help ... how can make this program

[taroot]

how can make program with vb
using this alogarithm
subsets of a set

three algorithms are described to answer the problem how to generate all the subsets of a finite set

algorithm : to generate all the subsets of a finite set.

input: a set a{x1,x2,...,xn}
output: all the subsets of s

the idea behind the algorith is ti construct a characteristis function to identify the elements of s for each subset. if s has n elements , the binary strtings with n digits serve the purpose. for a given binary string , each digit corresponds to an x in s. if the digit is 1 then include x in the subset; if the digit is 0 then exclude x .

method : m <--- 0

while m < 2^n :

express m as a binary string of length n
(m=a1 2^n + a2 2n^n-1 + ... + an 2^0)
define the characteristic function
( ci <--- ai for i=1,2,...,n)
choose the subset y correspnding to m
(if ci = 1 then include xi in y)
record y (print or store in a file)
m <--- m+1

Example 1 : find all the subset of s ={a,b,c} using algorith

method : if the set s is empty , then fiy is the only subset of s ; record fiy

otherwise select arbitraily an element x ( s
find all the subsets of s - {X} and
for each subset y of s={x} , record {x} U y .

the idea behind this algorith is to use a recursive aproach . the statment find all the subset of (s-{X}) invoves a recursive call. the sets s,s-{x} , ... form a strictly decreasing sequence , for each set is a proper subset of the noe befor. the sequence must end with the empty set , fiy , since s is finite
hence the recursion will terminate

[jemidiah]

Could you elaborate on this section?

Originally posted by taroot
otherwise select arbitraily an element x ( s
find all the subsets of s - {X} and
for each subset y of s={x} , record {x} U y .