# Power Set in Lexicographic order

Examples :

`Input : abcOutput : 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`

## Javascript

 ``

## PHP

 ``

Output

```a ab b c ca cab cb

```

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

Method (binary numbers)

The idea is to use binary numbers  to generate the power set of a given set of elements in lexicographical order

• Sort the given set in lexicographical order.
• Define a variable “n” to represent the size of the set.
• Use a loop to generate all possible binary numbers of length “n”.
• For each binary number, convert it to a string of 0s and 1s,
• Add the current subset to the output list.
• Sort the output list in lexicographical order.
• Print the sorted list of subsets.

## C++

 `#include ` `#include ` `#include ` `#include ` `using` `namespace` `std;`   `void` `generate_power_set(string s)` `{` `    ``// Sort the set in lexicographical order` `    ``sort(s.begin(), s.end());`   `    ``int` `n = s.length();` `    ``vector subsets;`   `    ``// Generate all possible binary strings of length n` `    ``for` `(``int` `i = 0; i < (1 << n); i++) {` `        ``string binary = ``""``;` `        ``int` `num = i;`   `        ``// Convert the integer i to a binary string of` `        ``// length n` `        ``for` `(``int` `j = 0; j < n; j++) {` `            ``binary = ``char``(``'0'` `+ num % 2) + binary;` `            ``num /= 2;` `        ``}`   `        ``// Generate the subset based on the binary string` `        ``string subset = ``""``;` `        ``for` `(``int` `j = 0; j < n; j++) {` `            ``if` `(binary[j] == ``'1'``) {` `                ``subset += s[j];` `            ``}` `        ``}` `        ``subsets.push_back(subset);` `    ``}`   `    ``// Sort the subsets in lexicographically order` `    ``sort(subsets.begin(), subsets.end());`   `    ``// Print the subsets in sorted order` `    ``for` `(``auto``& subset : subsets) {` `        ``cout << subset << ``" "``;` `    ``}` `    ``cout << endl;` `}`   `int` `main()` `{` `    ``string s = ``"abc"``;` `    ``generate_power_set(s);` `    ``return` `0;` `}`   `// This code is contributed by abhinav_m22`

## Java

 `import` `java.util.ArrayList;` `import` `java.util.Arrays;` `import` `java.util.List;`   `class` `Program {` `    ``// Function to generate the power set of a string` `    ``static` `void` `generatePowerSet(String s) {` `        ``// Convert the string to a character array` `        ``char``[] charArray = s.toCharArray();` `        ``// Sort the character array` `        ``Arrays.sort(charArray);` `        ``String sortedString = ``new` `String(charArray);`   `        ``int` `n = sortedString.length();` `        ``List subsets = ``new` `ArrayList<>();`   `        ``// Generate all possible binary strings of length n` `        ``for` `(``int` `i = ``0``; i < (``1` `<< n); i++) {` `            ``StringBuilder binary = ``new` `StringBuilder();` `            ``int` `num = i;`   `            ``// Convert the integer i to a binary string of length n` `            ``for` `(``int` `j = ``0``; j < n; j++) {` `                ``binary.insert(``0``, num % ``2``);` `                ``num /= ``2``;` `            ``}`   `            ``// Generate the subset based on the binary string` `            ``StringBuilder subset = ``new` `StringBuilder();` `            ``for` `(``int` `j = ``0``; j < n; j++) {` `                ``if` `(binary.charAt(j) == ``'1'``) {` `                    ``subset.append(sortedString.charAt(j));` `                ``}` `            ``}` `            ``subsets.add(subset.toString());` `        ``}`   `        ``// Sort the subsets in lexicographically order` `        ``subsets.sort(``null``);`   `        ``// Print the subsets in sorted order` `        ``for` `(String subset : subsets) {` `            ``System.out.print(subset + ``" "``);` `        ``}` `        ``System.out.println();` `    ``}`   `    ``public` `static` `void` `main(String[] args) {` `        ``String s = ``"abc"``;` `        ``generatePowerSet(s);` `    ``}` `}`

