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Evaluate this product $n \times \frac{n-1}{2} \times \dots \times \frac{n-(2^k-1)}{2^k}$
For $k = \lfloor \log_{2}(n+1) \rfloor - 1$ evaluate
$n \times \frac{n-1}{2} \times\frac{n-3}{4} \times \frac{n-7}{8} \times \dots \times \frac{n-(2^{k}-1)}{2^k}$
So the product goes up to $k$ and I ...
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amortized analysis
a) define f(k) as the largest power of 2 that divides k.
For example, f(25) = 1, f(42) = 2, f(144) = 16.
What is ${1 \over k}\sum_1^k f(k)$?
b) define f(k) as the square of largest power of 2 that ...
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