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Recursive program to generate power set

Given a set represented as string, write a recursive code to print all subsets of it. The subsets can be printed in any order.

Examples:

```Input :  set = "abc"
Output : "". "a", "b", "c", "ab", "ac", "bc", "abc"

Input : set = "abcd"
Output : "" "a" "ab" "abc" "abcd" "abd" "ac" "acd"
"ad" "b" "bc" "bcd" "bd" "c" "cd" "d"
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Method 1 : The idea is to fix a prefix, generate all subsets beginning with current prefix. After all subsets with a prefix are generated, replace last character with one of the remaining characters.

## C++

 `// CPP program to generate power set``#include ``using` `namespace` `std;`` ` `// str : Stores input string``// curr : Stores current subset``// index : Index in current subset, curr``void` `powerSet(string str, ``int` `index = -1,``              ``string curr = ``""``)``{``    ``int` `n = str.length();`` ` `    ``// base case``    ``if` `(index == n)``        ``return``;`` ` `    ``// First print current subset``    ``cout << curr << ``"\n"``;`` ` `    ``// Try appending remaining characters``    ``// to current subset``    ``for` `(``int` `i = index + 1; i < n; i++) {`` ` `        ``curr += str[i];``        ``powerSet(str, i, curr);`` ` `        ``// Once all subsets beginning with``        ``// initial "curr" are printed, remove``        ``// last character to consider a different``        ``// prefix of subsets.``        ``curr.erase(curr.size() - 1);``    ``}``    ``return``;``}`` ` `// Driver code``int` `main()``{``    ``string str = ``"abc"``;``    ``powerSet(str);``    ``return` `0;``}`

## Java

 `// Java program to generate power set``import` `java.util.*;`` ` `class` `GFG ``{`` ` `    ``// str : Stores input string ``    ``// curr : Stores current subset ``    ``// index : Index in current subset, curr ``    ``static` `void` `powerSet(String str, ``int` `index,``                            ``String curr) ``    ``{``        ``int` `n = str.length();`` ` `        ``// base case ``        ``if` `(index == n)``        ``{``            ``return``;``        ``}`` ` `        ``// First print current subset ``        ``System.out.println(curr);`` ` `        ``// Try appending remaining characters ``        ``// to current subset ``        ``for` `(``int` `i = index + ``1``; i < n; i++) ``        ``{``            ``curr += str.charAt(i);``            ``powerSet(str, i, curr);`` ` `            ``// Once all subsets beginning with ``            ``// initial "curr" are printed, remove ``            ``// last character to consider a different ``            ``// prefix of subsets. ``            ``curr = curr.substring(``0``, curr.length() - ``1``);``        ``}``    ``}`` ` `    ``// Driver code ``    ``public` `static` `void` `main(String[] args) ``    ``{``        ``String str = ``"abc"``;``        ``int` `index = -``1``;``        ``String curr = ``""``;``        ``powerSet(str, index, curr);``    ``}``} `` ` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 program to generate power set`` ` `# str : Stores input string``# curr : Stores current subset``# index : Index in current subset, curr``def` `powerSet(str1, index, curr):``    ``n ``=` `len``(str1)`` ` `    ``# base case``    ``if` `(index ``=``=` `n):``        ``return`` ` `    ``# First print current subset``    ``print``(curr)`` ` `    ``# Try appending remaining characters``    ``# to current subset``    ``for` `i ``in` `range``(index ``+` `1``, n):``        ``curr ``+``=` `str1[i]``        ``powerSet(str1, i, curr)`` ` `        ``# Once all subsets beginning with``        ``# initial "curr" are printed, remove``        ``# last character to consider a different``        ``# prefix of subsets.``        ``curr ``=` `curr.replace(curr[``len``(curr) ``-` `1``], "")`` ` `    ``return`` ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``str` `=` `"abc"``;``    ``powerSet(``str``, ``-``1``, "")`` ` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# program to generate power set``using` `System;`` ` `class` `GFG ``{`` ` `    ``// str : Stores input string ``    ``// curr : Stores current subset ``    ``// index : Index in current subset, curr ``    ``static` `void` `powerSet(``string` `str, ``int` `index,``                            ``string` `curr) ``    ``{``        ``int` `n = str.Length;`` ` `        ``// base case ``        ``if` `(index == n)``        ``{``            ``return``;``        ``}`` ` `        ``// First print current subset ``        ``Console.WriteLine(curr);`` ` `        ``// Try appending remaining characters ``        ``// to current subset ``        ``for` `(``int` `i = index + 1; i < n; i++) ``        ``{``            ``curr += str[i];``            ``powerSet(str, i, curr);`` ` `            ``// Once all subsets beginning with ``            ``// initial "curr" are printed, remove ``            ``// last character to consider a different ``            ``// prefix of subsets. ``            ``curr = curr.Substring(0, curr.Length - 1);``        ``}``    ``}`` ` `    ``// Driver code ``    ``public` `static` `void` `Main() ``    ``{``        ``string` `str = ``"abc"``;``        ``int` `index = -1;``        ``string` `curr = ``""``;``        ``powerSet(str, index, curr);``    ``}``} `` ` `// This code is contributed by Ita_c.`` `
Output:
```
a
ab
abc
ac
b
bc
c
```

Method 2 : The idea is to consider two cases for every character. (i) Consider current character as part of current subset (ii) Do not consider current character as part of current subset.

## C++

 `// CPP program to generate power set``#include ``using` `namespace` `std;`` ` `// str : Stores input string``// curr : Stores current subset``// index : Index in current subset, curr``void` `powerSet(string str, ``int` `index = 0,``              ``string curr = ``""``)``{``    ``int` `n = str.length();`` ` `    ``// base case``    ``if` `(index == n) {``        ``cout << curr << endl;``        ``return``;``    ``}`` ` `    ``// Two cases for every character``    ``// (i) We consider the character``    ``// as part of current subset``    ``// (ii) We do not consider current``    ``// character as part of current``    ``// subset``    ``powerSet(str, index + 1, curr + str[index]);``    ``powerSet(str, index + 1, curr);``}`` ` `// Driver code``int` `main()``{``    ``string str = ``"abc"``;``    ``powerSet(str);``    ``return` `0;``}`

## Java

 `// Java program to generate power set``class` `GFG {`` ` `// str : Stores input string ``// curr : Stores current subset ``// index : Index in current subset, curr ``static` `void` `powerSet(String str, ``int` `index, ``            ``String curr) ``     ` `{ ``    ``int` `n = str.length(); `` ` `    ``// base case ``    ``if` `(index == n)``    ``{ ``        ``System.out.println(curr);``        ``return``; ``    ``} `` ` `    ``// Two cases for every character ``    ``// (i) We consider the character ``    ``// as part of current subset ``    ``// (ii) We do not consider current ``    ``// character as part of current ``    ``// subset ``    ``powerSet(str, index + ``1``, curr + str.charAt(index)); ``    ``powerSet(str, index + ``1``, curr);`` ` `} `` ` `// Driver code ``public` `static` `void` `main(String[] args) ``{``    ``String str = ``"abc"``; ``        ``int` `index = ``0``;``        ``String curr=``""``;``    ``powerSet(str,index,curr); `` ` `    ``}``} ``// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to generate power set``def` `powerSet(string , index , curr):``     ` `    ``# string : Stores input string ``    ``# curr : Stores current subset ``    ``# index : Index in current subset, curr ``    ``if` `index ``=``=` `len``(string):``        ``print``(curr)``        ``return``     ` `    ``powerSet(string, index ``+` `1``, ``             ``curr ``+` `string[index])``    ``powerSet(string, index ``+` `1``, curr) ``     ` `# Driver Code ``if` `__name__ ``=``=` `"__main__"``: `` ` `    ``s1 ``=` `"abc"``    ``index ``=` `0``    ``curr ``=` `""``    ``powerSet(s1, index , curr) `` ` `# This code is contributed by Ekta Singh`

## C#

 `// C# program to generate power set``using` `System;`` ` `class` `GFG``{`` ` `    ``// str : Stores input string ``    ``// curr : Stores current subset ``    ``// index : Index in current subset, curr ``    ``static` `void` `powerSet(String str, ``int` `index, ``                ``String curr) `` ` `    ``{ ``        ``int` `n = str.Length; `` ` `        ``// base case ``        ``if` `(index == n)``        ``{ ``            ``Console.WriteLine(curr);``            ``return``; ``        ``} `` ` `        ``// Two cases for every character ``        ``// (i) We consider the character ``        ``// as part of current subset ``        ``// (ii) We do not consider current ``        ``// character as part of current ``        ``// subset ``        ``powerSet(str, index + 1, curr + str[index]); ``        ``powerSet(str, index + 1, curr);``    ``} `` ` `    ``// Driver code ``    ``public` `static` `void` `Main() ``    ``{``        ``String str = ``"abc"``; ``        ``int` `index = 0;``        ``String curr=``""``;``        ``powerSet(str,index,curr); ``    ``}``}`` ` `//This code is contributed by Rajput-Ji`
Output:

