# 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 obe`
`        ``for` `(``int` `i = ``0``; i < (``1``<<n); i++)`
`        ``{`
`            ``System.out.print(``"{ "``);`
`            ``// Print current subset`
`            ``for` `(``int` `j = ``0``; j < n; j++)`
`                ``// (1<<j) is a number with jth bit 1`
`                ``// so when we 'and' them with the`
`                ``// subset number we get which numbers`
`                ``// are present in the subset and which`
`                ``// are not`
`                ``if` `((i & (``1` `<< j)) > ``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 }
```

Disclaimer: This does not belong to TechCodeBit, its an article taken from the below
source and credits.
source and credits: http://www.geeksforgeeks.org
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