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C++ program to print all possible subset of a set

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mahmoud2506
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2022-05-05
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Print all possible subset of a set

Example:

    input : {1,2,3,4}
    output :
            {}
            {1}
            {2}
            {1,2}
            {3}
            {1,3}
            {2,3}
            {1,2,3}
            {4}
            {1,4}
            {2,4}
            {1,2,4}
            {3,4}
            {1,3,4}
            {2,3,4}
            {1,2,3,4}

Explanation:

The total number of possible subset a set can have is 2^n, where n is the number of elements in the set.

We can generate all possible subset using binary counter.

For example:

Consider a set 'A' having elements {a, b, c}. So we will generate binary number upto 2^n - 1 (as we will include 0 also).

  • Here n is 3 so we will generate binary number upto 2^3 - 1 (i.e 8-1 = 7)
  • Then we will check which bit in binary counter is set or unset.
  • If ith bit is set , include ith element from the set in current subset.
  • If ith bit is unset , exclude ith element from the set in current subset.
Binary counter subset formed Explanation
000 { } as all bits are unset , so exclude all
001 { a } as only 1st bit is set , we will include only 1st element from the set i.e 'a'
010 { b } as only 2nd bit is set , we will include only 2nd element from the set i.e 'b'
011 { a ,b } as 1st and 2nd bits are set , we will include 1st and 2nd element from the set i.e 'a' and 'b'
100 { c } as only 3rd bit is set , we will include 3rd element from the set i.e 'c'
101 { a ,c } as 1st and 3rd bits are set , we will include 1st and 3rd element from the set i.e 'a' and 'c'
110 { b, c } as 2nd and 3rd bits are set , we will include 2nd and 3rd element from the set i.e 'b' and 'c'
111 { a , b, c } all bits are set , include all elements from the set.
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All Answers

mahmoud2506
2022-05-05
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Program:

#include <bits/stdc++.h>
using namespace std;

void allPossibleSubset(int arr[], int n)
{
    int count = pow(2, n);
    // The outer for loop will run 2^n times to print all subset .
    // Here variable i will act as a binary counter
    for (int i = 0; i < count; i++) {
        // The inner for loop will run n times , 
        // As the maximum number of elements a set can have is n
        // This loop will generate a subset
        for (int j = 0; j < n; j++) {
            // This if condition will check if jth bit in 
            // binary representation of  i  is set or not
            // if the value of (i & (1 << j)) is not 0 , 
            // include arr[j] in the current subset
            // otherwise exclude arr[j]
            if ((i & (1 << j)) != 0)
                cout << arr[j] << " ";
        }
        cout << "\n";
    }
}

int main()
{
    int n;
    
    cout << "Enter size of the set\n";
    cin >> n;

    int arr[n];
    cout << "Enter Elements of the set\n";
    for (int i = 0; i < n; i++)
        cin >> arr[i];

    allPossibleSubset(arr, n);

    return 0;
}

Output

 
Enter size of the set
4
Enter Elements of the set
1 2 3 4

1
2
1 2
3
1 3
2 3
1 2 3
4
1 4
2 4
1 2 4
3 4
1 3 4
2 3 4
1 2 3 4

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