Question

Let $S$ be a set of $n$ distinct real numbers and let $k$ be a positive integer with $1<k<n$. Give a $T(n)$ time RAM algorithm to determine the middle $k$ entries of $S$. The input entries of $S$ should not be assumed ordered; however, if the elements of $S$ are such that $s_1<s_2<\ldots<s_n$, then the output of the algorithm is the (unsorted) set $$ \left\{s_{\frac{n-k}{2}}, s_{\frac{n-k}{2}+1}, \ldots, s_{\frac{n+k}{2}-1}\right\} $$ $T(n)$, sorting $S$ should not be part of the algorithm.

   Let $S$ be a set of $n$ distinct real numbers and let $k$ be a positive integer with $1<k<n$. Give a $T(n)$ time RAM algorithm to determine the middle $k$ entries of $S$. The input entries of $S$ should not be assumed ordered; however, if the elements of $S$ are such that $s_1<s_2<\ldots<s_n$, then the output of the algorithm is the (unsorted) set

$$
\left\{s_{\frac{n-k}{2}}, s_{\frac{n-k}{2}+1}, \ldots, s_{\frac{n+k}{2}-1}\right\}
$$

$T(n)$, sorting $S$ should not be part of the algorithm.

Algorithms Sequential and Parallel: A unified Approach

Russ Miller,… 1st Edition

Chapter 9, Problem 9

Instant Answer

Step 1

The middle $ k $ entries correspond to the elements at indices $ \frac{n-k}{2} $ to $ \frac{n+k}{2}-1 $ in the sorted version of $ S $. Show more…

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Let $S$ be a set of $n$ distinct real numbers and let $k$ be a positive integer with $1<k<n$. Give a $T(n)$ time RAM algorithm to determine the middle $k$ entries of $S$. The input entries of $S$ should not be assumed ordered; however, if the elements of $S$ are such that $s_1<s_2<\ldots<s_n$, then the output of the algorithm is the (unsorted) set $$ \left\{s_{\frac{n-k}{2}}, s_{\frac{n-k}{2}+1}, \ldots, s_{\frac{n+k}{2}-1}\right\} $$ $T(n)$, sorting $S$ should not be part of the algorithm.

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