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Recursive program to generate power set

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Given a set represented as a string, write a recursive code to print all subsets of it. The subsets can be printed in any order. 

Examples:  

Input :  set = “abc”
Output : { “”, “a”, “b”, “c”, “ab”, “ac”, “bc”, “abc”}

Input : set = “abcd”
Output : { “”, “a” ,”ab” ,”abc” ,”abcd”, “abd” ,”ac” ,”acd”, “ad” ,”b”, “bc” ,”bcd” ,”bd” ,”c” ,”cd” ,”d” }

Recursive program to generate power set using Backtracking:

The idea is to fix a prefix, and generate all subsets beginning with the current prefix. After all subsets with a prefix are generated, replace the last character with one of the remaining characters.

Follow the approach to implement the above idea:

  • The base condition of the recursive approach is when the current index reaches the size of the given string (i.e, index == n), then return
  • First, print the current subset
  • Iterate over the given string from the current index (i.e, index) to less than the size of the string
    • Appending the remaining characters to the current subset
    • Make the recursive call for the next index.
    • Once all subsets beginning with the initial “curr” are printed, remove the last character to consider a different prefix of subsets.

Follow the steps below to implement the above approach:

C++




// CPP program to generate power set
#include <bits/stdc++.h>
using namespace std;
 
// str : Stores input string
// curr : Stores current subset
// index : Index in current subset, curr
void powerSet(string str, int index = -1, string curr = "")
{
    int n = str.length();
 
    // base case
    if (index == n)
        return;
 
    // First print current subset
    cout << curr << "\n";
 
    // Try appending remaining characters
    // to current subset
    for (int i = index + 1; i < n; i++) {
 
        curr += str[i];
        powerSet(str, i, curr);
 
        // Once all subsets beginning with
        // initial "curr" are printed, remove
        // last character to consider a different
        // prefix of subsets.
        curr.erase(curr.size() - 1);
    }
    return;
}
 
// Driver code
int main()
{
    string str = "abc";
    powerSet(str);
    return 0;
}

Java




// Java program to generate power set
import java.util.*;
 
class GFG {
 
    // str : Stores input string
    // curr : Stores current subset
    // index : Index in current subset, curr
    static void powerSet(String str, int index, String curr)
    {
        int n = str.length();
 
        // base case
        if (index == n) {
            return;
        }
 
        // First print current subset
        System.out.println(curr);
 
        // Try appending remaining characters
        // to current subset
        for (int i = index + 1; i < n; i++) {
            curr += str.charAt(i);
            powerSet(str, i, curr);
 
            // Once all subsets beginning with
            // initial "curr" are printed, remove
            // last character to consider a different
            // prefix of subsets.
            curr = curr.substring(0, curr.length() - 1);
        }
    }
 
    // Driver code
    public static void main(String[] args)
    {
        String str = "abc";
        int index = -1;
        String curr = "";
        powerSet(str, index, curr);
    }
}
 
// This code is contributed by PrinciRaj1992

Python3




# Python3 program to generate power set
 
# str : Stores input string
# curr : Stores current subset
# index : Index in current subset, curr
 
 
def powerSet(str1, index, curr):
    n = len(str1)
 
    # base case
    if (index == n):
        return
 
    # First print current subset
    print(curr)
 
    # Try appending remaining characters
    # to current subset
    for i in range(index + 1, n):
        curr += str1[i]
        powerSet(str1, i, curr)
 
        # Once all subsets beginning with
        # initial "curr" are printed, remove
        # last character to consider a different
        # prefix of subsets.
        curr = curr.replace(curr[len(curr) - 1], "")
 
    return
 
 
# Driver code
if __name__ == '__main__':
    str = "abc"
    powerSet(str, -1, "")
 
# This code is contributed by
# Surendra_Gangwar

C#




// C# program to generate power set
using System;
 
class GFG {
 
    // str : Stores input string
    // curr : Stores current subset
    // index : Index in current subset, curr
    static void powerSet(string str, int index, string curr)
    {
        int n = str.Length;
 
