2.) Analysis i <-- n; while(i > 1) { j = i; //%% CAUTION: this DOES NOT START AT O while (j

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
Chapter1: Introduction
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2.) Analysis
i <-- n;
while(i > 1) {
j = i;
//%% CAUTION: this DOES NOT START AT O
while (j<n) {
k <-- 0;
while (kn) {
k = k + 2;
}
j <-- j * 2;
}
i <i / 2;
}
What is the asymptotic upper bound of the code above?
Transcribed Image Text:2.) Analysis i <-- n; while(i > 1) { j = i; //%% CAUTION: this DOES NOT START AT O while (j<n) { k <-- 0; while (kn) { k = k + 2; } j <-- j * 2; } i <i / 2; } What is the asymptotic upper bound of the code above?
Expert Solution
Step 1

O (n log2 n) 
 i values in the outer while loop are n, n/2, n/4, ..., 4, 2, 1     so, number of iterations of the outer while loop is O(log n) middle loop iterates from i to n     so, number of iterations of the middle while loop is n-i = O(n) k values in the outer loop are 1, 2, 4, 8, ..., n/4, n/2, n     so,

 

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