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++



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// 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;
}

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Java














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// 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 */



















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Python3














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# 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 



















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C#














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// 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 



















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PHP














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<?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 


?> 



















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Output :


a
ab
abc
ac
b
bc
c






          
          
          

          

    

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