Definition:In-Order Traversal of Labeled Tree
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Definition
Let $T$ be a binary labeled tree.
In-order traversal of $T$ is an algorithm designed to obtain a string representation of $T$.
The steps are as follows:
Variant 1
$\mathtt{Inorder} (T):$
- $n \gets t$, where $t$ is the root node of $T$.
- If $n$ is a leaf node, output the label of $n$, and stop.
- Let $T_1$ and $T_2$ be the left and right subtrees of $T$.
- If $n$ has only one child, skip this step. Output $\mathtt{Inorder} (T_1)$.
- Output the label of $n$.
- Output $\mathtt{Inorder} (T_2)$.
- Stop.
Variant 2
$\mathtt{Inorder} (T):$
- $n \gets t$, where $t$ is the root node of $T$.
- If $n$ is a leaf node, output the label of $n$, and stop.
- Let $T_1$ and $T_2$ be the left and right subtrees of $T$.
- Output a left bracket $($.
- If $n$ has only one child, skip this step. Output $\mathtt{Inorder} (T_1)$.
- Output the label of $n$.
- Output $\mathtt{Inorder} (T_2)$.
- Output a right bracket $)$.
- Stop.