# engineering mathematics 2 vtu

A complete binary tree is a binary tree in which every level of the binary tree is completely filled except the last level. 2. Almost complete Binary Tree. A full binary tree is a tree in which every node in the tree has two children except the leaves of the tree. 1. Calculate the number of nodes (count) in the binary tree. Complete Binary Tree: A Binary Tree is a complete Binary Tree if all the levels are completely filled except possibly the last level and the last level has all keys as left as possible The following are examples of Complete Binary Trees . A binary tree of depth “d” is an almost complete binary tree if each leaf in the tree is either at level “d” or at level “d–1” and for any node “n” in the tree with a right descendent at level “d” all the left descendants of “n” that are leaves, are also at level “d”. In the unfilled level, the nodes are attached starting from the left-most position. A binary tree of depth d is an almost-binary tree if any node n at level d-1 has two children and for any node n in the tree with a right or left child at level l, the node must have a left child(if it has a right child) and all the nodes on the left side must have two children. have $2^k$ nodes), and the level $h$ is … Shape Property: Heap data structure is always a Complete Binary Tree, which means all levels of the tree are fully filled. If the current node under examination is NULL, then … 18 / \ 15 30 / \ … Start recursion of the binary tree from the root node of the binary tree with index (i) being set as 0 and the number of nodes in the binary (count). Heap Property: All nodes are either greater than or equal to or less than or equal to each of its children. So, you are talking about a binary tree with $h$ levels, for which all levels with numbers $k \in [0,h-1]$ are completely filled up (i.e.