Finding all subsets of a given set in Java
Problem: Find all the subsets of a given set.
Input:
S = {a, b, c, d}
Output:
{}, {a} , {b}, {c}, {d}, {a,b}, {a,c},
{a,d}, {b,c}, {b,d}, {c,d}, {a,b,c},
{a,b,d}, {a,c,d}, {b,c,d}, {a,b,c,d}
The total number of subsets of any given set is equal to 2^ (no. of elements in the set). If we carefully notice it is nothing but binary numbers from 0 to 15 which can be shown as below:
0000 |
{} |
0001 |
{a} |
0010 |
{b} |
0011 |
{a, b} |
0100 |
{c} |
0101 |
{a, c} |
0110 |
{b, c} |
0111 |
{a, b, c} |
1000 |
{d} |
1001 |
{a, d} |
1010 |
{b, d} |
1011 |
{a, b, d} |
1100 |
{c, d} |
1101 |
{a, c, d} |
1110 |
{b, c, d} |
1111 |
{a, b, c, d} |
Starting from right, 1 at ith position shows that the ith element of the set is present as 0 shows that the element is absent. Therefore, what we have to do is just generate the binary numbers from 0 to 2^n – 1, where n is the length of the set or the numbers of elements in the set.
Implementation:
Java
import java.io.IOException;
class Main
{
static void printSubsets( char set[])
{
int n = set.length;
for ( int i = 0 ; i < ( 1 <<n); i++)
{
System.out.print( "{ " );
for ( int j = 0 ; j < n; j++)
if ((i & ( 1 << j)) > 0 )
System.out.print(set[j] + " " );
System.out.println( "}" );
}
}
public static void main(String[] args)
{
char set[] = { 'a' , 'b' , 'c' };
printSubsets(set);
}
}
|
Output
{ }
{ a }
{ b }
{ a b }
{ c }
{ a c }
{ b c }
{ a b c }
Time complexity: O(n * (2^n)) as the outer loop runs for O(2^n) and the inner loop runs for O(n).
Auxiliary Space :O(1), since no extra space is used.
Related Post:
Finding all subsets of a Set in C/C++
Last Updated :
28 Feb, 2023
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