COP3530 TREES
What is the minimum number of internal nodes in a binary tree with 8 nodes?
4
What is the minimum number of nodes in a full binary tree with height 3?
7
Which statement is false? Every node in a binary tree has exactly two children Every non-empty binary tree has exactly one root node Every binary tree has at least one node Every non-root node in a binary tree has exactly one parent None of the above
Every binary tree has at least one node
Select the one true statement.
Every binary tree is either complete or full Every complete binary tree is also a full binary tree Every full binary tree is also a complete binary tree No binary tree is both complete and full None of the above
What do we use trees for?
Family trees - names of the family decision trees file systems expression trees search trees
BST search, insert, and delete operations typically run in time O(d). What is d?
The depth of the relevant node in the tree
what is a full binary tree
a binary tree where all nodes have either 2 children or 0 children (leaf nodes)
What is a binary tree
a tree with each node consisting of at MOST 2 children
What is a binary search tree
an ordered binary tree all values go down as you go down so if we start with 51 as you go down it should be lower
all nodes that can be reached by moving only in an upward direction are
ancestors
The successors of a node are?
children
BST Traversals
depth first strategy in order , preorder,postoder breadth first strategy strategy
nodes that can be reached by moving only in a downward direction in the tree are
descendents
A binary tree is another name for a BST.
false
If you are given the order of the nodes as visited by a preorder traversal and the order of the nodes as visited by a postorder traversal, do you have enough information to reconstruct the original tree? Assume that the nodes all have unique values.
false
predecessors of a node's parent are?
grandparent
the ___ of a tree is the number of nodes in the longest path from the root node to a leaf node
height we can start with 1 or 0
What are some applications of trees?
include prioritizing jobs, describing mathematical expressions and the syntactic elements of computer programs, or organizing the information needed to drive data compression algorithms.
nodes with no children are called AT ALL
leaf nodes or external nodes
Euler Tour
left down back up right down up
postorder traversal
left subtree, right subtree, root
what is a complete binary tree
level h -1 at level h all towards to the left height is log n
the ___ of a node is the distance of that node from the root
levels
Trees are what order?
non linear
So, every binary tree node has two children, but
not every binary tree has a node.
Full binary trees is a
nternal node with exactly two non-empty children or (2) a leaf.
Trees have 3 properties
one root, each node has one parent, and has no cycles
Predecessors of a node are?
parent every child has 1 parent except the root .
What is the node at the top of the tree called?
root
all nodes that have the same parent node are?
siblings
a _ of a node is a tree whose root is a child of that node
subtree
What is an N-ary tree?
the normal tree a tree with each node consisting of at most n children
what is a perfect binary tree?
there have to be children filled to the last level height h with exactly 2^h - 1 height of the tree is o(log n )
The n nodes in a binary tree can be visited in:
theta n time
Traversal vs search
traversal requires you to visit each nodes not necessarily in search like it may jsut go to one side
If you are given the order of the nodes as visited by a preorder traversal and the order of the nodes as visited by an inorder traversal, do you have enough information to reconstruct the original tree? Assume that the nodes all have unique values.
true
inorder traversal
visit the left subtree visit the root visit the right subtree
preorder traversal
visit the root, visit the left subtree, visit the right subtree
level order
zig zag
