Method Subsets

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Subsets<T>(IEnumerable<T>)

Returns a sequence of IList<T> representing all of the subsets of any size that are part of the original sequence. In mathematics, it is equivalent to the power set of a set.

Declaration
public static IEnumerable<IList<T>> Subsets<T>(this IEnumerable<T> sequence)
Parameters
Type Name Description
IEnumerable<T> sequence

Sequence for which to produce subsets
Returns
Type Description
IEnumerable<IList<T>>

A sequence of lists that represent the all subsets of the original sequence
Type Parameters
Name Description
T

The type of the elements in the sequence
Remarks

This operator produces all of the subsets of a given sequence. Subsets are returned in increasing cardinality, starting with the empty set and terminating with the entire original sequence. Subsets are produced in a deferred, streaming manner; however, each subset is returned as a materialized list. There are 2^N subsets of a given sequence, where N = sequence.Count().

This method is implemented by using deferred execution. However, sequence will be consumed in it's entirety immediately when first element of the returned sequence is consumed.

Examples

The following code example demonstrates how to get all subsets of a sequence using Subsets.

var sequence = Enumerable.Range(0, 4);

// check that sequence starts with a known sequence of values
var result = sequence
    .Subsets();

Console.WriteLine(
    "[" + Environment.NewLine + 
    string.Join(
        ", " + Environment.NewLine,
        result.Select(c => "   [" + string.Join(", ", c) + "]")) +
    Environment.NewLine + "]");

// This code produces the following output:
// [
//    [],
//    [0],
//    [1],
//    [2],
//    [3],
//    [0, 1],
//    [0, 2],
//    [0, 3],
//    [1, 2],
//    [1, 3],
//    [2, 3],
//    [0, 1, 2],
//    [0, 1, 3],
//    [0, 2, 3],
//    [1, 2, 3],
//    [0, 1, 2, 3]
// ]
Exceptions
Type Condition
ArgumentNullException

sequence is null
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Subsets<T>(IEnumerable<T>, int)

Returns a sequence of IList<T> representing all subsets of a given size that are part of the original sequence. In mathematics, it is equivalent to the combinations or k-subsets of a set.

Declaration
public static IEnumerable<IList<T>> Subsets<T>(this IEnumerable<T> sequence, int subsetSize)
Parameters
Type Name Description
IEnumerable<T> sequence

Sequence for which to produce subsets
int subsetSize

The size of the subsets to produce
Returns
Type Description
IEnumerable<IList<T>>

A sequence of lists that represents of K-sized subsets of the original sequence
Type Parameters
Name Description
T

The type of the elements in the sequence
Examples

The following code example demonstrates how get all subsets of a particular length using Subsets.

var sequence = Enumerable.Range(0, 4);

// check that sequence starts with a known sequence of values
var result = sequence
    .Subsets(2);

Console.WriteLine(
    "[" + Environment.NewLine + 
    string.Join(
        ", " + Environment.NewLine,
        result.Select(c => "   [" + string.Join(", ", c) + "]")) +
    Environment.NewLine + "]");

// This code produces the following output:
// [
//    [0, 1],
//    [0, 2],
//    [0, 3],
//    [1, 2],
//    [1, 3],
//    [2, 3]
// ]
Exceptions
Type Condition
ArgumentNullException

sequence is null
ArgumentOutOfRangeException

subsetSize is less than 0.