        // base case
        if (index == n) {
            return;
        }
 
        // First print current subset
        Console.WriteLine(curr);
 
        // Try appending remaining characters
        // to current subset
        for (int i = index + 1; i < n; i++) {
            curr += str[i];
            powerSet(str, i, curr);
 
            // Once all subsets beginning with
            // initial "curr" are printed, remove
            // last character to consider a different
            // prefix of subsets.
            curr = curr.Substring(0, curr.Length - 1);
        }
    }
 
    // Driver code
    public static void Main()
    {
        string str = "abc";
        int index = -1;
        string curr = "";
        powerSet(str, index, curr);
    }
}
 
// This code is contributed by Ita_c.

Javascript




<script>
// Javascript program to generate power set
     
    // str : Stores input string
    // curr : Stores current subset
    // index : Index in current subset, curr
    function powerSet(str,index,curr)
    {
        let n = str.length;
   
        // base case
        if (index == n)
        {
            return;
        }
   
        // First print current subset
        document.write(curr+"<br>");
   
        // Try appending remaining characters
        // to current subset
        for (let i = index + 1; i < n; i++)
        {
            curr += str[i];
            powerSet(str, i, curr);
   
            // Once all subsets beginning with
            // initial "curr" are printed, remove
            // last character to consider a different
            // prefix of subsets.
            curr = curr.substring(0, curr.length - 1);
        }
    }
     
    // Driver code
    let str = "abc";
    let index = -1;
    let curr = "";
    powerSet(str, index, curr);
     
     
    // This code is contributed by rag2127
</script>

Output

a
ab
abc
ac
b
bc
c

Time Complexity: O(2n)
Auxiliary Space: O(n), For recursive call stack

Recursive program to generate power set using Recursion:

The idea is to consider two cases for every character.
(i) Consider current character as part of current subset
(ii) Do not consider current character as part of the current subset.  

Follow the approach to implement the above idea:

  • The base condition of the recursive approach is when the current index reaches the size of the given string (i.e, index == n). then print the current string say, curr.
  • Make two recursive calls for the two cases for every character
    • We consider the character as part of the current subset
    • We do not consider current character as part of the current subset

Follow the steps below to implement the above approach:

C++




// CPP program to generate power set
#include <bits/stdc++.h>
using namespace std;
 
// str : Stores input string
// curr : Stores current subset
// index : Index in current subset, curr
void powerSet(string str, int index = 0, string curr = "")
{
    int n = str.length();
 
    // base case
    if (index == n) {
        cout << curr << endl;
        return;
    }
 
    // Two cases for every character
    // (i) We consider the character
    // as part of current subset
    // (ii) We do not consider current
    // character as part of current
    // subset
    powerSet(str, index + 1, curr + str[index]);
    powerSet(str, index + 1, curr);
}
 
// Driver code
int main()
{
    string str = "abc";
    powerSet(str);
    return 0;
}

Java




// Java program to generate power set
class GFG {
 
    // str : Stores input string
    // curr : Stores current subset
    // index : Index in current subset, curr
    static void powerSet(String str, int index, String curr)
 
    {
        int n = str.length();
 
        // base case
        if (index == n) {
            System.out.println(curr);
            return;
        }
 
        // Two cases for every character
        // (i) We consider the character
        // as part of current subset
        // (ii) We do not consider current
        // character as part of current
        // subset
        powerSet(str, index + 1, curr + str.charAt(index));
        powerSet(str, index + 1, curr);
    }
 
    // Driver code
    public static void main(String[] args)
    {
        String str = "abc";
        int index = 0;
        String curr = "";
        powerSet(str, index, curr);
    }
}
// This code is contributed by 29AjayKumar

Python3




# Python3 program to generate power set
def powerSet(string, index, curr):
 
    # string : Stores input string
    # curr : Stores current subset
    # index : Index in current subset, curr
    if index == len(string):
        print(curr)
        return
 
    powerSet(string, index + 1,
             curr + string[index])
    powerSet(string, index + 1, curr)
 
