Power Set in Lexicographic order

22 Jun, 2022
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++
Java
Python3
C#
PHP
Javascript
// CPP program to generate power set in// lexicographic order.#include <bits/stdc++.h>using namespace std; // str : Stores input string// n : Length of str.void func(string s, vector<string>& 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<string> 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 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 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, currdef 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 orderdef powerSet(string):    string = ''.join(sorted(string))    permuteRec(string, len(string)) # Driver Codeif __name__ == "__main__":    string = "cab"    powerSet(string) # This code is contributed by vibhu4agarwal
// 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// 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, currfunction 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?>
<script>// javascript 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,  curr) {        // base case        if (index == n) {            return;        }        document.write(curr+" ");        for (var 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.    function powerSet(str) {        var arr = str.split("");        arr.sort();        permuteRec(arr, str.length, -1, "");    }     // Driver code             var str = "cab";        powerSet(str); // This code contributed by umadevi9616</script>
a ab b c ca cab cb 
Time Complexity: O(n*2n) Auxiliary Space: O(1)
Mithun Kumar
vibhu4agarwal
princiraj1992
Rajput-Ji
srivatsa vatsa
maddler
umadevi9616
youmailmahibagi
Backtracking
Recursion
Strings
Strings
Recursion
Backtracking
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