Power Set in Lexicographic order

This article is about generating Power set in lexicographical order.

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.

C++



filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to generate power set in
// lexicographic order.
#include <bits/stdc++.h>
using namespace std;
  
// str : Stores input string
// n : Length of str.
// curr : Stores current permutation
// index : Index in current permutation, curr
void permuteRec(string str, int n,
                int index = -1, string curr = "")
{
    // base case
    if (index == n)
        return;
  
    cout << curr << "\n";
    for (int i = index + 1; i < n; i++) {
  
        curr += str[i];
        permuteRec(str, n, i, curr);
  
        // backtracking
        curr = curr.erase(curr.size() - 1);
    }
    return;
}
  
// Generates power set in lexicographic
// order.
void powerSet(string str)
{
    sort(str.begin(), str.end());
    permuteRec(str, str.size());
}
  
// Driver code
int main()
{
    string str = "cab";
    powerSet(str);
    return 0;
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// 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 */



















                        chevron_right







                        filter_none









Python3














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# 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 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// 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 



















                        chevron_right







                        filter_none









PHP














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















<?php 


// PHP 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 


function permuteRec($str, $n, $index = -1,  


                              $curr = "") 


{ 


    // base case 


    if ($index == $n)  


        return; 


  


    echo $curr."\n"; 


    for ($i = $index + 1; $i < $n; $i++)  


    { 


  


        $curr=$curr.$str[$i]; 


        permuteRec($str, $n, $i, $curr); 


  


        // backtracking 


        $curr ="";  


    } 


    return; 


} 


  


// Generates power set in lexicographic 


// order. 


function powerSet($str) 


{ 


  


    $str = str_split($str); 


    sort($str); 


    permuteRec($str, sizeof($str)); 


} 


  


// Driver code 


$str = "cab"; 


powerSet($str); 


  


// This code is contributed by Mithun Kumar 


?> 



















                        chevron_right







                        filter_none











Output :


a
ab
abc
ac
b
bc
c






          
          
          
          

            

    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:
Ashish Kaktan
Check out this Author's contributed articles.
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on  the "Improve Article" button below.