Determine the boxes containing pearls

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Assignment:

Suppose you are given a set of small boxes, numbered 1 to n, identical in every respect except that each of the first p contain a pearl whereas the remaining n - p are empty. You also have two magic wands that can each test whether a box is empty or not in a single touch, except that a wand disappears if you test it on an empty box. Show that, without knowing the value of p, you can use the two wands to determine all the boxes containing pearls using at most o(n) wand touches.

Express, as a function of n, the asymptotic number of wand touches needed. Give the algorithm of your solution to this wand-pearl problem and analyze it. Note that o(n) (little-oh of n) means strictly less than n in an asymptotic sense, so f(n) = o(g(n)) means for all c > 0 there exists some m > 0 such that 0 ≤ f(n) < cg(n) for all n ≥ m. The value of m must not depend on n, but may depend on c.

Reference no: EM133267985

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