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Finding all subsets of a given set in Java

Problem:Find all the subsets of a given set.

Input:  S = {a, b, c, d} Output: {}, {a} , {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c},  {a,b,d}, {a,c,d}, {b,c,d}, {a,b,c,d}

Solution:The total number of subsets of any given set is equal to 2^ (no. of elements in the set). If we carefully notice it is nothing but binary numbers from 0 to 15 which can be shown as below:

0000

{}

0001

{a}

0010

{b}

0011

{a, b}

0100

{c}

0101

{a, c}

0110

{b, c}

0111

{a, b, c}

1000

{d}

1001

{a, d}

1010

{b, d}

1011

{a, b, d}

1100

{c, d}

1101

{a, c, d}

1110

{b, c, d}

1111

{a, b, c, d}

Starting from right, 1 at ith position shows that the ith element of the set is present as 0 shows that the element is absent. Therefore, what we have to do is just generate the binary numbers from 0 to 2^n – 1, where n is the length of the set or the numbers of elements in the set.

// A Java program to print all subsets of a set import java.io.IOException; import java.util.Scanner;  class Main {     // Print all subsets of given set[]     static void printSubsets(char set[])     {         int n = set.length;          // Run a loop for printing all 2^n         // subsets one by obe         for (int i = 0; i < (1<<n); i++)         {             System.out.print("{ ");              // Print current subset             for (int j = 0; j < n; j++)                  // (1<<j) is a number with jth bit 1                 // so when we 'and' them with the                 // subset number we get which numbers                 // are present in the subset and which                 // are not                 if ((i & (1 << j)) > 0)                     System.out.print(set[j] + " ");              System.out.println("}");         }     }      // Driver code     public static void main(String[] args)     {         char set[] = {'a', 'b', 'c'};         printSubsets(set);     } }

Output:

{ } { a } { b } { a b } { c } { a c } { b c } { a b c }

This article is contributed by Nikhil Tekwani. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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