[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 →