Please write an analysis report for the program with the following structure and instructions: Analysis Report Structure

Analytical

Summary of analytical and empirical results.$$

Performance critical code section$($s$)$

Compress trivial code segments to better present the critical code control structure.$$ This is typically found in the main$()$ method, or one level of abstraction beneath.$$

Step count analysis of each critical section.$$

Space analysis of each critical section.

Determine overall space and time complexity.

Predict runtime performance

Empirical

Describe test plan and rational for test data sets

Graph runtime performance with trend line

Determine program limitations given $3$ second time constraint and $256$MB working space.