## Python3

 `def` `generate_power_set(s):` `    ``# Sort the set in lexicographical order` `    ``s ``=` `''.join(``sorted``(s))`   `    ``n ``=` `len``(s)` `    ``subsets ``=` `[]` `    ``# Generate all possible binary strings of length n` `    ``for` `i ``in` `range``(``2``*``*``n):` `        ``# Convert the integer i to a binary string of length n` `        ``binary ``=` `bin``(i)[``2``:].zfill(n)` `        ``# Generate the subset based on the binary string` `        ``subset ``=` `'``'.join([s[j] for j in range(n) if binary[j] == '``1``'])` `        ``subsets.append(subset)` `    ``# Sort the subsets in lexicographically order` `    ``subsets.sort()` `    ``# Print the subsets in sorted order` `    ``for` `subset ``in` `subsets:` `        ``print``(subset)`   `# Example usage` `s ``=` `'abc'` `generate_power_set(s)`

## C#

 `using` `System;` `using` `System.Collections.Generic;` `using` `System.Linq;`   `class` `Program {` `    ``// Function to generate the power set of a string` `    ``static` `void` `GeneratePowerSet(``string` `s)` `    ``{` `        ``// Sort the set in lexicographical order` `        ``char``[] charArray = s.ToCharArray();` `        ``Array.Sort(charArray);` `        ``string` `sortedString = ``new` `string``(charArray);`   `        ``int` `n = sortedString.Length;` `        ``List<``string``> subsets = ``new` `List<``string``>();`   `        ``// Generate all possible binary strings of length n` `        ``for` `(``int` `i = 0; i < (1 << n); i++) {` `            ``string` `binary = ``""``;` `            ``int` `num = i;`   `            ``// Convert the integer i to a binary string of` `            ``// length n` `            ``for` `(``int` `j = 0; j < n; j++) {` `                ``binary = (num % 2) + binary;` `                ``num /= 2;` `            ``}`   `            ``// Generate the subset based on the binary` `            ``// string` `            ``string` `subset = ``""``;` `            ``for` `(``int` `j = 0; j < n; j++) {` `                ``if` `(binary[j] == ``'1'``) {` `                    ``subset += sortedString[j];` `                ``}` `            ``}` `            ``subsets.Add(subset);` `        ``}`   `        ``// Sort the subsets in lexicographically order` `        ``subsets.Sort();`   `        ``// Print the subsets in sorted order` `        ``foreach``(``var` `subset ``in` `subsets)` `        ``{` `            ``Console.Write(subset + ``" "``);` `        ``}` `        ``Console.WriteLine();` `    ``}`   `    ``static` `void` `Main()` `    ``{` `        ``string` `s = ``"abc"``;` `        ``GeneratePowerSet(s);` `    ``}` `}`

## Javascript

 `function` `generatePowerSet(s) {` `    ``// Convert the string to an array of characters` `    ``let charArray = Array.from(s);` `    ``// Sort the character array` `    ``charArray.sort();` `    ``let sortedString = charArray.join(``''``);`   `    ``let n = sortedString.length;` `    ``let subsets = [];`   `    ``// Generate all possible binary strings of length n` `    ``for` `(let i = 0; i < (1 << n); i++) {` `        ``let binary = ``''``;` `        ``let num = i;`   `        ``// Convert the integer i to a binary string of length n` `        ``for` `(let j = 0; j < n; j++) {` `            ``binary = (num % 2) + binary;` `            ``num = Math.floor(num / 2);` `        ``}`   `        ``// Generate the subset based on the binary string` `        ``let subset = ``''``;` `        ``for` `(let j = 0; j < n; j++) {` `            ``if` `(binary.charAt(j) === ``'1'``) {` `                ``subset += sortedString.charAt(j);` `            ``}` `        ``}` `        ``subsets.push(subset);` `    ``}`   `    ``// Sort the subsets in lexicographically order` `    ``subsets.sort();`   `    ``// Print the subsets in sorted order` `    ``console.log(subsets.join(``' '``));` `}`   `let s = ``'abc'``;` `generatePowerSet(s);`

Output

```a
ab
abc
ac
b
bc
c

```

Time complexity :O(2^n * n), where n is the length of the input set.
Space complexity  :O(2^n * n), since the output list of subsets can potentially contain 2^n elements

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