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Power Set

  • Difficulty Level : Medium
  • Last Updated : 16 Sep, 2021

Power Set Power set P(S) of a set S is the set of all subsets of S. For example S = {a, b, c} then P(s) = {{}, {a}, {b}, {c}, {a,b}, {a, c}, {b, c}, {a, b, c}}.
If S has n elements in it then P(s) will have 2^n elements
 

Algorithm: 
 

Input: Set[], set_size
1. Get the size of power set
    powet_set_size = pow(2, set_size)
2  Loop for counter from 0 to pow_set_size
     (a) Loop for i = 0 to set_size
          (i) If ith bit in counter is set
               Print ith element from set for this subset
     (b) Print separator for subsets i.e., newline

Example: 
 

Set  = [a,b,c]
power_set_size = pow(2, 3) = 8
Run for binary counter = 000 to 111

Value of Counter            Subset
    000                    -> Empty set
    001                    -> a
    010                    -> b
    011                    -> ab
    100                    -> c
    101                    -> ac
    110                    -> bc
    111                    -> abc

Method 1: 
 

C++




// C++ Program of above approach
#include <iostream>
#include <math.h>
using namespace std;
 
class gfg
{
     
public:
void printPowerSet(char *set, int set_size)
{
    /*set_size of power set of a set with set_size
    n is (2**n -1)*/
    unsigned int pow_set_size = pow(2, set_size);
    int counter, j;
 
    /*Run from counter 000..0 to 111..1*/
    for(counter = 0; counter < pow_set_size; counter++)
    {
    for(j = 0; j < set_size; j++)
    {
        /* Check if jth bit in the counter is set
            If set then print jth element from set */
        if(counter & (1 << j))
            cout << set[j];
    }
    cout << endl;
    }
}
};
 
/*Driver code*/
int main()
{
    gfg g;
    char set[] = {'a','b','c'};
    g.printPowerSet(set, 3);
    return 0;
}
 
// This code is contributed by SoM15242

C




#include <stdio.h>
#include <math.h>
 
void printPowerSet(char *set, int set_size)
{
    /*set_size of power set of a set with set_size
      n is (2**n -1)*/
    unsigned int pow_set_size = pow(2, set_size);
    int counter, j;
 
    /*Run from counter 000..0 to 111..1*/
    for(counter = 0; counter < pow_set_size; counter++)
    {
      for(j = 0; j < set_size; j++)
       {
          /* Check if jth bit in the counter is set
             If set then print jth element from set */
          if(counter & (1<<j))
            printf("%c", set[j]);
       }
       printf("\n");
    }
}
 
/*Driver program to test printPowerSet*/
int main()
{
    char set[] = {'a','b','c'};
    printPowerSet(set, 3);
    return 0;
}

Java




// Java program for power set
import java .io.*;
 
public class GFG {
     
    static void printPowerSet(char []set,
                            int set_size)
    {
         
        /*set_size of power set of a set
        with set_size n is (2**n -1)*/
        long pow_set_size =
            (long)Math.pow(2, set_size);
        int counter, j;
     
        /*Run from counter 000..0 to
        111..1*/
        for(counter = 0; counter <
                pow_set_size; counter++)
        {
            for(j = 0; j < set_size; j++)
            {
                /* Check if jth bit in the
                counter is set If set then
                print jth element from set */
                if((counter & (1 << j)) > 0)
                    System.out.print(set[j]);
            }
             
            System.out.println();
        }
    }
     
    // Driver program to test printPowerSet
    public static void main (String[] args)
    {
        char []set = {'a', 'b', 'c'};
        printPowerSet(set, 3);
    }
}
 
// This code is contributed by anuj_67.

