1.
First Year BA (IT)
CT1120 Algorithms
Lecture 17
Dr. Zia Ush Shamszaman
z.shamszaman1@nuigalway.ie
1
School of Computer Science, College of Science and Engineering
14-02-2020

2.
Overview
• Data Structure
– Stack implementation
– Queue implementation
– Tree
– Binary tree
• Feedback and Assessment
214-02-2020

3.
• Given the following sequence of stack
operations, what is the top item on the stack
when the sequence is complete?
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m = Stack()
m.push('x')
m.push('y')
m.pop()
m.push('z')
m.peek()

4.
• Given the following sequence of stack
operations, what is the top item on the stack
when the sequence is complete?
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m = Stack()
m.push('x')
m.push('y')
m.pop()
m.push('z')
m.peek()

5.
What this code is doing?
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stack = []
stack.append('a')
stack.append('b')
stack.append('c')
print('Initial stack')
print(stack)
print('nElements poped from stack:')
print(stack.pop())
print(stack.pop())
print(stack.pop())
print('nStack after elements are poped:')
print(stack)

6.
Stack implementation code
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stack = []
stack.append('a')
stack.append('b')
stack.append('c')
print('Initial stack')
print(stack)
print('nElements poped from stack:')
print(stack.pop())
print(stack.pop())
print(stack.pop())
print('nStack after elements are poped:')
print(stack)
OUTPUT
Initial stack
['a', 'b', 'c']
Elements poped from stack:
c
b
a
Stack after elements are poped:
[]

7.
What this code is doing?
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queue = []
queue.append('a')
queue.append('b')
queue.append('c')
print("Initial queue")
print(queue)
print("nElements dequeued from queue")
print(queue.pop(0))
print(queue.pop(0))
print(queue.pop(0))
print("nQueue after removing elements")
print(queue)

8.
What this code is doing?
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queue = []
queue.append('a')
queue.append('b')
queue.append('c')
print("Initial queue")
print(queue)
print("nElements dequeued from queue")
print(queue.pop(0))
print(queue.pop(0))
print(queue.pop(0))
print("nQueue after removing elements")
print(queue)
Output
Initial queue
['a', 'b', 'c']
Elements dequeued from queue
a
b
c
Queue after removing elements
[]

9.
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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10.
Applications of Tree
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Main applications of trees include:
1. Manipulate hierarchical data.
2. Make information easy to search (see tree
traversal).
3. Manipulate sorted lists of data.
4. As a workflow for compositing digital images for
visual effects.
5. Router algorithms
6. Form of a multi-stage decision-making (see
business chess).

11.
Binary Tree
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• A tree whose elements have at most 2 children is called a
binary tree.
• Since each element in a binary tree can have only 2
children, we typically name the left child and right child.

12.
Binary Tree
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• A tree whose elements have at most 2 children is called a
binary tree.
• Since each element in a binary tree can have only 2
children, we typically name the left child and right child.
((7+3)∗(5−2))

13.
Binary Tree
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• A tree whose elements have at most 2 children is called a
binary tree.
• Since each element in a binary tree can have only 2
children, we typically name the left child and right child.
• A Binary Tree node contains following parts.
• Data
• Pointer to left child
• Pointer to right child

14.
Python code of
Binary Tree
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# A class that represents an individual node in a
# Binary Tree
class Node:
def __init__(self,key):
self.left = None
self.right = None
self.val = key
# create root
root = Node(1)
''' following is the tree after above statement
1
/
None None'''
root.left = Node(2);
root.right = Node(3);
''' 2 and 3 become left and right children of 1
1
/
2 3
/ /
None None None None''’
root.left.left = Node(4);
'''4 becomes left child of 2
1
/
2 3
/ /
4 None None None
/
None None'''
"__init__" is a reseved method in python classes. It is
called as a constructor in object oriented terminology. This
method is called when an object is created from a class
and it allows the class to initialize the attributes of the
class.

