Calculate time complexity using amortized analysis

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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Calculate time complexity using amortized analysis

Please calculate the time complexity of below pseudocode.
for (i=1; i<n; i++)
{
for (j-0; j<n; j=j+5)
if (j mod i == 0)
do operation n² times
else
do operation 2 times
}
}
Transcribed Image Text:Please calculate the time complexity of below pseudocode. for (i=1; i<n; i++) { for (j-0; j<n; j=j+5) if (j mod i == 0) do operation n² times else do operation 2 times } }
Expert Solution
Step 1

Amortized analysis:

  • Amortized Analysis is utilized in algorithms when one operation is relatively slow but the majority of all the other operations are much quicker.
  • Programmers use Amortized Analysis to examine a sequence of processes and ensure a worst-case average time that is less than the worst-case time of a, particularly costly activity.
  • Amortized complexity analysis is most often used for data structures having persistent states between actions.
  • The underlying notion is that a costly operation might change the situation so that the worst-case scenario cannot occur again for a long period, thus amortizing its cost.
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