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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]
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 ...
This motivates the following general definition: For a string s over an alphabet Σ, let shift(s) denote the set of circular shifts of s, and for a set L of strings, let shift(L) denote the set of all circular shifts of strings in L. If L is a cyclic code, then shift(L) ⊆ L; this is a necessary condition for L being a cyclic language.
The rotation distance between any two binary trees with the same number of nodes is the minimum number of rotations needed to transform one into the other. With this distance, the set of n-node binary trees becomes a metric space: the distance is symmetric, positive when given two different trees, and satisfies the triangle inequality.
The size of an internal node is the sum of sizes of its two children, plus one: (size[n] = size[n.left] + size[n.right] + 1). Based on the size, one defines the weight to be weight[n] = size[n] + 1. [a] Weight has the advantage that the weight of a node is simply the sum of the weights of its left and right children. Binary tree rotations.
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
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 by subtracting the exponents and using the barrel shifter to shift the smaller number to the right ...
An isoclinic rotation will form a Villarceau circle on the torus, while a simple rotation will form a circle parallel or perpendicular to the central axis. [ 1 ] For each rotation R of 4-space (fixing the origin), there is at least one pair of orthogonal 2-planes A and B each of which is invariant and whose direct sum A ⊕ B is all of 4-space.