Recent questions tagged binary-tree

A binary tree $T$ has $n$ leaf nodes. The number of nodes of degree $2$ in $T$ is$\log_2 n$$n-1$$n$$2^n$

A rooted tree with $12$ nodes has its nodes numbered $1$ to $12$ in pre-order. When the tree is traversed in post-order, the nodes are visited in the order $3, 5, 4, 2, 7...

Prove by the principal of mathematical induction that for any binary tree, in which every non-leaf node has $2$-descendants, the number of leaves in the tree is one more ...

A size-balanced binary tree is a binary tree in which for every node the difference between the number of nodes in the left and right subtree is at most $1$. The distance...

In a binary tree with $n$ nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree ...

The height of a tree is defined as the number of edges on the longest path in the tree. The function shown in the pseudo-code below is invoked as height (root) to compute...

We are given a set of $n$ distinct elements and an unlabeled binary tree with $n$ nodes. In how many ways can we populate the tree with the given set so that it becomes a...

Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly $4$ nodes is...

Draw the binary tree with node labels $\text{a, b, c, d, e, f and g}$ for which the inorder and postorder traversals result in the following sequences:Inorder: $\text{a f...

Consider the following C program segment where $\text{CellNode}$ represents a node in a binary tree:struct CellNode { struct CellNode *leftChild; int element; struct Cell...

The inorder and preorder traversal of a binary tree are$\text{d b e a f c g}$ and $\text{a b d e c f g}$, respectivelyThe postorder traversal of the binary tree is:$\text...

The maximum number of binary trees that can be formed with three unlabeled nodes is:$1$$5$$4$$3$

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is:$2^h -1$$2^{h-1} -1$$2^...

Consider the following C program segmentstruct CellNode{ struct CellNode *leftChild int element; struct CellNode *rightChild; }; int Dosomething (struct CellNode *ptr) { ...

Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pairs identify a tree uniquely?preorder and postorderi...

A scheme for storing binary trees in an array $X$ is as follows. Indexing of $X$ starts at $1$ instead of $0$. the root is stored at $X $. For a node stored at $X[i]$, th...

Draw all binary trees having exactly three nodes labeled $A, B$ and $C$ on which preorder traversal gives the sequence $C, B, A$.

A weight-balanced tree is a binary tree in which for each node, the number of nodes in the left sub tree is at least half and at most twice the number of nodes in the rig...

Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal respectively, of a complete binary tree. Which of the foll...

Consider the following nested representation of binary trees: $(X \ Y \ Z)$ indicates $Y$ and $Z$ are the left and right subtrees, respectively, of node $X$. Note that $Y...

Consider the binary tree in the figure below:What structure is represented by the binary tree?

The weighted external path length of the binary tree in figure is ______

If the binary tree in figure is traversed in inorder, then the order in which the nodes will be visited is ______