An algorithm to determine a subset sequence in O(n)?

Question

How can i aproach this problem by induction?

Suppose that you are given an algorithm as a black box you cannot see how it is designed it has the following properties: if you input any sequence of real numbers and an integer k, the algorithm will answer YES or NO indicating whether there is a subset of numbers whose sum is exactly k. Show how to use this black box to find the subset of a given sequence {X1, …., Xn} whose sum is k. You can use the black box O(n) times.

Any idea?

So the problem is to show how to use the black box to find the starting index of such a subset in a sequence of numbers? — Jordan, Sep 11 '13 at 19:14
The problem is about using induction with dynamic programming... — john nash, Sep 11 '13 at 23:46

score 4 · Answer 1 · answered Sep 11 '13 at 19:21

I'm not entirely convinced that induction is necessary here.

Here's my two cents:

Suppose you have a sequence of numbers S, and integer k, and you already know that there exists a subset of numbers whose sum is k. Now, remove a number from your sequence (call it i), and use your black box on what remains (using the same k as before).

If the algorithm returns YES on the new sequence, what does that tell you about i and any subset of S whose sum is k?
If the algorithm returns NO on the new sequence, what does that tell you about i and any subset of S whose sum is k?

This is the way to go. +1 for not explicitly answering a homework question. — Vincent van der Weele, Sep 11 '13 at 20:17

An algorithm to determine a subset sequence in O(n)?

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