Left-child Right-sibling Binary Tree
Every multi-way or k-ary tree structure studied in computer science admits a representation as a binary tree, which goes by various names including child-sibling representation, left-child, right-sibling binary tree, doubly chained tree or filial-heir chain. In a binary tree that represents a multi-way tree , each node corresponds to a node in and has two pointers: one to the node's first child, and one to its next sibling in . The children of a node thus form a singly-linked list. To find a node 's 'th child, one needs to traverse this list: procedure kth-child(n, k): child ← n.child while k ≠ 0 and child ≠ nil: child ← child.next-sibling k ← k − 1 return child ''// may return nil'' The process of converting from a k-ary tree to an LC-RS binary tree is sometimes called the '' Knuth transform''. To form a binary tree from an arbitrary k-ary tree by this method, the root of the original tree is made the root of the binary tree. The ...
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N-ary To Binary
-ary may refer to: * The arity of a function, operation, or relation ** -ary associativity, a specific rule attached to -ary functions *** -ary group, a generalization of group * The radix of a numerical representation system * The number of letters in an alphabet (formal languages) ** An -ary code *** An -ary Gray code *** An -ary Huffman code * An -ary tree See also * n- (other)#Mathematics, science and technology * Unary (other) * Binary (other) * Ternary (other) Ternary (from Latin ''ternarius'') or trinary is an adjective meaning "composed of three items". It can refer to: Mathematics and logic * Ternary numeral system, a base-3 counting system ** Balanced ternary, a positional numeral system, useful ...

Multi-way Tree
In computing, a rose tree is a term for the value of a Tree (data structure), tree data structure with a variable and unbounded number of branches per node. The term is mostly used in the functional programming community, e.g., in the context of the Bird–Meertens formalism. Apart from the multi-branching property, the most essential characteristic of rose trees is the coincidence of bisimilarity with Identity (object-oriented programming), identity: two distinct rose trees are never bisimilar. Naming The name "rose tree" was coined by Lambert Meertens to evoke the similarly named, and similarly structured, common rhododendron. We shall call such trees ''rose trees'', a literal translation of ''rhododendron'' (Greek = rose, = tree), because of resemblance to the habitus of this shrub, except that the latter does not grow upside-down on the Northern hemisphere. Recursive definition Well-founded relation, Well-founded rose trees can be defined by a recursive construction o ...
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