 
# Driver Code
if __name__ == "__main__":
 
    s1 = "abc"
    index = 0
    curr = ""
    powerSet(s1, index, curr)
 
# This code is contributed by Ekta Singh

C#




// C# program to generate power set
using System;
 
class GFG {
 
    // str : Stores input string
    // curr : Stores current subset
    // index : Index in current subset, curr
    static void powerSet(String str, int index, String curr)
 
    {
        int n = str.Length;
 
        // base case
        if (index == n) {
            Console.WriteLine(curr);
            return;
        }
 
        // Two cases for every character
        // (i) We consider the character
        // as part of current subset
        // (ii) We do not consider current
        // character as part of current
        // subset
        powerSet(str, index + 1, curr + str[index]);
        powerSet(str, index + 1, curr);
    }
 
    // Driver code
    public static void Main()
    {
        String str = "abc";
        int index = 0;
        String curr = "";
        powerSet(str, index, curr);
    }
}
 
// This code is contributed by Rajput-Ji

Javascript




<script>
// Javascript program to generate power set
     
    // str : Stores input string
// curr : Stores current subset
// index : Index in current subset, curr
    function powerSet(str,index,curr)
    {
        let n = str.length;
  
    // base case
    if (index == n)
    {
        document.write(curr+"<br>");
        return;
    }
  
    // Two cases for every character
    // (i) We consider the character
    // as part of current subset
    // (ii) We do not consider current
    // character as part of current
    // subset
    powerSet(str, index + 1, curr + str[index]);
    powerSet(str, index + 1, curr);
    }
     
    // Driver code
    let str = "abc";
    let index = 0;
    let curr="";
    powerSet(str,index,curr);
     
     
// This code is contributed by avanitrachhadiya2155
</script>

Output

abc
ab
ac
a
bc
b
c

Time Complexity: O(2n)
Auxiliary Space: O(n), For recursive call stack

Recursive program to generate power set using Backtracking using Bottom Up Approach:

The idea is to pick each element one by one from the input set, then generate a subset for the same, and we follow this process recursively. 

Follow the steps below to implement the above idea:

  • The base condition for the recursive call, when the current index becomes negative then add empty list into the allSubsets.
  • Make recursive call for the current index – 1, then we’ll receive allSubsets list from 0 to index -1
  • Create a list of list moreSubsets
  • Iterate over all the subsets that are received from above recursive call 
    • Copy all the subset into newSubset
    • Add the current item into newSebset
    • Add newSebset into moreSubsets
  • Add moreSubsets into allSubsets
  • Finally, return allSubsets.

Follow the steps below to implement the above approach:

Java




// Java Recursive code to print
// all subsets of set using ArrayList
import java.util.ArrayList;
 
public class PowerSet {
 
    public static void main(String[] args)
    {
 
        String[] set = { "a", "b", "c" };
 
        int index = set.length - 1;
        ArrayList<ArrayList<String> > result
            = getSubset(set, index);
        System.out.println(result);
    }
 
    static ArrayList<ArrayList<String> >
    getSubset(String[] set, int index)
    {
        ArrayList<ArrayList<String> > allSubsets;
        if (index < 0) {
            allSubsets
                = new ArrayList<ArrayList<String> >();
            allSubsets.add(new ArrayList<String>());
        }
 
        else {
            allSubsets = getSubset(set, index - 1);
            String item = set[index];
            ArrayList<ArrayList<String> > moreSubsets
                = new ArrayList<ArrayList<String> >();
 
            for (ArrayList<String> subset : allSubsets) {
                ArrayList<String> newSubset
                    = new ArrayList<String>();
                newSubset.addAll(subset);
                newSubset.add(item);
                moreSubsets.add(newSubset);
            }
            allSubsets.addAll(moreSubsets);
        }
        return allSubsets;
    }
}

Output

[[], [a], [b], [a, b], , [a, c], [b, c], [a, b, c]]

Time Complexity: O(n*2n)
Auxiliary Space: O(n), For recursive call stack

Iterative program for the power set.


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