#include<stdio.h>
#include<stdlib.h>
#include<math.h>


  typedef struct partitionnode 
  {
    int m;
    int numparts;
    int parts[101];
  } partition;
  partition a;

  int SubSets[8][20];
  int index[8][20];
  int MultiSet[100];
  int n,q,rho,r;

int IsIn(int x,int s,partition a)
{
	int i;
	for(i=1;i<=a.parts[s];i++)
		if(x==SubSets[s][i]) return(1);
	return(0);
}

int searchdss(int s,int t,int M,partition a)
/*
** search one DSS with given partition
*/
{
	int i,j,k,l;
	int isdss,isperfect;

	isdss=1;
	isperfect=1;

	if(s>=2)//To check M is not given to any existing element.
	{
		for(i=1;i<=s-1;i++)
			if(IsIn(M,i,a)==1) //if M has been assigned to any existing element
				if(M==n) return(0);
				else 
				{
					if(M<n-a.parts[s]+t) //M does not reach the value bound
						return(searchdss(s,t,M+1,a))!
 ;
					else return(0);
				}

	}
	SubSets[s][t]=M;
	if(s==a.numparts && t==a.parts[s]) //All elements of all subsets are given values.
	{
		for(i=1;i<=n;i++) MultiSet[i]=0;
		for(i=1;i<=a.numparts-1;i++)
		
or(k=i+1;k<=a.numparts;k++)
				for(j=1;j<=a.parts[i];j++)
					for(l=1;l<=a.parts[k];l++)
					{
						MultiSet[((SubSets[i][j]-SubSets[k][l]+n)%n)]++;
						MultiSet[((SubSets[k][l]-SubSets[i][j]+n)%n)]++;
					}
				
		for(i=1;i<=n-1;i++) 
		{
			if(MultiSet[i]<rho) isdss=0;
			if(isdss==0) break;
			if(MultiSet[i]>rho) isperfect=0;
		}
			
		if(isdss==0)//
		{
			if(M!=n) return(searchdss(s,t,M+1,a));
			else return(0);
		}
		else
		{
			printf("\n\nFind one DSS!\n");
			printf("Subsets: \n");
			for(i=1;i<=a.numparts;i++)
			{
				printf("{");
				for(j=1;j<=a.parts[i];j++)
				{
					if(j==a.parts[i]) printf("%d!
 }\n",SubSets[i][j]);
					else printf("%d,",SubSets[i][j]);!
 
				
}
			}
			printf("Multiset:\n{");
			for(i=1;i<=n-1;i++)
			{
				if(i==n-1) printf("%d(%d)}\n",n-1,MultiSet[n-1]);
				else printf("%d(%d),",i,MultiSet[i]);
			}
			if(isperfect==1) printf("This DSS is perfect!\n");
			printf("\n");
			return(1);
		}
	}
	else // Not reach the last element of the last subset
	{
		if(t<a.parts[s])// not reach the last element of any subset
		{
			if(searchdss(s,t+1,M+1,a)==1) //search with next element is M+1
				return(1);
			else if(M<n-a.parts[s]+t) //search with current element is M+1 if it does not reache the value bound
				return(searchdss(s,t,M+1,a));
			else return(0); // current element has reached value bound
		}
		else// t=a.parts[s]:reach the last element of some subset (not the last one)
		{
			if(searchdss(s+1,1,2,a)==1) 
				return(1);
			else if(M<n) 
				return(searchdss(s,t,M+1,a));
			else return(0);
		}
	}
}

!
 int search(partition a)
/*
**  search out the partition a
*/
{
 int i,j,sum;

 printf("r = %d = ",a.m);
 for(i=1;i<=a.numparts;i++)
 {
    j = a.parts[i];
    printf("%d",j);
    if (i != a.numparts
br>      printf("+");
 }
 printf("\n");

 sum=0;
 for(i=1;i<=a.numparts-1;i++)
	 for(j=i+1;j<=a.numparts;j++)
	 {
		 sum=sum+2*a.parts[i]*a.parts[j];
	 }
 printf("2*(Q_i * Q_j)=%d",sum);
 if(sum<(n-1)*rho) 
 {
	 printf(" < %d=(n-1)*rho",(n-1)*rho);
	 return(0);
 }

 SubSets[1][1]=1;
 if(a.parts[1]>1) // there are more than 2 elements in the first subset
	 return(searchdss(1,2,2,a));
 else // there is only one element in 1st subset
	 return(searchdss(2,1,2,a));
}

void RecPartition(partition a, int r, int q, int N)
/*
**  generate all q partitions 
**  recursive procedure used in other procedures
*/
{
 int i;
 if(q==0)
 {
   a.n!
 umparts = N;   
   if(search(a)==1) 
   {
		//printf(!
 "Find on
e!\n");
   }
   else printf("\nNone!\n\n");
 }
 else
 {
   for (i=r-q+1;i>=(int)ceil((r/(float)q));i--)
   {
     if(N==0 || N>=1 && a.parts[N]>=i)
	 {
		 a.parts[N+1] = i;
		 RecPartition(a,r-i,q-1,N+1);
	 }
   }
 }
}

void GenPartitions(int r, int q)
/*
**  generate all partitions of r
*/
{
 a.m =  r;
 RecPartition(a,r,q,0);
}


int main()
{ 

  printf("n=");
  scanf("%d",&n);
  printf("q=");
  scanf("%d",&q);
  printf("rho=");
  scanf("%d",&rho);

  r=(int)ceil(sqrt(q*rho*(n-1)/(float)(q-1)));
  
  GenPartitions(r,q);

  return(0);
}