2.1）download source code： https://github.com/pacosonTang/dataStructure-algorithmAnalysis/tree/master/chapter9/p237_prim 2.2）source code at a glance（for complete code , please click the given link above）：
#include "prim.h"//allocate the memory for initializing unweighted table
WeightedTable *initWeightedTable(int size)
{ WeightedTable* table;int i;table = (WeightedTable*)malloc(sizeof(WeightedTable) * size);if(!table){Error("out of space ,from func initWeightedTable");return NULL;}for(i = 0; i < size; i++){table[i] = makeEmptyWeightedTable(); if(!table[i])return NULL;}return table;
} // allocate the memory for every element in unweighted table
WeightedTable makeEmptyWeightedTable()
{WeightedTable element;element = (WeightedTable)malloc(sizeof(struct WeightedTable));if(!element){Error("out of space ,from func makeEmptyWeightedTable");return NULL;} element->known = 0; // 1 refers to accessed , also 0 refers to not accessedelement->distance = MaxInt;element->path = -1; // index starts from 0 and -1 means the startup vertex unreaches other vertexsreturn element;
}// allocate the memory for storing index of vertex in heap and let every element -1int *makeEmptyArray(int size)
{int *array;int i;array = (int*)malloc(size * sizeof(int));if(!array){Error("out of space ,from func makeEmptyArray");return NULL;} for(i=0; i<size; i++)array[i] = -1;returnarray;
}//computing the unweighted shortest path between the vertex under initIndex and other vertexsvoid prim(AdjTable* adj, int size, int startVertex, BinaryHeap bh)
{ int adjVertex; int tempDistance;WeightedTable* table;int vertex; AdjTable temp; Distance tempDisStruct;int *indexOfVertexInHeap;int indexOfHeap;table = initWeightedTable(size); tempDisStruct = makeEmptyDistance();indexOfVertexInHeap = makeEmptyArray(size);tempDisStruct->distance = table[startVertex-1]->distance;tempDisStruct->vertexIndex = startVertex-1;insert(tempDisStruct, bh, indexOfVertexInHeap); // insert the (startVertex-1) into the binary heap table[startVertex-1]->distance = 0;// update the distance table[startVertex-1]->path = 0;// update the path of starting vertexwhile(!isEmpty(bh)){ vertex = deleteMin(bh, indexOfVertexInHeap).vertexIndex; // return the minimal element in binary heap//printBinaryHeap(bh);table[vertex]->known = 1; // update the vertex as accessed, also let responding known be 1temp = adj[vertex]->next;while(temp){adjVertex = temp->index; if(table[adjVertex]->known == 1) // judge whether table[adjVertex]->known is 1 or not{temp = temp->next;continue;}//tempDistance = table[vertex]->distance + temp->weight; // update the distancetempDistance = temp->weight;if(tempDistance < table[adjVertex]->distance){table[adjVertex]->distance = tempDistance;table[adjVertex]->path = vertex; //update the path of adjVertex, also responding path evaluated as vertex // key, we should judge whether adjVertex was added into the binary heap //if true , obviously the element has been added into the binary heap(so we can't add the element into heap once again)if(indexOfVertexInHeap[adjVertex] != -1) {indexOfHeap = indexOfVertexInHeap[adjVertex];bh->elements[indexOfHeap]->distance = tempDistance; // update the distance of corresponding vertex in binary heap}else// if not ture{tempDisStruct->distance = table[adjVertex]->distance;tempDisStruct->vertexIndex = adjVertex;insert(tempDisStruct, bh, indexOfVertexInHeap); // insert the adjVertex into the binary heap}} temp = temp->next; } printPrim(table, size, startVertex); printBinaryHeap(bh);printf("\n");} printf("\n");
} //print unweighted tablevoid printPrim(WeightedTable* table, int size, int startVertex)
{int i; char *str[4] = {"vertex","known","distance","path"};printf("\n\t === storage table related to Prim alg as follows: === "); printf("\n\t %6s%6s%9s%5s", str[0], str[1], str[2], str[3]); for(i=0; i<size; i++){ if(i != startVertex-1 && table[i]->path!=-1) printf("\n\t %-3d %3d %5d v%-3d ", i+1, table[i]->known, table[i]->distance, table[i]->path+1);elseif(table[i]->path == -1)printf("\n\t %-3d %3d %5d %-3d ", i+1, table[i]->known, table[i]->distance, table[i]->path);elseprintf("\n\t *%-3d %3d %5d %-3d ", i+1, table[i]->known, table[i]->distance, 0);}
}int main()
{ AdjTable* adj; BinaryHeap bh;int size = 7;int capacity;int i;int j; int startVertex;int adjTable[7][7] = {{0, 2, 4, 1, 0, 0, 0},{2, 0, 0, 3, 10, 0, 0},{4, 0, 0, 2, 0, 5, 0},{1, 3, 2, 0, 7, 8, 4},{0, 10, 0, 7, 0, 0, 6},{0, 0, 5, 8, 0, 0, 1},{0, 0, 0, 4, 6, 1, 0},};printf("\n\n\t ====== test for Prim alg finding weighted shortest path from adjoining table ======\n");adj = initAdjTable(size); printf("\n\n\t ====== the initial weighted adjoining table is as follows:======\n");for(i = 0; i < size; i++)for(j = 0; j < size; j++) if(adjTable[i][j]) insertAdj(adj, j, i, adjTable[i][j]); // insertAdj the adjoining table overprintAdjTable(adj, size); capacity = 7;bh = initBinaryHeap(capacity+1);//conducting prim alg to find minimum spanning tree(MST)startVertex = 1; // you should know our index for storing vertex starts from 0prim(adj, size, startVertex, bh); return0;
}
