The document discusses various data structures including stacks, queues, and trees, outlining their definitions, operations, and characteristics. It explains fundamental operations like insertion, deletion, and traversal, and provides examples of code implementations for each data structure. Additionally, it emphasizes the importance of selecting an appropriate data structure based on the relationship between data elements and ease of processing.

1. First Year BA (IT)
CT1120 Algorithms
Lecture 15
Dr. Zia Ush Shamszaman
z.shamszaman1@nuigalway.ie
1
School of Computer Science, College of Science and Engineering
31-01-2020

2. Overview
• Data Structure
– Stack
– Queue
– Tree
• Reviewing previous lectures
• Feedback and Assessment
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3. 3
Data Structure Concepts
• Data Structures are containers:
– they hold other data
– arrays are a data structure
– ... so are lists
• Other types of data structures:
– stack, queue, tree,
binary search tree, hash table,
dictionary or map, set, and on and on
• Different types of data structures are
optimized for certain types of operations
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4. Basic Data Structure
Basic Data Structures
Linear Data Structures Non-Linear Data Structures
Arrays Linked Lists Stacks Queues Trees Graphs Hash Tables
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5. Array
Linked list
Tree
Queue
Stack
Linear Data Structure
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6. 6
Data Structure Operations
• Data Structures will have 3 core operations
– a way to add things
– a way to remove things
– a way to access things
• Details of these operations depend on the data
structure
– Example: List, add at the end, access by
location, remove by location
• More operations added depending on what data
structure is designed to do
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7. Data Structure Operations
Ø Traversing: Accessing each record exactly once so that certain
items in the record may be processed.
Ø Searching: Finding the location of the record with a given key value,
or finding the locations of all records which satisfy one or more
conditions.
Ø Insertion: Adding a new record to the structure.
Ø Deletion: Removing a record from the structure.
Following two are special operations:
Ø Sorting: Arranging the records in some logical order.
Ø Merging: Combining the records in two different sorted files into a
single sorted file.
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8. Selection of Data Structure
• The choice of particular data model depends
on two consideration:
– It must be rich enough in structure to
represent the relationship between data
elements
– The structure should be simple enough that
one can effectively process the data when
necessary
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9. Stack
• A Stack is a list of elements in which an
element may be inserted or deleted at
one end which is known as TOP of the
stack.
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10. Stack
• Collection with access only to the last
element inserted
• Last in First out (LIFO)
• Insert/Push
• Remove/Pop
• Top
• Make empty
TopData4
Data3
Data2
Data1
push
pop
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11. Stack Operation
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• Stack() creates a new stack that is empty. It needs no
parameters and returns an empty stack.
• push(item) adds a new item to the top of the stack. It needs
the item and returns nothing.
• pop() removes the top item from the stack. It needs no
parameters and returns the item. The stack is modified.
• peek() returns the top item from the stack but does not
remove it. It needs no parameters. The stack is not
modified.
• isEmpty() tests to see whether the stack is empty. It needs
no parameters and returns a boolean value.
• size() returns the number of items on the stack. It needs no
parameters and returns an integer.

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13. Example
from pythonds.basic import Stack
s=Stack()
print(s.isEmpty())
s.push(4)
s.push('dog')
print(s.peek())
s.push(True)
print(s.size())
print(s.isEmpty())
s.push(8.4)
print(s.pop())
print(s.pop())
print(s.size())
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True
dog
3
False
8.4
True
2
Output

14. Queue
• A queue is an ordered collection of items where
the addition of new items happens at one end,
called the “rear,” and the removal of existing
items occurs at the other end, commonly called
the “front.”
• As an element enters the queue it starts at the
rear and makes its way toward the front, waiting
until that time when it is the next element to be
removed..
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15. Queue
• Collection with access only to the item that has
been present the longest
• Last in Last Out (LILO)/First in First Out(FIFO)
• enqueue, dequeue, front
• priority queues and dequeue
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16. Basic Operation
• Queue() creates a new queue that is empty. It needs no
parameters and returns an empty queue.
• enqueue(item) adds a new item to the rear of the
queue. It needs the item and returns nothing.
• dequeue() removes the front item from the queue. It
needs no parameters and returns the item. The queue
is modified.
• isEmpty() tests to see whether the queue is empty. It
needs no parameters and returns a boolean value.
• size() returns the number of items in the queue. It
needs no parameters and returns an integer.
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18. Example
q=Queue()
q.enqueue(4)
q.enqueue('dog')
q.enqueue(True)
print(q.size())
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19. Tree
• A Tree is a collection of elements called nodes.
• One of the node is distinguished as a root, along with a
relation (“parenthood”) that places a hierarchical
structure on the nodes.
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20. Vocabulary & Definitions
• Node
– A node is a fundamental part of a tree. It can have a
name, which we call the “key.” A node may also have
additional information. We call this additional information
the “payload.” While the payload information is not
central to many tree algorithms, it is often critical in
applications that make use of trees.
• Edge
– An edge is another fundamental part of a tree. An edge
connects two nodes to show that there is a relationship
between them. Every node (except the root) is connected
by exactly one incoming edge from another node. Each
node may have several outgoing edges.
• Root
– The root of the tree is the only node in the tree that has
no incoming edges.
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21. Vocabulary & Definitions
• Path
– A path is an ordered list of nodes that are connected by
edges. For example, Mammal → Carnivora → Felidae →
Felis → Domestica is a path.
• Children
– The set of nodes 𝑐 that have incoming edges from the
same node to are said to be the children of that node.
• Parent
– A node is the parent of all the nodes it connects to with
outgoing edges.
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22. Vocabulary & Definitions
• Sibling
– Nodes in the tree that are children of the same parent
are said to be siblings.
• Subtree
– A subtree is a set of nodes and edges comprised of a
parent and all the descendants of that parent.
• Leaf Node
– A leaf node is a node that has no children. For example,
Human and Chimpanzee are leaf nodes
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23. Next Lecture
Class test
Syllabus (all three lectures)
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24. Useful Links
• http://www.csanimated.com/animation.php?t=Quicksort
• http://www.hakansozer.com/category/c/
• http://www.nczonline.net/blog/2012/11/27/computer-science-in-
javascript-quicksort/
• http://www.sorting-algorithms.com/shell-sort
• https://www.tutorialspoint.com/
• https://www.hackerearth.com/
• www.khanacademy.org/computing/computer-science/algorithms
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25. Feedback & Assessment
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