```abc
ab
ac
a
bc
b
c

```

Method 3 : The idea is to pick each element one by one from the input set, then generate subset for the same and we follow this process recursively.
We’ll use ArrayList for this purpose
For ex,
f(0) = {a}, {} // {} when we don’t include any element from the set, it is null i.e {}.
f(1) = {a}, {}, {b}, {a, b} // We have to copy all the elements from f(0) and then include the very next element from the set i.e b. So f(1) = f(0) + 1;
f(2) = {a}, {}, {b}, {a, b}, {a, c}, {c}, {b, c}, {a, b, c} .So f(2) = f(1) +2;

The general form becomes f(n) = f(n-1) + n;

 `// Java Recursive code to print``// all subsets of set using ArrayList``import` `java.util.ArrayList;`` ` `public` `class` `PowerSet {`` ` `    ``public` `static` `void` `main(String[] args)``    ``{`` ` `        ``String[] set = { ``"a"``, ``"b"``, ``"c"` `};`` ` `        ``int` `index = set.length - ``1``;``        ``ArrayList > result = getSubset(set, index);``        ``System.out.println(result);``    ``}`` ` `    ``static` `ArrayList > getSubset(String[] set, ``int` `index)``    ``{``        ``ArrayList > allSubsets;``        ``if` `(index < ``0``) {``            ``allSubsets = ``new` `ArrayList >();``            ``allSubsets.add(``new` `ArrayList());``        ``}`` ` `        ``else` `{``            ``allSubsets = getSubset(set, index - ``1``);``            ``String item = set[index];``            ``ArrayList > moreSubsets ``                ``= ``new` `ArrayList >();`` ` `            ``for` `(ArrayList subset : allSubsets) {``                ``ArrayList newSubset = ``new` `ArrayList();``                ``newSubset.addAll(subset);``                ``newSubset.add(item);``                ``moreSubsets.add(newSubset);``            ``}``            ``allSubsets.addAll(moreSubsets);``        ``}``        ``return` `allSubsets;``    ``}``}`
Output:
```[[], [a], [b], [a, b], , [a, c], [b, c], [a, b, c]]
```

Iterative program for power set.

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