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# Power Set in Lexicographic order

• Difficulty Level : Medium
• Last Updated : 05 Aug, 2022

Examples :

```Input : abc
Output : a ab abc ac b bc c```

The idea is to sort array first. After sorting, one by one fix characters and recursively generates all subsets starting from them. After every recursive call, we remove last character so that next permutation can be generated.

Implementation:

## C++

 `// CPP program to generate power set in``// lexicographic order.``#include ``using` `namespace` `std;` `// str : Stores input string``// n : Length of str.``void` `func(string s, vector& str, ``int` `n, ``int` `pow_set)``{``    ``int` `i, j;``    ``for` `(i = 0; i < pow_set; i++) {``        ``string x;``        ``for` `(j = 0; j < n; j++) {``            ``if` `(i & 1 << j) {``                ``x = x + s[j];``            ``}``        ``}``        ``if` `(i != 0)``            ``str.push_back(x);``    ``}``}``int` `main()``{``    ``int` `n;``    ``string s;``    ``vector str;``    ``s = ``"cab"``;``    ``n = s.length();``    ``int` `pow_set = ``pow``(2, n);``    ``func(s, str, n, pow_set);``    ``sort(str.begin(), str.end());``    ``for` `(``int` `i = 0; i < str.size(); i++)``        ``cout << str[i] << ``" "``;``    ``cout << endl;` `    ``return` `0;``}`

## Java

 `// Java program to generate power set in``// lexicographic order.``import` `java.util.*;` `class` `GFG {` `    ``// str : Stores input string``    ``// n : Length of str.``    ``// curr : Stores current permutation``    ``// index : Index in current permutation, curr``    ``static` `void` `permuteRec(String str, ``int` `n,``                           ``int` `index, String curr)``    ``{``        ``// base case``        ``if` `(index == n) {``            ``return``;``        ``}``        ``System.out.println(curr);``        ``for` `(``int` `i = index + ``1``; i < n; i++) {` `            ``curr += str.charAt(i);``            ``permuteRec(str, n, i, curr);` `            ``// backtracking``            ``curr = curr.substring(``0``, curr.length() - ``1``);``        ``}``        ``return``;``    ``}` `    ``// Generates power set in lexicographic``    ``// order.``    ``static` `void` `powerSet(String str)``    ``{``        ``char``[] arr = str.toCharArray();``        ``Arrays.sort(arr);``        ``permuteRec(``new` `String(arr), str.length(), -``1``, ``""``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``String str = ``"cab"``;``        ``powerSet(str);``    ``}``}` `/* This code contributed by PrinciRaj1992 */`

## Python3

 `# Python3 program to generate power``# set in lexicographic order.` `# str : Stores input string``# n : Length of str.``# curr : Stores current permutation``# index : Index in current permutation, curr``def` `permuteRec(string, n, index ``=` `-``1``, curr ``=` `""):` `    ``# base case``    ``if` `index ``=``=` `n:``        ``return` `    ``if` `len``(curr) > ``0``:``        ``print``(curr)` `    ``for` `i ``in` `range``(index ``+` `1``, n):``        ``curr ``+``=` `string[i]``        ``permuteRec(string, n, i, curr)` `        ``# backtracking``        ``curr ``=` `curr[:``len``(curr) ``-` `1``]` `# Generates power set in lexicographic order``def` `powerSet(string):``    ``string ``=` `''.join(``sorted``(string))``    ``permuteRec(string, ``len``(string))` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``string ``=` `"cab"``    ``powerSet(string)` `# This code is contributed by vibhu4agarwal`

## C#

 `// C# program to generate power set in``// lexicographic order.``using` `System;` `class` `GFG {` `    ``// str : Stores input string``    ``// n : Length of str.``    ``// curr : Stores current permutation``    ``// index : Index in current permutation, curr``    ``static` `void` `permuteRec(String str, ``int` `n,``                           ``int` `index, String curr)``    ``{``        ``// base case``        ``if` `(index == n) {``            ``return``;``        ``}``        ``Console.WriteLine(curr);``        ``for` `(``int` `i = index + 1; i < n; i++) {` `            ``curr += str[i];``            ``permuteRec(str, n, i, curr);` `            ``// backtracking``            ``curr = curr.Substring(0, curr.Length - 1);``        ``}``        ``return``;``    ``}` `    ``// Generates power set in lexicographic``    ``// order.``    ``static` `void` `powerSet(String str)``    ``{``        ``char``[] arr = str.ToCharArray();``        ``Array.Sort(arr);``        ``permuteRec(``new` `String(arr), str.Length, -1, ``""``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``String str = ``"cab"``;``        ``powerSet(str);``    ``}``}` `// This code contributed by Rajput-Ji`

## PHP

 ``

## Javascript

 ``

Output

`a ab b c ca cab cb `

Time Complexity: O(n*2n
Auxiliary Space: O(1)

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