3.27

Let's put into the black box whole set [math]\displaystyle{ S=\{x_i\}_{i=1}^n }[/math]. If [math]\displaystyle{ bb(S) }[/math] is True, then such a subset exists and we can go on:

1. R:=S
2. for i:=1 to n do
   1. If [math]\displaystyle{ bb(R/\{x_i\}) }[/math] is True then [math]\displaystyle{ R:=R/\{x_i\} }[/math]

When this iteration is finished R will be subset of S that adds up to k.

Above solution works even when there are multiple subsets that add up to k.

Back to Chapter 3