DFS algorithm vs Parent-child in tree category - algorithm

Question

I need to implement a category tree like this:
laguages
.... Web
........ PHP
........ Python
........ HTML
.... System
........ C
........ C++
........ GO
........ RUST
So I have a table like this:
id | title | parent_id
1 | system| 0
2 | c | 1
3 | c++ | 1
4 | rust | 1
5 | web | 0
6 | php | 5
7 | python| 5
8 | html | 5
If i want to implement tree structure I have two solutions.
using a recursive function and create a parent-child array
using
DFS search to make this structure that I need to add left and
right column in the database table.
So my question is: what is deferences between this two solutions? and which one is better?

Answer 1

If the search operations will be more frequent, I would suggest array based approach because of the advantage of random access. In tree based structures, the search operations tend to be O(height) costly and the best height for balanced trees is O(log n).
On the contrary if update operations are more frequent, then I would go for Tree-based approach, since insertion and deletion is not very efficient in arrays due to shifting of elements involved.
Custom Approach
My Approach would have been the adjacency list data structure if, your child arrays Web or System are reasonably small. One could access the list for Web or System in constant time O(1) . Coming to deletion linked lists overcome arrays in case of insertion and deletions, and since the lists are not that long, search wont cause that much of problem time-wise.

Answer 2

I think if the three structure isn't more than what you described (2 levels) and not n levels isn't a right question but one of things you should have in mind.
in php =script language we do it much simple(the case of 2 levels) :
<?php
$source=Array(' system',Array(' php ',' c++ ',' html '),' web ',Array(' c ',' rust ',' python'));
function br(){echo('<br>');}
function printr($ar){
if(is_array($ar)){
foreach($ar as $key){
print(' |____'.$key);
br();
}
}else{
print('['.$ar.']');br();
}
return true;
}
array_map("printr", $source);
?>
the output:
[ system]
|____ php
|____ c++
|____ html
[ web ]
|____ c
|____ rust
|____ python
this array :
$source=Array(
' system',
Array(' php ',' c++ ',' html '),
' web ',
Array(' c ',' rust ',' python')
);
you should obtain it with a "generator" input from a form ,from a internal file created with another generator (web,compiler any kind)...
the maximum results comes when perfect input optimizations is stored in a intelligent structure can avoid use of LOTS CALCULATIONS ,Iterations( DFS algorithm or Parent-child or any OTHER method)
/*
Also using of serialize
functions you can store an entirely array,
unserialize will help you to restore your array
*/
$source=unserialize($from_a_table_1_row_forever);
// $from_a_table_1_row_forever=obtained from some your function to read it from a database,file ...etc
//now is good to use in memory,i mean that multi array
//when you want to store changes in some generator:
$for_a_table_1_row_forever=serialize($source);
good_to_write_it_in_a_single_table_row($for_a_table_1_row_forever);
// (some your function to write in a database,file ...etc)