The rotation of the tree of the binary tree learning notes
Tree rotation is a subtree adjustment operation in a binary tree. Each rotation does not affect the result of the in-order traversal of the binary tree.
Tree rotation is often used where you need to adjust the local balance of the tree.
Left-handed and right-handed
The rotation of the tree has two basic operations, left-handed (counterclockwise rotation) and right-handed (clockwise rotation).
Tree rotation consists of two different ways, left rotation (with P as the axis of rotation) and right rotation (with Q as the axis of rotation). Both rotations are mirror images and are inverse to each other.
The following figure shows the initial and final states of the subtree during the two tree rotations.
+---+ +---+ | Q | | P | +---+ +---+ / \ right rotation / \ +---+ +---+ -------------> +---+ +---+ | P | | Z | | X | | Q | +---+ +---+ <------------- +---+ +---+ / \ left rotation / \ +---+ +---+ +---+ +---+ | X | | Y | | Y | | Z | +---+ +---+ +---+ +---+The detailed steps of the right rotation are as shown in the following three steps: R0, R1, and R2, and the left rotation is as shown in the three steps of L0, L1, and L2.
__ / \ +---+ / +---+ | Q | / | Q | +---+ +---+ +---+ / +---+ +---+ | P | / \ R1 | P |/ / \ +---+ | Q | R0 +---+ / +---+ -----> +---+ / +---+ R2 | P | +---+ -----> / \ / | Z | / / | Z | -----> +---+ / \ +---+ +---+ +---+ +---+ +---+ +---+ / \ +---+ +---+ | X | | Y | | X | | Y | +---+ +---+ | P | | Z | +---+ +---+ +---+ +---+ | X | | Q | +---+ +---+ __ +---+ +---+ / \ / \ / \ +---+ +---+ L2 +---+ \ +---+ L0 +---+ +---+ | X | | Y | <----- | P | \ | P | <----- | Y | | Z | +---+ +---+ +---+ \ +---+ L1 +---+ +---+ +---+ +---+ / \ \| Q | <----- / \ | Q | +---+ \ +---+ +---+ \ +---+ | X | \ \ | X | \ / \ +---+ +---+ +---+ +---+ +---+ +---+ | Y | | Z | | Y | | Z | +---+ +---+ +---+ +---+
AVL tree adjustment
The basic operation of the AVL tree generally involves operating the same algorithm as the unbalanced binary search tree. But do the so-called "AVL rotation" one or more times in advance or later.
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