# C++ Program to Generate All Subsets of a Given Set in the Lexico Graphic Order

C++Server Side ProgrammingProgramming

This is C++ Program to Generate All Subsets of a Given Set in the Lexico Graphic Order. This algorithm prints all the possible combination of each length from the given set of array in increasing order. The time complexity of this algorithm is O(n*(2^n)).

## Algorithm

Begin
For each length ‘i’ GenAllSubset() function is called:
1) In GenAllSubset(), if currLen is more than the reqLen then return.
2) Otherwise, if currLen is equal to reqLen then there will be a new sequence generated, print it.
3) If proceed with a start as ‘true’ and recursively call GenAllSubset() with incremented value of ‘currLen’ and ‘s’.
else
proceed with a start as ‘false’ and recursively call GenAllSubset() with incremented value of ‘s’.
End

## Example

#include<iostream>
using namespace std;
void Sorting(int a[], int n) //array sorting {
int i, j, t;
for(i = 0; i < n; i++) {
for(j = i+1; j < n; j++) {
if(a[i] > a[j]) {
t = a[i];
a[i] = a[j];
a[j] = t;
}
}
}
}
void GenAllSubset(int a[], int reqLen, int s, int currLen, bool check[], int len) {
if(currLen > reqLen)
return;
else if (currLen == reqLen) {
cout<<"\t";
cout<<"{ ";
for (int i = 0; i < len; i++) {
if (check[i] == true) {
cout<<a[i]<<" ";
}
}
cout<<"}\n";
return;
}
if (s == len) {
return;
}
check[s] = true;
GenAllSubset(a, reqLen, s + 1, currLen + 1, check, len);
check[s] = false;
GenAllSubset(a, reqLen, s + 1, currLen, check, len);
}
int main() {
int i, n;
bool ch[n];
cout<<"Enter the number of element array have: ";
cin>>n;
int arr[n];
cout<<"\n";
for (i = 0; i < n; i++) {
cout<<"Enter "<<i+1<<" element: ";
cin>>arr[i];
ch[i] = false;
}
Sorting(arr, n);
cout<<"\nThe all subset of the given set in the lexicographic order: \n";
cout<<"\t{ }\n";
for(i = 1; i <= n; i++) {
GenAllSubset(arr, i, 0, 0, ch, n);
}
return 0;
}

## Output

Enter the number of element array have: 6
Enter 1 element:3
Enter 2 element: 2
Enter 3 element: 1
Enter 4 element:7
Enter 5 element:6
Enter 6 element: 5
The all subset of the given set in the lexicographic order:
{ }
{ 1 }
{ 2 }
{ 3 }
{ 5 }
{ 6 }
{ 7 }
{ 1 2 }
{ 1 3 }
{ 1 5 }
{ 1 6 }
{ 1 7 }
{ 2 3 }
{ 2 5 }
{ 2 6 }
{ 2 7 }
{ 3 5 }
{ 3 6 }
{ 3 7 }
{ 5 6 }
{ 5 7 }
{ 6 7 }
{ 1 2 3 }
{ 1 2 5 }
{ 1 2 6 }
{ 1 2 7 }
{ 1 3 5 }
{ 1 3 6 }
{ 1 3 7 }
{ 1 5 6 }
{ 1 5 7 }
{ 1 6 7 }
{ 2 3 5 }
{ 2 3 6 }
{ 2 3 7 }
{ 2 5 6 }
{ 2 5 7 }
{ 2 6 7 }
{ 3 5 6 }
{ 3 5 7 }
{ 3 6 7 }
{ 5 6 7 }
{ 1 2 3 5 }
{ 1 2 3 6 }
{ 1 2 3 7 }
{ 1 2 5 6 }
{ 1 2 5 7 }
{ 1 2 6 7 }
{ 1 3 5 6 }
{ 1 3 5 7 }
{ 1 3 6 7 }
{ 1 5 6 7 }
{ 2 3 5 6 }
{ 2 3 5 7 }
{ 2 3 6 7 }
{ 2 5 6 7 }
{ 3 5 6 7 }
{ 1 2 3 5 6 }
{ 1 2 3 5 7 }
{ 1 2 3 6 7 }
{ 1 2 5 6 7 }
{ 1 3 5 6 7 }
{ 2 3 5 6 7 }
{ 1 2 3 5 6 7 }