Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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4. Consider an algorithm that works as follows: Starting with an input of size n, it
divides the input into two or more groups, solves each group separately, and then
combines the answers from each group to form its output.
Suppose the algorithm creates k groups of sizes n₁,...,nk. Then it takes the
algorithm O(n, log ni) time to solve the ith group whose size is nį and O(n + k)
time to divide the input into k groups and combine the partial results to generate
the output.
a.
Determine an upper bound on the running time of the whole algorithm
in terms of n. Note that k and the n's are not fixed values but depend instead
on the input.
b.
Now redo the question when it takes the algorithm O(n) time to solve
the ith group of size n; and O(n²+ k) time to divide the input into k and
groups
assemble the partial results to form the output.
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Transcribed Image Text:4. Consider an algorithm that works as follows: Starting with an input of size n, it divides the input into two or more groups, solves each group separately, and then combines the answers from each group to form its output. Suppose the algorithm creates k groups of sizes n₁,...,nk. Then it takes the algorithm O(n, log ni) time to solve the ith group whose size is nį and O(n + k) time to divide the input into k groups and combine the partial results to generate the output. a. Determine an upper bound on the running time of the whole algorithm in terms of n. Note that k and the n's are not fixed values but depend instead on the input. b. Now redo the question when it takes the algorithm O(n) time to solve the ith group of size n; and O(n²+ k) time to divide the input into k and groups assemble the partial results to form the output.
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