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In a binary search tree, a right rotation is the movement of a node, X, down to the right. 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 ...
There are also double rotations, which are combinations of left and right rotations. A double left rotation at X can be defined to be a right rotation at the right child of X followed by a left rotation at X; similarly, a double right rotation at X can be defined to be a left rotation at the left child of X followed by a right rotation at X.
It can also be described as the shortest path distance in a rotation graph, a graph that has a vertex for each binary tree on a given left-to-right sequence of nodes and an edge for each rotation between two trees. [2] This rotation graph is exactly the graph of vertices and edges of an associahedron. [3]
A common usage of a barrel shifter is in the hardware implementation of floating-point arithmetic. For a floating-point add or subtract operation, the significands of the two numbers must be aligned, which requires shifting the smaller number to the right, increasing its exponent, until it matches the exponent of the larger number. This is done ...
A geometric rotation transforms lines to lines, and preserves ratios of distances between points. From these properties it can be shown that a rotation is a linear transformation of the vectors, and thus can be written in matrix form, Q p .
In computer programming, a bitwise rotation, also known as a circular shift, is a bitwise operation that shifts all bits of its operand. Unlike an arithmetic shift , a circular shift does not preserve a number's sign bit or distinguish a floating-point number 's exponent from its significand .
The formal definition of an arithmetic shift, from Federal Standard 1037C is that it is: . A shift, applied to the representation of a number in a fixed radix numeration system and in a fixed-point representation system, and in which only the characters representing the fixed-point part of the number are moved.
The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its fixed points. They exist only in n = 3. The plane of rotation is a plane that is invariant under the rotation. Unlike the axis, its points are not fixed themselves.