ランダムエッジ選択の方法でランダムグラフを作成するC++プログラム

このプログラムでは、ランダムな頂点とエッジに対してランダムなグラフが生成されます。このプログラムの時間計算量はO（v * e）です。ここで、vは頂点の数、eはエッジの数です。

アルゴリズム

Begin
   Develop a function GenRandomGraphs(), with ‘e’ as the
   number of edges and ‘v’ as the number of vertexes, in the argument list.
   Assign random values to the number of vertex and edges of the graph, Using rand() function.
      Print the connections of each vertex, irrespective of the direction.
      Print “Isolated vertex” for the vertex having no degree.
End

例

#include<iostream>
#include<stdlib.h>
using namespace std;
void GenRandomGraphs(int NOEdge, int NOVertex) {
   int i, j, edge[NOEdge][2], count;
   i = 0;
   //Assign random values to the number of vertex and edges of the graph, Using rand().
   while(i < NOEdge) {
      edge[i][0] = rand()%NOVertex+1;
      edge[i][1] = rand()%NOVertex+1;
      //Print the connections of each vertex, irrespective of the direction.
      if(edge[i][0] == edge[i][1])
         continue;
      else {
         for(j = 0; j < i; j++) {
            if((edge[i][0] == edge[j][0] && edge[i][1] == edge[j][1]) || (edge[i][0] == edge[j][1] && edge[i][1] == edge[j][0]))i--;
         }
      }
      i++;
   }
   cout<<"\nThe generated random graph is: ";
   for(i = 0; i < NOVertex; i++) {
      count = 0;
      cout<<"\n\t"<<i+1<<"-> { ";
      for(j = 0; j < NOEdge; j++) {
         if(edge[j][0] == i+1) {
            cout<<edge[j][1]<<" ";
            count++;
         } else if(edge[j][1] == i+1) {
            cout<<edge[j][0]<<" ";
            count++;
         } else if(j== NOEdge-1&& count == 0)cout<<"Isolated Vertex!";
         //Print “Isolated vertex” for the vertex having no degree.
      }
      cout<<" }";
   }
}
int main() {
   int i, e, n;
   cout<<"Random graph generation: ";
   n= 7 + rand()%6;
   cout<<"\nThe graph has "<<n<<" vertices";
   e = rand()%((n*(n-1))/2);
   cout<<"\nand has "<<e<<" edges.";
   GenRandomGraphs(e, n);
}

出力

Random graph generation:
The graph has 8 vertices
and has 18 edges.
The generated random graph is:
   1-> { 5 4 2 }
   2-> { 4 8 6 3 1 5 }
   3-> { 5 4 7 2 }
   4-> { 2 3 7 1 8 5 }
   5-> { 3 1 7 4 2 8 }
   6-> { 2 8 7 }
   7-> { 4 3 5 6 }
   8-> { 2 6 4 5 }