C++ Prim算法

来源：互联网发布：张大奕淘宝店叫啥编辑：程序博客网时间：2024/06/07 10:53

Prim算法用于在加权连通图中搜索最小生成树，即搜索到的边子集所构成的树中，不但包括了连通图里的所有顶点，且其所有边的权值之和亦为最小。中心思想就是用1个数组存放父节点的index，以记录表示整个树形态，另外个数组用于存放权值，先将起始点对每个顶点权值写入，无连接用infinite表示，选出权值最小的点，并且在数组中将这个点置为0，然后用这个最小点到各点的权值比较数组中存放的权值，如果更小（0排除在外），则覆盖写入，并且存放父节点index，重复这个过程即可

代码实现：

#include<iostream>#define MAX_VERTEX 100#define INFINITE 65535using namespace std;//array char vertex_infos[MAX_VERTEX];int matrix[MAX_VERTEX][MAX_VERTEX];//list  struct Side{        int index;    int weight;    Side* next;};       struct Vertex{        char data;      Side* first;    };      typedef Vertex AdjList[MAX_VERTEX];        struct AdjGraph {      AdjList adjlist;        int num_vertex;        int num_side;   };  //commonint weight_array[MAX_VERTEX];int vertex_parent[MAX_VERTEX];int main(){ for(int i=0;i<MAX_VERTEX;i++){    vertex_parent[i]=0;        weight_array[i]=INFINITE;    }//array /*for(int i=0;i<MAX_VERTEX;i++){         vertex_infos[i]=0;        for(int j=0;j<MAX_VERTEX;j++){             matrix[i][j]=INFINITE;             matrix[i][j]=INFINITE;         }     }         cout<<"input vertex and side nums:";     int num_vertex;     int num_side;     cin>>num_vertex>>num_side;          cout<<"input vertex char data:";     for(int i=0;i<num_vertex;i++){         cin>>vertex_infos[i];     }          for(int i=0;i<num_side;i++){         int v1;         int v2;         int weight;        cout<<"input two vertex:";         cin>>v1>>v2;         cout<<"input weight:";         cin>>weight;         matrix[v1][v2]=weight;        matrix[v2][v1]=weight;    }             //start from v0    for(int i=1;i<MAX_VERTEX;i++){    if(vertex_infos[i]==0){    break;    }        weight_array[i]=matrix[0][i];    }    for(int i=1;i<MAX_VERTEX;i++){    if(vertex_infos[i]==0){    break;    }        int k=0;int min=INFINITE;for(int j=1;j<MAX_VERTEX;j++){if(weight_array[j]!=0&&weight_array[j]<min){min=weight_array[j];k=j;}}weight_array[k]=0;for(int j=1;j<MAX_VERTEX;j++){if(weight_array[j]!=0&&matrix[k][j]<weight_array[j]){weight_array[j]=matrix[k][j];vertex_parent[j]=k;}}    }    for(int i=0;i<MAX_VERTEX;i++){    if(vertex_infos[i]==0){    break;    }    cout<<vertex_parent[i];    }    cout<<endl;*/                 //list      AdjGraph adjGraph;            for(int i=0;i<MAX_VERTEX;i++){        adjGraph.adjlist[i].data=0;          adjGraph.adjlist[i].first=0;      }            cout<<"input vertex and side nums:";        cin>>adjGraph.num_vertex>>adjGraph.num_side;            cout<<"input vertex char data:";      for(int i=0;i<adjGraph.num_vertex;i++){          cin>>adjGraph.adjlist[i].data;      }          for(int i=0;i<adjGraph.num_side;i++){          int v1;          int v2;          int weight;        cout<<"input two vertex:";          cin>>v1>>v2;          cout<<"input weight:";         cin>>weight;        Side* side1=new Side();          side1->index=v2;          side1->weight=weight;        Side* side2=new Side();          side2->index=v1;          side2->weight=weight;        if(adjGraph.adjlist[v1].first==0){              adjGraph.adjlist[v1].first=side1;          }          else{              Side* temp=adjGraph.adjlist[v1].first;              adjGraph.adjlist[v1].first=side1;              side1->next=temp;          }                    if(adjGraph.adjlist[v2].first==0){              adjGraph.adjlist[v2].first=side2;          }          else{              Side* temp=adjGraph.adjlist[v2].first;              adjGraph.adjlist[v2].first=side2;              side2->next=temp;          }             }                Side* p=adjGraph.adjlist[0].first;while(p!=0){if(p->weight<weight_array[p->index]){weight_array[p->index]=p->weight;}p=p->next;}weight_array[0]=0;for(int i=1;i<MAX_VERTEX;i++){if(adjGraph.adjlist[i].data==0){break;}int k=0;int min=INFINITE;for(int j=1;j<MAX_VERTEX;j++){if(weight_array[j]!=0&&weight_array[j]<min){min=weight_array[j];k=j;}}weight_array[k]=0;p=adjGraph.adjlist[k].first;while(p!=0){if(p->weight<weight_array[p->index]){weight_array[p->index]=p->weight;vertex_parent[p->index]=k;}p=p->next;}}     for(int i=0;i<MAX_VERTEX;i++){     if(adjGraph.adjlist[i].data==0){break;}    cout<<vertex_parent[i];    }    cout<<endl;return 0;}

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