How to balance binary tree in PHP without rotating parent?

[Submiss]

I will try to make myself as clear as possible. Based from Adjacency List Model: http://articles.sitepoint.com/article/hierarchical-data-databaseI need a way to balance this tree\[code\] 0 / \ 1 2 / / \ 3 4 5 \ \ 6 7\[/code\]to something like:\[code\] 0 / \ 1 2 / \ / \ 3 4 5 6 / 7\[/code\]Based from the sample Code:\[code\]<?php function display_children($parent, $level) { $result = mysql_query('SELECT title FROM tree '. 'WHERE parent="'.$parent.'";'); while ($row = mysql_fetch_array($result)) { echo str_repeat(' ',$level).$row['title']."\n"; display_children($row['title'], $level+1); } } ?>\[/code\]I modified the code so it can output a flat html table like this:$super_parent = '0000'left Node entries into flat list:\[code\] ____________________________________________________| No. | Date of Entry | Account ID | Placement|------------------------------------------------------| 1 | 2010-08-24 11:19:19 | 1111a | a || 2 | 2010-08-24 11:19:19 | 22221a_a | a || 3 | 2010-08-24 11:19:19 | 33_2aa | b | | 4 | 2010-08-24 11:19:19 | 33_2Ra | a | | 5 | 2010-08-24 11:19:19 | 22221a_b | b || 6 | 2010-08-24 11:19:19 | 33_2ba | a || 7 | 2010-08-24 11:19:19 | 33_2bb | b |------------------------------------------------------\[/code\]But I need a way to reorganize all this into a balanced tree without moving or rotating the parent. Although I can think of creating a duplicate table in the db and do a second query to display or create another Binaray tree, I thought it may be possible to reorganize a flat tree like this into:\[code\] 0 / \ 1 2 / \ / \ 3 4 5 6 / 7\[/code\]From left to right. 0 represents the parent or super_parent 0000.The reason I would like to do this is so I can create a virtual tree from the original tree that will be the basis of another algorithm in my project.Thanks in advance.Bob