algorithm - AVL tree rotation and red-black tree color flips -

as know, insertion , deletion require o(log n). avl tree require o(log n), because need o(log n) insert , o(log n) rotation balance.

rb tree require o(log n), because need o(log n) insert, in introduction algorithms third edition, rb-insert-fixup need o(log n) case 1(color flips), , @ 2 times rotation. seems avl require 2o(log n), rb tree require 2o(log n)+c.

why think rb tree more faster avl in insertion? because rotation need more time color flips? rotation , color flips both require o(1), why rotation more time-consuming color flips? thanks!:)

if understand question correctly, yes true rb-trees , avl-trees both offer lookup, insertion, deletion in o(logn) time.

avl-trees more rigidly balanced rb-trees. attain this, lot of rotations required, time consuming. rb-trees unbalanced, have weaker rules balancing, need lesser operations insertion , deletion. consequence, lookup in avl-trees faster rb-trees, insertion , deletion faster in rb-trees.

edit

please read this blog post. point rb trees balance faster avl trees after insertion. yes, rotation take o(1) time in avl trees, @ 2 rotations need done, point of rotation still needs found, , time rotation becomes o(logn). whereas in rb trees, rebalancing after insertion runs in amortized constant time. so, o(1) amortized time color flips, not o(logn).