# 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.

 `// A Java program to print all subsets of a set ` `import` `java.io.IOException; ` ` `  `class` `Main ` `{ ` `    ``// Print all subsets of given set[] ` `    ``static` `void` `printSubsets(``char` `set[]) ` `    ``{ ` `        ``int` `n = set.length; ` ` `  `        ``// Run a loop for printing all 2^n ` `        ``// subsets one by one ` `        ``for` `(``int` `i = ``0``; i < (``1``< ``0``) ` `                    ``System.out.print(set[j] + ``" "``); ` ` `  `            ``System.out.println(``"}"``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``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 }
```

Related Post:
Finding all subsets of a Set in C/C++

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