# C program to create a subsets using backtracking method

Levels of difficulty: / perform operation:

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. `

### C Program

```#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
*/
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("%d\t",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]);
}
}
}
```