ef find$\_$overlap$($w$1,$ w$2)$:

# Find the longest overlap of w$1$ suffix and w$2$ prefix

max$\_$overlap $=0$

for i in range$(1,$ min$($len$($w$1),$ len$($w$2)))$:

if w$1[-$i:$]==$ w$2[$:i$]$:

max$\_$overlap $=$ i

return max$\_$overlap

def dfs$($word$,$ word$\_$list, visited, current$\_$path, current$\_$score, best$\_$path, best$\_$score$)$:

visited.add$($word$)$

current$\_$path.append$($word$)$

# Check if current path is better than the best path

if current$\_$score $>$ best$\_$score$[0]$:

best$\_$score$[0]=$ current$\_$score$[0]$

best$\_$path$[$:$]=$ current$\_$path$[$:$]$

for next$\_$word in word$\_$list:

if next$\_$word not in visited:

overlap $=$ find$\_$overlap$($word$,$ next$\_$word$)$

if overlap $>1$:

new$\_$score $=$ current$\_$score$[0]+$ overlap$**2$

dfs$($next$\_$word, word$\_$list, visited, current$\_$path, $[$new$\_$score$],$ best$\_$path, best$\_$score$)$

visited.remove$($word$)$

current$\_$path.pop$()$

def find$\_$best$\_$wordsnake$($words$)$:

best$\_$path $=[]$

best$\_$score $=[0]$ # Use a list to allow modification within dfs

for word in words:

dfs$($word$,$ words, set$(),[],[0],$ best$\_$path, best$\_$score$)$

return best$\_$path, best$\_$score$[0]$

def main$()$:

import sys

input $=$ sys$.$stdin.read

data $=$ input$().$splitlines$()$

n $=$ int$($data$[0])$ # Number of words

words $=$ data$[1$:n$+1]$

best$\_$path, best$\_$score $=$ find$\_$best$\_$wordsnake$($words$)$

# Output the results

for word in best$\_$path:

print$($word$)$

print$($best$\_$score$)$

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

main$()$

For the code above please write an anlysis report with the following 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.