Chapter 23 -Trees

List the steps of a postorder traversal of a binary tree.

1. Visit all the nodes in the root's left subtree 2. Visit all the nodes in the root's right subtree 3. visit the root

List the steps of an inorder traversal of a binary tree.

1. Visit all the nodes in the root's left subtree 2. Visit the root 3. Visit all the nodes in the roots right subtree

List the steps of a preorder traversal of a binary tree.

1. Visit the root 2. Visit all the nodes in the root's left subtree 3. Visit all the nodes in the root's right subtree

How many nodes are in a full binary tree of height 8?

2^8 - 1 or 256 - 1 = 255

How many nodes are in a full binary tree of height 5?

31

What is the height of a complete tree that contains 11 nodes?

4

A level-order traversal of a binary tree is an example of a depth-first traversal.

False

Completely balance binary trees are not necessarily full.

False

Every general tree is an n-ary tree.

False

The path between a tree's root and any other node is not unique.

False

An example of a data organization that is hierarchical is a(n)

Family tree. University administration structure. File directories

A tree is a set of _____ connected by edges that indicate the relationships among the nodes.

Nodes

A _____ is a set of nodes connected by edges that indicate the relationships among the nodes.

Tree

A preorder traversal of a binary tree is an example of a depth-first traversal.

True

A subtree of a tree is a subtree of the tree'sroot.

True

All leaves in a full binary tree are on the same level.

True

All nodes in a balanced binary tree are balanced.

True

An inorder traversal is not well defined for a general tree.

True

Every node in a binary search tree is the root of a binary search tree.

True

In a tree, nodes are arranged in levels that indicate the nodes' hierarchy.

True

In a tree, the root is the only node that has no parent.

True

The height of a tree equals the number of nodes along the longest path between the root and a leaf.

True

A subtree of a node is a tree rooted at

a child of that node

A node in a binary tree whose subtrees differ in height by no more than 1 is known as a(n) _____ node.

balanced

A tree in which each node may have at most two children is called a(n) _____ tree.

binary

The nodes at each successive level of a tree are called _____.

children

The nodes in a binary search tree contain _____ objects.

comparable

When a binary tree is full to its next-to-last level and its leaves on the last level are filled from left to right, the tree is said to be

complete

A tree is a set of nodes connected by _____ that indicate the relationships among the nodes.

edges

When a binary tree of height h has all of its leaves at level hand every nonleaf has exactly two children, the tree is said to be

full

A tree in which each node may have an arbitrary number of children is called a(n) _____ tree.

general

The number of levels in a tree is called the

height

A family tree is typically organized into a(n) _____ order.

hierarchical

When you classify data into groups and subgroups, you are using a(n) _____ order.

hierarchical

In a _____ traversal of a binary tree, you visit the root of a binary tree between visiting the nodes o the root's subtrees.

inorder

A node with no children is called a(n) _____.

leaf

In a _____ traversal of a binary tree, you begin at the root and visit nodes one level at a time.

level order

What is the height of a complete tree that contains 18 nodes?

log2(18+1) rounded up is 5

The height of a complete tree that has n nodes is

log2(n+1)

The height of a full tree that has n nodes is

log2(n+1)

A _____ is a complete binary tree such that each node in the tree contains a Comparable object that is greater than or equal to the objects in the node's descendants.

maxheap

A tree in which each node may have no more than n children is called a(n) _____ tree.

n-ary

A node that has children is called a(n) _____.

nonleaf interlor node

A node that has children is a(n) _____.

parents

In a _____ traversal of a binary tree, you visit the root of a binary tree after you visit the root's subtrees.

postorder

In a _____ traversal of a binary tree, you visit the root node before you visit the root's subtrees.

preorder

At the top level of a tree is a single node called the _____.

root

The _____ node is the only node that has no parent.

root

Nodes that are children of the same parent node are called _____.

siblings

Any node and its descendants form a _____ of the original tree.

subtree

A binary tree has at most two children called

the left child the right child