Sets Problem

This is a discussion on Sets Problem within the C++ Programming forums, part of the General Programming Boards category; How do you write a recursive algorithm for finding all the subsets of a given number: i.e if 2 is ...

  1. #1
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    Sets Problem

    How do you write a recursive algorithm for finding all the subsets of a given number:
    i.e if 2 is entered it should give
    1,2,12
    and if it is 3
    1,2,3,12,13,23,123

    It has to be recursive and has you are allowed to use only 1 iteration. I know how do do this non-recursively but I'm not sure how to do it recursively.

    BTW this is a console application.

    Thanks for your help!

  2. #2
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    What's your best attempt?

    What do you think you should recurse on? What should be your stopping point?

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    I realized you have to recurse on size-1 and then iterate each with a number in front. i.e.
    for an input of size 5, the size 2 array will be:

    12
    13
    14
    15
    23
    24
    25
    34
    35
    45

    the size 3 array will be:

    123
    124
    125
    134
    135
    145
    234
    235
    245
    345

    The only changes are the numbers in bold, but I cant exactly figure out how to write the algorithm. The stopping point is going to be size one.
    Last edited by inevitable; 04-03-2008 at 10:01 AM.

  4. #4
    Registered User nepper271's Avatar
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    I believe you should do your recursion as:
    1 - The subsets of n are all subsets of n - 1, and all subsets of n - 1, each increased by the element n.
    ex:
    Code:
    P(2) = { O, {1}, {2}, {1,2} }
    P(3) = { O, {1} , {2} , {3} , {1,2} , {1,3} , {2,3} , {1,2,3} }
     = { O, {1}, {2}, {1,2} } U { OU{3}, {1}U{3}, {2}U{3} , {1,2}U{3} }
    where O is the empty set, and U is the union operator. See that we have a set of sets.

  5. #5
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    This uses a different recursive strategy. I need one that refers to it's previous set size rather than the previous n.
    Last edited by inevitable; 04-03-2008 at 12:24 PM.

  6. #6
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    Quote Originally Posted by inevitable View Post
    This uses a different recursive strategy. I need one that refers to it's previous set size rather than the previous n.
    not sure if it's exactly what you're looking for here, but to compute all possible combinations of X length words of values [1,Y-1], count from 0->(X^Y) in base y.

    here's something i c&p'd out of an old PHP project.

    Code:
    $test_base = 9;
    $steps_x = 5;
    $steps_y = pow($test_base,$steps_x);
    for($i=0;$i<$steps_y;$i++)
    {
    	$row = base_convert($i,10,$test_base);
    	print($row);
    }

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