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#include<stdio.h>
#include<conio.h>
#define TRUE 1
#define FALSE 0
int inc[50],w[50],sum,n;
int promising(int i,int wt,int total)
{
 return(((wt+total)>=sum)&&((wt==sum)||(wt+w[i+1]<=sum)));
}
/*
* You can find this program on GitHub 
* https://github.com/snadahalli/cprograms/blob/master/subsets.c
*/
void main()
{
 int i,j,n,temp,total=0;
 clrscr();
 printf("n Enter how many numbers:n");
 scanf("%d",&n);
 printf("n Enter %d numbers to th set:n",n);
 for(i=0;i<n;i++)
 {
  scanf("%d",&w[i]);
  total+=w[i];
 }
 printf("n Input the sum value to create sub set:n");
 scanf("%d",&sum);
 for(i=0;i<=n;i++)
  for(j=0;j<n-1;j++)
   if(w[j]>w[j+1])
   {
    temp=w[j];
    w[j]=w[j+1];
    w[j+1]=temp;
   }
 printf("n The given %d numbers in ascending order:n",n);
 for(i=0;i<n;i++)
  printf("%d t",w[i]);
 if((total<sum))
  printf("n Subset construction is not possible");
 else
 {
  for(i=0;i<n;i++)
   inc[i]=0;
  printf("n The solution using backtracking is:n");
  sumset(-1,0,total);
 }
 getch();
}
void sumset(int i,int wt,int total)
{
 int j;
 if(promising(i,wt,total))
 {
  if(wt==sum)
  {
   printf("n{t");
   for(j=0;j<=i;j++)
    if(inc[j])
     printf("%dt",w[j]);
   printf("}n");
  }
  else
  {
   inc[i+1]=TRUE;
   sumset(i+1,wt+w[i+1],total-w[i+1]);
   inc[i+1]=FALSE;
   sumset(i+1,wt,total-w[i+1]);
  }
 }
}

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