Two sorted files containing sn and sm records respectively can be merged together to obtain one sorted file in time O(sn + 8m). When more than two sorted files are to be merged together, the merge can be accomplished by repeatedly merging sorted files in pairs. Thus, if four files X; of size si, 1 < i < 4 are to be merged we could first merge X1 and X2 to get a file Y1. Then we could merge Y1 and X3 to get Y2. Finally, Y2 and X4 can be merged to obtain the desired sorted file. Alternatively, we could first merge X1 and X2 getting Yı, then merge X3 and X4 getting Y2 and finally Yı and Y2 getting the desired sorted file. Given n sorted files X; of sizes si, 1 < i < n there are many ways in which to pairwise merge them into a sorted file. Different pairings require differing amounts of computing time. (a) Give C/C++ pseudocode for a greedy algorithm to determine an optimal (i.e., one requiring the fewest comparisons) way to pairwise merge n sorted files together. (b) How much time does your algorithm require? (c) Does your algorithm always find the optimal pairwise merge? Either sketch a proof or give a counter-example.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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1. Greedy Pairwise Merge.
Two sorted files containing sSn and sm records respectively can be merged together to obtain one sorted
file in time O(8n + Sm). When more than two sorted files are to be merged together, the merge can
be accomplished by repeatedly merging sorted files in pairs. Thus, if four files X; of size si, 1 sis 4
are to be merged we could first merge X1 and X2 to get a file Y1. Then we could merge Yı and X3
to get Y2. Finally, Y2 and X4 can be merged to obtain the desired sorted file. Alternatively, we could
first merge X1 and X2 getting Y1, then merge X3 and X4 getting Y2 and finally Y1 and Y2 getting the
desired sorted file.
Given n sorted files X; of sizes s;, 1 < i < n there are many ways in which to pairwise merge them
into a sorted file. Different pairings require differing amounts of computing time.
(a) Give C/C++ pseudocode for a greedy algorithm to determine an optimal (i.e., one requiring the
fewest comparisons) way to pairwise merge n sorted files together.
(b) How much time does your algorithm require?
(c) Does your algorithm always find the optimal pairwise merge? Either sketch a proof or give a
counter-example.
Transcribed Image Text:1. Greedy Pairwise Merge. Two sorted files containing sSn and sm records respectively can be merged together to obtain one sorted file in time O(8n + Sm). When more than two sorted files are to be merged together, the merge can be accomplished by repeatedly merging sorted files in pairs. Thus, if four files X; of size si, 1 sis 4 are to be merged we could first merge X1 and X2 to get a file Y1. Then we could merge Yı and X3 to get Y2. Finally, Y2 and X4 can be merged to obtain the desired sorted file. Alternatively, we could first merge X1 and X2 getting Y1, then merge X3 and X4 getting Y2 and finally Y1 and Y2 getting the desired sorted file. Given n sorted files X; of sizes s;, 1 < i < n there are many ways in which to pairwise merge them into a sorted file. Different pairings require differing amounts of computing time. (a) Give C/C++ pseudocode for a greedy algorithm to determine an optimal (i.e., one requiring the fewest comparisons) way to pairwise merge n sorted files together. (b) How much time does your algorithm require? (c) Does your algorithm always find the optimal pairwise merge? Either sketch a proof or give a counter-example.
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