AVL tree rotations

acoustic, folk, soulful, warm

Listen on 93

Lyrics

[Verse 1]
Binary search trees gettin' heavy on one side
Balance factors screamin' negative two, can't hide
When your left child's subtree towers above the right
AVL rotation protocol ignites
Four cases memorize, LL and RR clean
LR and RL need that double rotation scene
Height difference triggers when we cross that line
Adelson-Velsky Landis keepin' search time fine

[Chorus]
Left-left rotate right, pivot on that parent node
Right-right rotate left, watch the structure decompose and reload
Left-right double spin, first left then right again
Right-left flip the script, balance factors back in check my friend
Logarithmic access guaranteed when trees stay tight
AVL rotations keep your data structure right

[Verse 2]
Check that balance factor after every insertion
Minus two or plus two means we need conversion
LL case simple, single right rotation flows
Grandparent becomes right child, that's how it goes
RR case mirror image, single left rotation
Parent moves up top in this transformation
Height of subtrees matters, count those levels deep
Self-balancing magic puts performance fears to sleep

[Chorus]
Left-left rotate right, pivot on that parent node
Right-right rotate left, watch the structure decompose and reload
Left-right double spin, first left then right again
Right-left flip the script, balance factors back in check my friend
Logarithmic access guaranteed when trees stay tight
AVL rotations keep your data structure right

[Bridge]
LR case tricky, gotta break it down in stages
First rotate left on child, rewrite those tree pages
Then rotate right on parent, now we're back in line
RL case opposite, but follows same design
Update heights bottom up, recalculate the metrics
Binary search property preserved through all gymnastics

[Verse 3]
Deletion triggers rotations just like insertion does
Trace back up that path, fix imbalance because
Every node stores height, compare left versus right
Absolute difference greater than one ain't right
Four rotation patterns burned into your brain
Constant time operations keep the tree domain
Worst case search and insert stay log N tight
AVL mathematics guarantee optimal sight

[Outro]
Balance factors guide the way, negative one to positive one
Outside heavy needs single, inside heavy needs double done
Tree rotation mastery keeps your searches clean
AVL algorithm reign supreme

← Binary search tree operations | Red-black tree balancing →