Python3




# python3 program for power set
 
import math;
 
def printPowerSet(set,set_size):
     
    # set_size of power set of a set
    # with set_size n is (2**n -1)
    pow_set_size = (int) (math.pow(2, set_size));
    counter = 0;
    j = 0;
     
    # Run from counter 000..0 to 111..1
    for counter in range(0, pow_set_size):
        for j in range(0, set_size):
             
            # Check if jth bit in the
            # counter is set If set then
            # print jth element from set
            if((counter & (1 << j)) > 0):
                print(set[j], end = "");
        print("");
 
# Driver program to test printPowerSet
set = ['a', 'b', 'c'];
printPowerSet(set, 3);
 
# This code is contributed by mits.

C#




// C# program for power set
using System;
 
class GFG {
     
    static void printPowerSet(char []set,
                            int set_size)
    {
        /*set_size of power set of a set
        with set_size n is (2**n -1)*/
        uint pow_set_size =
              (uint)Math.Pow(2, set_size);
        int counter, j;
     
        /*Run from counter 000..0 to
        111..1*/
        for(counter = 0; counter <
                   pow_set_size; counter++)
        {
            for(j = 0; j < set_size; j++)
            {
                /* Check if jth bit in the
                counter is set If set then
                print jth element from set */
                if((counter & (1 << j)) > 0)
                    Console.Write(set[j]);
            }
             
            Console.WriteLine();
        }
    }
     
    // Driver program to test printPowerSet
    public static void Main ()
    {
        char []set = {'a', 'b', 'c'};
        printPowerSet(set, 3);
    }
}
 
// This code is contributed by anuj_67.

PHP




<?php
// PHP program for power set
 
function printPowerSet($set, $set_size)
{
 
    // set_size of power set of
    // a set with set_size
    // n is (2**n -1)
    $pow_set_size = pow(2, $set_size);
    $counter; $j;
 
    // Run from counter 000..0 to
    // 111..1
    for($counter = 0; $counter < $pow_set_size;
                                    $counter++)
    {
        for($j = 0; $j < $set_size; $j++)
        {
             
            /* Check if jth bit in
               the counter is set
               If set then print
               jth element from set */
            if($counter & (1 << $j))
                echo $set[$j];
        }
         
    echo "\n";
    }
}
 
    // Driver Code
    $set = array('a','b','c');
    printPowerSet($set, 3);
 
// This code is contributed by Vishal Tripathi
?>

Javascript




<script>
// javascript program for power setpublic
 
    function printPowerSet(set, set_size)
    {
 
        /*
         * set_size of power set of a set with set_size n is (2**n -1)
         */
        var pow_set_size = parseInt(Math.pow(2, set_size));
        var counter, j;
 
        /*
         * Run from counter 000..0 to 111..1
         */
        for (counter = 0; counter < pow_set_size; counter++)
        {
            for (j = 0; j < set_size; j++)
            {
             
                /*
                 * Check if jth bit in the counter is set If set then print jth element from set
                 */
                if ((counter & (1 << j)) > 0)
                    document.write(set[j]);
            }
            document.write("<br/>");
        }
    }
 
    // Driver program to test printPowerSet
        let set = [ 'a', 'b', 'c' ];
        printPowerSet(set, 3);
 
// This code is contributed by shikhasingrajput
</script>
Output: 



a
b
ab
c
ac
bc
abc

 

Time Complexity: O(n2^n)

Auxiliary Space: O(1)
Method 2: 
This method is specific to the python programming language. We can iterate a loop over 0 to the length of the set to obtain and generate all possible combinations of that string with the iterable length. The program below will give the implementation of the above idea. 
 

Python3




#Python program to find powerset
from itertools import combinations
def print_powerset(string):
    for i in range(0,len(string)+1):
        for element in combinations(string,i):
            print(''.join(element))
string=['a','b','c']
print_powerset(string)
Output: 
a
b
c
ab
ac
bc
abc

 

Recursive program to generate power set
Refer Power Set in Java for implementation in Java and more methods to print power set.
References: 
http://en.wikipedia.org/wiki/Power_set
 

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