Recursive program to generate power set

Given a set represented as 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"

Method 1 : The idea is to fix a prefix, generate all subsets beginning with current prefix. After all subsets with a prefix are generated, replace last character with one of the remaining characters.

C++

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// 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;
}

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Java

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// 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

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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#

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// 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.
  

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Output:


a
ab
abc
ac
b
bc
c

Method 2 : 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 current subset.

C++

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// 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;
}

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Java

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// 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

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C#

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// 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

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Output:

abc
ab
ac
a
bc
b
c

Method 3 : The idea is to pick each element one by one from the input set, then generate subset for the same and we follow this process recursively.
We’ll use ArrayList for this purpose
For ex,
f(0) = {a}, {} // {} when we don’t include any element from the set, it is null i.e {}.
f(1) = {a}, {}, {b}, {a, b} // We have to copy all the elements from f(0) and then include the very next element from the set i.e b. So f(1) = f(0) + 1;
f(2) = {a}, {}, {b}, {a, b}, {a, c}, {c}, {b, c}, {a, b, c} .So f(2) = f(1) +2;

The general form becomes f(n) = f(n-1) + n;

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// 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;
    }
}

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Output:

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


Iterative program for power set.



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