Binary Trees and Types
Binary Tree
- A binary tree is the one where each node has atmost 2 children.
- A binary tree is a finite set of elements that is either empty or is partitioned into three disjoint subsets.
- The first subset contains a single element called the root
root of the tree. - The other two subsets are themselves binary trees, called the left and right subtrees of the original tree.
- Each element of a binary tree is called a node of the tree.
Types of Binary Trees
Strictly Binary Tree
- If every non leaf node in a binary tree has non empty left and right substrees, the tree is termed as strictly binary tree
- Every non-leaf node has degree 2.
Complete Binary Tree
- A complete binary tree of depth d is the strictly binary tree – all of whose leaves are at level d.
- A complete binary tree of depth d is the binary tree of depth d that contains exactly 2l nodes at each level l between 0 and d
Almost Complete Binary Tree
- A binary tree of depth d is an almost complete binary tree if: is an almost complete binary tree if: At any node in the tree with a right descendent at level d, node must have a left son and every left descendent of node is either a leaf at level d or has two sons i.e., the tree must be left filled.
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