i was provided this solution based on this question previously posed but i am getting these two errors

are you able to assist me to recitfy these errors below using the file below.

Extend your program in main.lua to also do the following:

$$ Opens a text file called graph.txt which contains values to be inserted in an AVL$-$tree data

structure in the following format

o Value $($on a single line$)$

o For example the file defining the tree above contains the following:

A

E

I

O

U

B

C

D

You may assume that values are single letters and that there are no duplicates

$$ Add support for the following two commands to your system:

Sub$-$question Description

Q$2-$A

Command: showchildren

Parameters: $1$ letter

Behaviour: The system must read a letter from the standard input stream and output all of the

nodes which are children $($or grand$-$children or great grand$-$children etc.$)$ of that node $($in alphabetic

order$).$ If there are no children then None must be output.

Expected output on test data with input $($B$)$: A C D

Expected output on test data with input $($C$)$: D

Expected output on test data with input $($O$)$: I U

Expected output on test data with input $($A$)$: None

Q$2-$B

Command: insert

Parameters: $1$ letter

Behaviour: The system must read a letter from the standard input stream, insert that value into the

tree, restore the AVL property, then output the nodes in the order they would be reached by a

breadth first traversal

Expected output on test data with input $($Z$)$:

E

B O

A C I U

D Z

Error one when calling showChildren function

Enter command: showchildren

Enter Node Value: a A

lua: main.lua:$130$: attempt to call global 'showChildren' $($a nil value$)$

stack traceback:

main.lua:$130$: in main chunk

$[$C$]$: $?$

Erro two when calling insert function

Enter command: insert

Enter Value to Insert: Z

lua: main.lua:$75$: attempt to index local 'avlTree' $($a nil value$)$

stack traceback:

main.lua:$75$: in function 'insert'

main.lua:$134$: in main chunk

$[$C$]$: $?$

function loadgrid$($filename$)$

local file $=$ io$.$open$($filename $,"$r$")$

if not file then

print$("$Error: unable to open file"$)$

return

end

local grid $=\{\}$

for line in file:lines$()$ do

local row $=\{\}$

for num in line:gmatch$("\%$S$+")$ do

table.insert$($row$,$ tonumber$($num$))$

end

table.insert$($grid$,$ row$)$

end

file:close$()$

return grid

end

function readGraph$($filename$,$ avlTree$)$

local file $=$ io$.$open$(\text{'}$graph$.$txt$\text{'},"$r$")$

if file then

for line in file:lines$()$ do

local value $=$ line:match$("\%$a$")$

if value then

avlTree:insert$($value$)$

end

end

file:close$()$

else

print$("$Error could not open file name $"..$ filename$)$

end

end

$--$check if the cities are neighbours on the grid

function areneighbours$($city$1,$ city$2,$ grid$)$

if city$1>=0$ and city$1<$ #grid and city$2>=0$ and city$2<$ #grid$[$city$1+1]$ then

return grid$[$city$1+1][$city$2+1]>0$

else

return false

end

end

$--$check if the set of cities are connected by a valid path

function ispath$($grid $,$ cities$)$

$--$ local cities $\{\}$

for i $=1,$ #cities $-1$ do

if grid$[$cities$[$i$]][$cities$[$i$+1]]==0$ then

return $"$No$"$

end

end

return "Yes"

end

$--$Function to show children

function showchildren$($avlTree$,$ nodeValue$)$

local children $=$ avlTree:getChildren$($nodevalue$)$

if #children $>0$ then

table.sort$($children$)$

print$($table$.$concat$($children$,""))$

else

print$("$None$")$

end

end

$--$Function to insert into tree

function insert$($avlTree$,$ value$)$

avlTree:insert$($value$)$

$--$Perform first traversal

local queue $=\{$avlTree$.$root$\}$

local result $=\{\}$

while #queue $>0$ do

local currentNode $=$ table.remove$($queue$,1)$

table.insert$($result$,$ currentNode.value$)$

if currentNode.left then

table.insert$($queue$,$ currentNode.left$)$

end

if currentNode.right then

table.insert$($queue$,$ currentNode.right$)$

end

end

print$($table$.$concat$($result$,""))$

end

AVLNode $=\{$

value $=$ nil,

left $=$ nil,

right $=$ nil,

height $=1$

$\}$

AVLTree $=\{$

root $=$ nil

$\}$

$--$Main Program

local grid $=$ loadgrid$("$grid$.$txt$")$

$--$readGraph$("$graph$.$txt$",$ avlTree$)--$ this errors if i leave this uncommented.

$--$Standard input commands

while true do

io$.$write$("$Enter command: $")$

local command $=$ io$.$read$()$

if command $==$"areneighbours" then

local city$1,$ city$2=$ io$.$read$("*$n$","*$n$")$

local result $=$ areneighbours$($city$1,$ city$2,$ grid$)$ and "Yes" or $"$No$"$

print$($result$)$

elseif command $==$"ispath" then

local cities $=\{\}$

for city in io$.$read$()$:gmatch$("\%$S$+")$ do

table.insert$($cities$,$ tonumber$($city$))$

end