Another problem by fakalin.

A data structure has the entropy bound if all queries have amortized time \(O(\sum_k p_k \log 1/p_k)\), where \(p_k\) is the fraction of the time that key \(k\) is queried. It has the working-set property if the time to search for an element \(x_i\) is \(O(\log t_i)\), where \(t_i\) is the number of elements queried since the last access to \(x_i\). Prove that the working-set property implies the entropy bound.

This isn’t really a data structure problem, per se.
(Read the article)

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There is something disturbing about electric heating, especially if the electricity used is generated by thermodynamic processes, such as burning coal or natural gas. Lots of heat is sacrificed at the power plant to be able to turn a fraction of the input energy into this superb high-quality electricity that can do mechanical work. Then at the other end, an electric heater just turns it right back into waste heat without doing anything else useful.

But something useful can be done. Instead of straight heating elements, I suggest a server farm. Maybe box it up like an electric heater, sell the CPU cycles back while still getting the same heat out.

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