Binary search trees are node-based binary trees where each node contains a key and value. Each internal node has between 1 and 2 children, while leaf nodes have no children. The root node is the highest node with no parent. Traversal of a binary search tree involves systematically visiting each node and can be done in pre-order, in-order, or post-order fashion where the order of visiting left/right subtrees and the root node differs for each.

1. Binary Search Trees
By Asseged Fikru

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 Outlines
• Tree
• Binary Search Tree
• Traversal

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Tree
Tree
Each node can have 0 or more children on
tree
Binary tree
• Tree with 0–2 children per node

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A binary search tree (BST)
 A binary search tree is node Based binary tree
data structure.
 Each node has A key and Associated value
parent
left child right child

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Properties of Trees and Nodes
» internal node has 1 or
more children,
root node
leaf nodes
internal
nodes

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Properties of Trees and Nodes
 root node is the
highest node in the tree
structure, and it has no parent
 siblings: two nodes that have
the same parent
 edge: the link from one node
to another
 null is Empty
root
siblings
edge

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TRAVERSAL
 Is systematic ways of vesting nodes in a three
There are three different types of depth-first
traversals
i. Pre-order traversal
ii. In-order traversal
iii. Post-order traversal

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Pre-order traversal
has 3 steps
 Visit Node
 traversal left sub-tree
 traversal Right sub-tree
23 18 12 20 44 35 52

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In-order traversal
 Traverse the left sub-tree
 Visit the root.
 traversal the Right sub-tree
12 18 20 23 35 44 52

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Post-order traversal
 Traverse the left sub-tree
 traversal the Right sub-tree
 Visit the root
12 20 18 35 52 44 23

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