完全图所有子图算法

#include

#include

#include

#include

#include

using namespace std;

void genSubgraphs(struct Graph*); //generate subgraphs

void combination(int, int,int**); //get the C(n, k) combinations and store in int** int factorial(int n); //get the factorial value of n

void getIndex(int, int&, int&); //used when getting combinations of edges void printGraph(struct Graph*); //print the subgraphs to a txt file

int calc_cv(int, int); //calculate the value of C(n, k)

struct Graph

{

int vernum;

int *vertices;

int **edges;

};

int main(int argc, char *argv[])

{

int vernum;

cout<<"请输入完全图的顶点数";

cin>>vernum;

//set values to origional graph

struct Graph* origGraph = new Graph;

origGraph->vernum = vernum;

int *vertices = new int[vernum];

for(int i = 1; i <= vernum; i++)

{

vertices[i-1] = i;

}

int **edges = new int*[vernum];

for(int i = 0; i < vernum; i++)

{

edges[i] = new int[vernum];

}

for(int i = 0; i < vernum; i++)

for(int j = 0; j < vernum; j++)

{

if(i == j) edges[i][j] = 0;

else edges[i][j] = 1;

}

origGraph->vertices = vertices;

origGraph->edges = edges;

//generate subgraphs

genSubgraphs(origGraph);

//free memory

for(int i = 0; i < vernum; i++)

delete(origGraph->edges[i]);

delete(origGraph->edges);

delete(origGraph->vertices);

delete(origGraph);

system("PAUSE");

return EXIT_SUCCESS;

}

void genSubgraphs(struct Graph* graph)

{

int vernum = graph->vernum;

int count=0; //记录非空子图的个数

for(int i = 1; i <= vernum; i++)

{

Graph* subgraph = new Graph;

subgraph->vernum = i;

//initialize the edges

int** edges = new int*[i];

for(int row = 0; row < i; row++)

edges[row] = new int[i];

subgraph->edges = edges;

//get all the combination of i vertices

int m=calc_cv(vernum,i);

int** vcombs = new int*[m];

for(int l = 0; l < m; l++)

vcombs[l] = new int[i];

combination(vernum,i,vcombs);

for(int j = 0; j < m; j++)

{

subgraph->vertices = vcombs[j];

//get all the conbinations of edges

int edgenum = i*(i-1)/2;

for(int edge_k = 0; edge_k <= edgenum; edge_k++) {

//set the edges

for(int row = 0; row < i; row++)

{

for(int col = 0; col < i; col++)

edges[row][col] = 0;

}

if(edge_k == 0)

{

printGraph(subgraph);

count++;

continue;

}

//select edges

int combnum = calc_cv(edgenum,edge_k);

int** ecombs = new int*[combnum];

for(int l = 0; l < combnum; l++)

ecombs[l] = new int[edge_k];

combination(edgenum,edge_k,ecombs);

for(int k = 0; k < combnum; k++)

{

//set the edges

for(int row = 0; row < i; row++)

{

for(int col = 0; col < i; col++)

edges[row][col] = 0;

}

for(int index = 0; index < edge_k; index++)

{

//get the vertices of the selected edges

int row, col;

getIndex(ecombs[k][index],row,col);

edges[row][col] = 1;

edges[col][row] = 1;

}

printGraph(subgraph);

count++;

delete(ecombs[k]);

}

delete(ecombs);

}

delete(vcombs[j]);

}

//free memory

delete(vcombs);

delete(subgraph);

}

cout<

}

void printGraph(struct Graph* graph)

{

char* filename = "graph_result.txt";

fstream fout;

fout.open(filename,ios::app|ios::out);

fout<

fout<

for(int i = 0; i < graph->vernum;i++)

{

fout<vertices[i];

}

fout<

for(int row = 0; row < graph->vernum; row++)

{

fout<vertices[row];

for(int col = 0; col vernum; col++)

{

fout<edges[row][col];

}

fout<

}

fout.close();

}

void combination(int n, int k,int** combs)

{

int p=0;

int* array = new int[k];

for(int i = 0; i < k; i++)

{

array[i] = i + 1;

}

int cur = k-1;

do{

if(array[cur]-cur <= n-k+1)

{

for(int i = 0; i < k; i++)

combs[p][i] = array[i];

p++;

array[cur]++;

continue;

}else{

if(cur == 0) break;

array[--cur]++;

for(int i = 1; i < k-cur; i++)

array[cur+i] = array[cur]+i;

if(array[cur]-cur < n-k+1)

cur = k-1;

}

}while(1);

delete array;

}

int calc_cv(int n, int k)

{

if(k > n/2) return calc_cv(n,n-k);

int s = 1;

for(int i = n; i > n-k; i--)

s *=i;

return s/factorial(k);

}

int factorial(int n)

{

if(n == 0) return 1;

int s = 1;

for(int i = 2; i <= n; i++) s=s*i;

return s;

}

void getIndex(int n, int &i, int &j)

{

int k=0,l=0,sum=0;

int temp = 0;

while(sum < n)

{

sum += k;

k++;

if((sum + k) >= n)

{

l = n - sum - 1;

break;

}

}

i = k; j = l;

}

The number of non-empty subgraph is 40068.