15.
Tree traversal
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Following are the generally used ways for traversing trees:
• Inorder: We recursively do an inorder traversal on the
left subtree, visit the root node, and finally do a recursive
inorder traversal of the right subtree.
• Preorder: We visit the root node first, then recursively
do a preorder traversal of the left subtree, followed by a
recursive preorder traversal of the right subtree.
• Postorder: We recursively do a postorder traversal of
the left subtree and the right subtree followed by a visit
to the root node.

16.
Tree traversal
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(a) Inorder (Left, Root, Right) : 4 2 5 1 3
(b) Preorder (Root, Left, Right) : 1 2 4 5 3
(c) Postorder (Left, Right, Root) : 4 5 2 3 1
Level Order Traversal : 1 2 3 4 5

17.
Tree traversal
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(a) Inorder (Left, Root, Right) : 4 2 5 1 3
(b) Preorder (Root, Left, Right) : 1 2 4 5 3
(c) Postorder (Left, Right, Root) : 4 5 2 3 1
Level Order Traversal : 1 2 3 4 5

18.
Tree traversal code
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# A class that represents an individual node in a
Binary Tree
class Node:
def __init__(self,key):
self.left = None
self.right = None
self.val = key
# A function to do inorder tree traversal
def printInorder(root):
if root:
# First recur on left child
printInorder(root.left)
# then print the data of node
print(root.val),
# now recur on right child
printInorder(root.right)
# A function to do postorder tree traversal
def printPostorder(root):
if root:
# First recur on left child
printPostorder(root.left)
# the recur on right child
printPostorder(root.right)
# now print the data of node
print(root.val),
# A function to do preorder tree traversal
def printPreorder(root):
if root:
# First print the data of node
print(root.val),
# Then recur on left child
printPreorder(root.left)
# Finally recur on right child
printPreorder(root.right)
# Driver code
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
print ("nPreorder traversal of binary tree is")
printPreorder(root)
print ("nInorder traversal of binary tree is")
printInorder(root)
print ("nPostorder traversal of binary tree is")
printPostorder(root)

19.
Inorder traversal without recursion
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# A binary tree node
class Node:
# Constructor to create a new node
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# Iterative function for inorder tree traversal
def inOrder(root):
# Set current to root of binary tree
current = root
stack = [] # initialize stack
done = 0
while True:
# Reach the left most Node of the current Node
if current is not None:
# Place pointer to a tree node on the stack
# before traversing the node's left subtree
stack.append(current)
current = current.left
# BackTrack from the empty subtree and visit the Nod
# at the top of the stack; however, if the stack is
# empty you are done
elif(stack):
current = stack.pop()
print(current.data, end=" ")
# Python 3 printing
# We have visited the node and its left
# subtree. Now, it's right subtree's turn
current = current.right
else:
break
print()
# Driver program to test above function
""" Constructed binary tree is
1
/
2 3
/
4 5 """
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
inOrder(root)

20.
Priority Queue
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• A priority queue acts like a queue in that you dequeue an item by
removing it from the front.
• In a priority queue the logical order of items inside a queue is
determined by their priority.
• The highest priority items are at the front of the queue and the lowest
priority items are at the back.
• When you enqueue an item on a priority queue, the new item may move
all the way to the front.

21.
Binary Heaps
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• A Heap is a special Tree-based data structure in
which the tree is a complete binary tree. Generally,
Heaps can be of two types:
• Max-Heap: The key present at the root node must be
greatest among the keys present at all of it’s children. The
same property must be recursively true for all sub-trees in
that Binary Tree.
• Min-Heap: The key present at the root node must be
minimum among the keys present at all of it’s children. The
same property must be recursively true for all sub-trees in
that Binary Tree.

22.
Binary Heap Operation
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The basic operations we will implement for our
binary heap are as follows:
• BinaryHeap() creates a new, empty, binary heap.
• insert(k) adds a new item to the heap.
• findMin() returns the item with the minimum key value,
leaving item in the heap.
• delMin() returns the item with the minimum key value,
removing the item from the heap.
• isEmpty() returns true if the heap is empty, false
otherwise.
• size() returns the number of items in the heap.
• buildHeap(list) builds a new heap from a list of keys.

23.
Next Lecture
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24.
• Binary Heap Implementation
• Binary Search Tree
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25.
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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26.
Feedback & Assessment
14-02-2020 26