Tree Traversal

Pre-order, post-order, and in-order are not “order types” in the general sense, but rather tree traversal methods used to visit all nodes in a tree structure. They define the order in which we visit the root, left subtree, and right subtree of each node. Here’s a breakdown of each:

Pre-order:

• Visit the root of the node.

• Recursively visit the left subtree.

• Recursively visit the right subtree.

Think of it as visiting the parent first, then the children, like inspecting a family photo by focusing on the parents before moving to their individual pictures.

In-order:

• Recursively visit the left subtree.

• Visit the root of the node.

• Recursively visit the right subtree.

Imagine reading a sentence word by word: you start at the leftmost word, move to the next, and so on, reaching the root (middle word) last.

Post-order:

• Recursively visit the left subtree.

• Recursively visit the right subtree.

• Visit the root of the node.

This is like cleaning up after a plant’s growth: you prune the left and right branches before finally taking care of the main trunk.

Here are some examples of how these traversals are used in real life:

• Pre-order: Building a file system where folders are processed before their contents, or printing the document outline with headings first.

• In-order: Sorting a list of numbers in ascending order using a binary search tree, or printing the words in a sentence in the correct order.

• Post-order: Evaluating an arithmetic expression where leaves (operands) are processed before the operators, or calculating the size of a directory by first traversing all subdirectories.