C program to create a subsets using backtracking method.

C Program to find the subsets in the set. We use the backtracking method to solve this problem. Backtracking is the refinement method of Brute-Force method. Backtrack method means it finds the number of sub solutions and each may have number of sub divisions, and solution chosen for exactly one. Backtracking method is a recursive method. Read more about C Programming Language .

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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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