CSE116/CSE504
IntroductiontoComputerScienceII
Dr. Carl Alphonce
343 Davis Hall
alphonce@buffalo.edu
Office hours:
Thursday 12:00 PM – 2:00 PM
Friday 8:30 AM – 10:30 AM
OR request appointment via e-mail
PROFESSIONALISM
Turn off and put away electronics:
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cell phones
pagers
laptops
tablets
etc.
ROADMAP
Where we’ve been
– Stack<E>
– Queue<E>
– Encapsulation discussion
• private instance variables
• exceptions
• Coming up
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Trees – binary trees – binary search trees
BRStruct<E> implementation and visitors
array-based implementation
(heaps/priority queues/JDT’s AST visitor)
asymptotic notation: O(-)
O(n2) and O(n log n) sorting algorithms
Write-upnextweek
One more visitor on LRStruct<E>, more involved.
Study visitors in repo.
Write-uptheweekAFTERnext
visitor on BRStruct<E>
Tree
• An empty tree is a tree.
• A node with a datum and children is a
tree if the children are all trees.
NODE
(NON-EMPTY TREE)
EMPTY TREE
Terminology
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Given a tree t with children c1…ck
– t is the parent of the ci’s
PARENT
CHILDREN
Terminology
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Given a tree t with children c1…ck
– t is the parent of the ci’s
– the ci’s are siblings of each other
SIBLINGS
SIBLINGS
Terminology
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Given a tree t with children c1…ck
– t is the parent of the ci’s
– the ci’s are siblings of each other
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A tree all of whose children are empty trees is called a leaf
LEAF
Terminology
•
Given a tree t with children c1…ck
– t is the parent of the ci’s
– the ci’s are siblings of each other
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A tree all of whose children are empty trees is called a leaf
A node of a tree t with no parent in t is called the root of t
ROOT
Terminology
•
Given a tree t with children c1…ck
– t is the parent of the ci’s
– the ci’s are siblings of each other
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A tree all of whose children are empty trees is called a leaf
A node of a tree t with no parent in t is called the root of t
A node which is neither a root nor a leaf is an interior node
INTERIOR NODE
Terminology
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Given a tree t with children c1…ck
– t is the parent of the ci’s
– the ci’s are siblings of each other
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A tree all of whose children are empty trees is called a leaf
A node of a tree t with no parent in t is called the root of t
A node which is neither a root nor a leaf is an interior node
The degree of a node is the number of children it has
ROOT
INTERIOR NODE
LEAF
EMPTY TREE
Terminology
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height(empty) = -1
height(nonEmpty) = 1 + max(height(children))
HEIGHT: +2
HEIGHT: +1
HEIGHT: +1
HEIGHT: 0
HEIGHT: 0
HEIGHT: -1
Terminology
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depth(root) = 0
depth(nonRoot) = 1 + depth(parent)
DEPTH: 0
DEPTH: 1
DEPTH: 2
DEPTH: 3
Terminology
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size(empty) = 0
size(nonEmpty) = 1 + Σ size(child)
SIZE: 9
SIZE: 4
SIZE: 1
SIZE: 3
SIZE: 1
SIZE: 0
Binarytree
• A tree in which the degree of every
nonEmpty tree is 2.
BRStruct design
MAIN
CHANGE
FROM
LRStruct
Whatisbasic(invariant)treefunctionality?
• insert new item at root
– emptyState to nonEmptyState transition
• remove item from root
– nonEmptyState to emptyState transition
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set/get root
set/get left / set/get right
execute a visitor
plus (in Java) methods inherited from Object
(toString, equals, etc)
Allowablestatetransitions
insertRoot(item)
item
removeRoot()
Largertreescanbeassembledfromsmallerones.
insertions can only happen at empty trees
removals can only happen when children are
empty
BinarySearchTree
A binary tree which maintains the BST order
condition:
For every nonEmpty tree:
everything in left subtree is <
datum
datum < everything in right
subtree
Note uniqueness assumption (no <= )