science

Left-child right-sibling binary tree

Left-child right-sibling binary tree is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Left-child right-sibling binary tree rather than just read about it. In short: 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 T, each node corresponds to a node in T and has two pointers: one to the node's first child, and one to its ne…

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Reference excerpt

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 T, each node corresponds to a node in T and has two pointers: one to the node's first child, and one to its next sibling in T. The children of a node thus form a singly-linked list. To find a node n's k'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. Then, starting with the root, each node's leftmost child in the original tree is made its left child in the binary tree, and its nearest sibling to the right in the original tree is made its right child in the binary tree. Doubly chained trees were described by Edward H. Sussenguth in 1963. Processing a k-ary tree to LC-RS binary tree, every node is linked and aligned with the left child, and the next nearest is a sibling. For example, we have a ternary tree below:

1 /|\ / | \ / | \ 2 3 4 / \ | 5 6 7 / \ 8 9

We can re-write it by putting the left child node to one level below its parents and by putting the sibling next to the child at the same level – it will be linear (same line).

1 / / / 2---3---4 / / 5---6 7 / 8---9

We can transform this tree to a binary tree by turning each sibling 45° clockwise.

1 / 2 / \ 5 3 \ \ 6 4 / 7 / 8 \ 9

Use cases The LCRS representation is more space-efficient than a traditional multiway tree, but comes at the cost that looking up a node's children by index becomes slower. Therefore, the LCRS representation is preferable if

Memory efficiency is a concern, and/or Random access of a node's children is not required. Case (1) applies when large multi-way trees are necessary, especially when the trees contains a large set of data. For example, if storing a phylogenetic tree, the LCRS representation might be suitable. Case (2) arises in specialized data structures in which the tree structure is being used in very specific ways. For example, many types of heap data structures that use multi-way trees can be space optimized by using the LCRS representation. (Examples include Fibonacci heaps, pairing heaps and weak heaps.) The main reason for this is that in heap data structures, the most common operations tend to be

Remove the root of a tree and process each of its children, or Join two trees together by making one tree a child of the other. Operation (1) it is very efficient. In LCRS representation, it organizes the tree to have a right child because it does not have a sibling, so it is easy to remove the root. Operation (2) it is also efficient. It is easy to join two trees together.

References

Illustrations

Worked examples

Example 1 — a first encounter with Left-child right-sibling binary tree

Start with the simplest possible case. Write down what Left-child right-sibling binary tree claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Left-child right-sibling binary tree before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Left-child right-sibling binary tree ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Left-child right-sibling binary tree

In research: Left-child right-sibling binary tree appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Left-child right-sibling binary tree in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Left-child right-sibling binary tree is common in secondary-school and first-year university syllabi. It links to neighbouring topics Binary trees, so understanding it makes those chapters shorter.
In everyday life: Look for Left-child right-sibling binary tree outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Left-child right-sibling binary tree in 20 minutes

Read the reference excerpt below once, without taking notes.
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Compare your version with the excerpt and mark what you missed.
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Frequently asked questions

What is Left-child right-sibling binary tree in simple terms?

Why does Left-child right-sibling binary tree matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Left-child right-sibling binary tree?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Left-child right-sibling binary tree.