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The tree rotation renders the inorder traversal of the binary tree invariant. This implies the order of the elements is not affected when a rotation is performed in any part of the tree. Here are the inorder traversals of the trees shown above: Left tree: ((A, P, B), Q, C) Right tree: (A, P, (B, Q, C))
Rotation distance was first defined by Karel Čulík II and Derick Wood in 1982. [1] Every two n-node binary trees have rotation distance at most 2n − 6, and some pairs of trees have exactly this distance. The computational complexity of computing the rotation distance is unknown. [2]
This rotation assumes that X has a left child (or subtree). X's left child, R, becomes X's parent node and R's right child becomes X's new left child. This rotation is done to balance the tree; specifically when the left subtree of node X has a significantly (depending on the type of tree) greater height than its right subtree.
This rotation assumes that X has a right child (or subtree). X's right child, R, becomes X's parent node and R's left child becomes X's new right child. This rotation is done to balance the tree; specifically when the right subtree of node X has a significantly (depends on the type of tree) greater height than its left subtree.
The increase in height can increase the height of its ancestors, possibly invalidating the AVL invariant of those nodes. This can be fixed either with a double rotation if invalid at the parent or a single left rotation if invalid higher in the tree, in both cases restoring the height for any further ancestor nodes.
Balancing a k-d tree requires care because k-d trees are sorted in multiple dimensions, so the tree-rotation technique cannot be used to balance them as this may break the invariant. Several variants of balanced k-d trees exist. They include divided k-d tree, pseudo k-d tree, K-D-B-tree, hB-tree and Bkd-tree.
The three-field system is a regime of crop rotation in which a field is planted with one set of crops one year, a different set in the second year, and left fallow in the third year. A set of crops is rotated from one field to another.
In forestry rotation analysis, economically optimum rotation can be defined as “that age of rotation when the harvest of stumpage will generate the maximum revenue or economic yield”. In an economically optimum forest rotation analysis, the decision regarding optimum rotation age is undertake by calculating the maximum net present value. It ...