Calculate the time complexity of this program code in each line, especially in the merge sort process, the total, and how the Big O notation is in the end. Give an explanation of the time complexity of each line, why it has that time complexity, and the summation flow of the time complexity until it ends up having the Big O that you got.

import sys

from PyQt$5.$QtWidgets import QApplication, QMainWindow, QComboBox, QPushButton, QTableWidget, QTableWidgetItem, QVBoxLayout, QWidget

from PyQt$5.$QtCore import Qt

class MainWindow$($QMainWindow$)$:

def $\_\_$init$\_\_($self$)$:

super$().\_\_$init$\_\_()$

self.setWindowTitle$("$Merge Sort GUI"$)$

self.central$\_$widget $=$ QWidget$()$

self.setCentralWidget$($self$.$central$\_$widget$)$

self.layout $=$ QVBoxLayout$()$

self.central$\_$widget.setLayout$($self$.$layout$)$

# Combo box for sorting options

self.sort$\_$combo $=$ QComboBox$()$

self.sort$\_$combo.addItems$(["$ID$",$ "Name", "GPA"$])$

self.layout.addWidget$($self$.$sort$\_$combo$)$

# Combo box for grouping by angkatan

self.group$\_$combo $=$ QComboBox$()$

self.group$\_$combo.addItems$(["$All Generations"$]+[$str$($year$)$ for year in range$(2016,2024)])$

self.layout.addWidget$($self$.$group$\_$combo$)$

# Button to perform sorting

self.sort$\_$button $=$ QPushButton$("$Sort$")$

self.sort$\_$button.clicked.connect$($self$.$perform$\_$sort$)$

self.layout.addWidget$($self$.$sort$\_$button$)$

# Table to display sorted data

self.table $=$ QTableWidget$()$

self.layout.addWidget$($self$.$table$)$

def merge$\_$sort$($self$,$ arr, key$)$:

if len$($arr$)<=1$: #O$(1)$

return arr

mid $=$ len$($arr$)//2$

left$\_$half $=$ arr$[$:mid$]$

right$\_$half $=$ arr$[$mid:$]$

left$\_$half $=$ self.merge$\_$sort$($left$\_$half, key$)$

right$\_$half $=$ self.merge$\_$sort$($right$\_$half, key$)$

return self.merge$($left$\_$half, right$\_$half, key$)$

def merge$($self$,$ left, right, key$)$:

result $=[]$

left$\_$index, right$\_$index $=0,0$

while left$\_$index $<$ len$($left$)$ and right$\_$index $<$ len$($right$)$:

if key $=="$ID$"$:

left$\_$val $=$ left$[$left$\_$index$][0]$

right$\_$val $=$ right$[$right$\_$index$][0]$

elif key $==$ "Name":

left$\_$val $=$ left$[$left$\_$index$][1]$

right$\_$val $=$ right$[$right$\_$index$][1]$

elif key $==$ "GPA":

right$\_$val $=$ left$[$left$\_$index$][2]$ #Descending

left$\_$val $=$ right$[$right$\_$index$][2]$

if left$\_$val $<$ right$\_$val:

result.append$($left$[$left$\_$index$])$

left$\_$index $+=1$

else:

result.append$($right$[$right$\_$index$])$

right$\_$index $+=1$

while left$\_$index $<$ len$($left$)$:

result.append$($left$[$left$\_$index$])$

left$\_$index $+=1$

while right$\_$index $<$ len$($right$)$:

result.append$($right$[$right$\_$index$])$

right$\_$index $+=1$

return result

def perform$\_$sort$($self$)$:

key $=$ self.sort$\_$combo.currentText$()$

group$\_$option $=$ self.group$\_$combo.currentText$()$

if group$\_$option $==$ "All Generations":

filtered$\_$data $=$ self.load$\_$student$\_$data$()$

else:

angkatan $=$ int$($group$\_$option$)$

filtered$\_$data $=[$student for student in self.load$\_$student$\_$data$()$ if int$($student$[0][2$:$4])==$ angkatan $\%2000]$

# Sort data

sorted$\_$data $=$ self.merge$\_$sort$($filtered$\_$data, key$)$

# Display sorted data in table

self.display$\_$data$($sorted$\_$data$)$

def display$\_$data$($self$,$ data$)$:

self.table.setRowCount$($len$($data$))$

self.table.setColumnCount$(3)$

self.table.setHorizontalHeaderLabels$(["$ID$",$ "Name", "GPA"$])$

for row, $($nim$,$ nama, ipk$)$ in enumerate$($data$)$:

nim$\_$item $=$ QTableWidgetItem$($str$($nim$))$

nim$\_$item.setTextAlignment$($Qt$.$AlignCenter$)$

self.table.setItem$($row$,0,$ nim$\_$item$)$

self.table.setItem$($row$,1,$ QTableWidgetItem$($nama$))$

ipk$\_$item $=$ QTableWidgetItem$($str$($ipk$))$

ipk$\_$item.setTextAlignment$($Qt$.$AlignCenter$)$

self.table.setItem$($row$,2,$ ipk$\_$item$)$

# Resize the columns to fit content

self.table.resizeColumnsToContents$()$

def load$\_$student$\_$data$($self$)$:

try:

with open$("$student$\_$data.txt$","$r$")$ as file:

lines $=$ file.readlines$()$

student$\_$data $=[$tuple$($line$.$strip$().$split$(","))$ for line in lines$]$

return student$\_$data

except FileNotFoundError:

print$("$File not found."$)$

return $[]$

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

app $=$ QApplication$($sys$.$argv$)$

window $=$ MainWindow$()$

window.setGeometry$(100,100,600,400)$

window.show$()$

sys$.$exit$($app$.$exec$\_())$