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Similar to Ternary Search
By 314rate, history, 6 years ago, In English

Hello!

For finding the minimum with Ternary Search we nead a function that respects this conditions :

for all a,b with A ≤ a < b ≤ x, we have f(a) < f(b), and

for all a,b with x ≤ a < b ≤ B, we have f(a) > f(b).

Is there an algorithm ( also running in logaritmic time ) for finding the minimum in a function like this :

for all a,b with A ≤ a < b ≤ x, we have f(a) <= f(b), and

 for all a,b with x ≤ a < b ≤ B, we have f(a) >= f(b).

Thank You!

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6 years ago, # |
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6 years ago, # |
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Short answer: No

Imagine running a ternary search in an array which contains n - 1 zeros and a single 1. Even if you compute f in n - 2 points you cannot be sure about the value of the last two points, given that all the n - 2 points had value 0. This means that, in fact, any search algorithm, and not just ternary search, will have worst case running time Θ(n).

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