; W=W->Next )            if ( V<W->adjv) { /* 避免重复录入无向图的边，只收V1<V2的边 */                edge.v1 = V;                edge.v2 = W->adjv;                edge.weight=W->weight;                //printf("abc %d\n",edge.weight );                InsertMinHeap(edgeheap,edge);            }return edgeheap;}Edge GetEdge( MinHeap edgeheap){    return DelMinHeap(edgeheap);}/*-------------------- 并查集定义结束 --------------------*/    int Kruskal( LGraph Graph, LGraph MST )    { /* 将最小生成树保存为邻接表存储的图MST，返回最小权重和 */        Weight TotalWeight;        int ECount;        SetType VSet; /* 顶点并查集 */        MinHeap edgeheap=NULL;    /* 边的最小堆 */       // printf("%p\n",edgeheap );exit(0);       Edge NextEdge;        InitializeVSet( VSet, Graph->Nv ); /* 初始化顶点并查集 */               edgeheap=InitializeESet( Graph ); /* 初始化边的最小堆 */        /* 创建包含所有顶点但没有边的图。注意用邻接表版本 */        MST = CreateGraph(Graph->Nv);        TotalWeight = 0; /* 初始化权重和     */        ECount = 0;      /* 初始化收录的边数 */                    while ( ECount < Graph->Nv-1 ) {  /* 当收集的边不足以构成树时 */            NextEdge = GetEdge( edgeheap ); /* 从边的最小堆de到最小边 */        //printf("%d\n", NextEdge.weight);            if (NextEdge.v1==-1) /* 边集已空 */                break;            /* 如果该边的加入不构成回路，即两端结点不属于同一连通集 */            if ( CheckCycle( VSet, NextEdge.v1, NextEdge.v2 )==true ) {                /* 将该边插入MST */                InsertEdge( MST, &NextEdge);                printf("%d<->%d weight:%d collected\n",NextEdge.v1,NextEdge.v2,NextEdge.weight);                TotalWeight += NextEdge.weight; /* 累计权重 */                ECount++; /* 生成树中边数加1 */            }        }        if ( ECount < Graph->Nv-1 )            TotalWeight = -1; /* 设置错误标记，表示生成树不存在 */             return TotalWeight;    }int main(){LGraph Graph=buildGraph();LGraph MST;printf("-------------------------------------------\n");printf("TotalWeight %d",Kruskal(Graph,MST));    return 0;}
0 0