3.27
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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:
- R:=S
- for i:=1 to n do
- 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.
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