The document discusses various tree data structures and algorithms. It defines common tree terminology like nodes, roots, leaves. It describes different types of trees like binary trees, binary search trees, and their properties. It explains tree traversal algorithms like preorder, inorder and postorder. It also summarizes minimum spanning tree algorithms like Kruskal's and Prim's, and single source shortest path algorithms like Dijkstra's.
Trie (aka radix tree or prefix tree), is an ordered tree data structure where the keys are usually strings. Tries have tremendous applications from all sorts of things like dictionary to
Trie (aka radix tree or prefix tree), is an ordered tree data structure where the keys are usually strings. Tries have tremendous applications from all sorts of things like dictionary to
Splay Trees and Self Organizing Data StructuresAmrinder Arora
Self Organizing Data Structures, such as Splay Trees, continue to adjust themselves based on the operation sequence. They are much easier to implement compared to AVL or RB Trees. Amortized time is O(log n), although worst case time may be O(n).
Splay Trees and Self Organizing Data StructuresAmrinder Arora
Self Organizing Data Structures, such as Splay Trees, continue to adjust themselves based on the operation sequence. They are much easier to implement compared to AVL or RB Trees. Amortized time is O(log n), although worst case time may be O(n).
a. Concept and Definition
b. Binary Tree
c. Introduction and application
d. Operation
e. Types of Binary Tree
• Complete
• Strictly
• Almost Complete
f. Huffman algorithm
g. Binary Search Tree
• Insertion
• Deletion
• Searching
h. Tree Traversal
• Pre-order traversal
• In-order traversal
• Post-order traversal
Slides at myblog
http://www.ashimlamichhane.com.np/2016/07/tree-slide-for-data-structure-and-algorithm/
Assignments at github
https://github.com/ashim888/dataStructureAndAlgorithm/tree/dev/Assignments/assignment_7
Concept and Definition of Data Structures
Introduction to Data Structures: Information and its meaning, Array in C++: The array as an ADT, Using one dimensional array, Two dimensional array, Multi dimensional array, Structure , Union, Classes in C++.
https://github.com/ashim888/dataStructureAndAlgorithm
Queues
a. Concept and Definition
b. Queue as an ADT
c. Implementation of Insert and Delete operation of:
• Linear Queue
• Circular Queue
For More:
https://github.com/ashim888/dataStructureAndAlgorithm
http://www.ashimlamichhane.com.np/
Understanding the concept of risk poolingHFG Project
Presented during Day Two of the 2016 Nigeria Health Care Financing Training Workshop. Presented by Dr. Gafar Alawode. More: https://www.hfgproject.org/hcf-training-nigeria
1. Briefly state the Master Theorem.What type of problem is it usefu.pdfsales98
1. Briefly state the Master Theorem.What type of problem is it useful for?
2. What is the balance condition of the AVL tree? Does this balance condition mean that the
depth of the highest and lowest leaves in the tree will be different by at most one?
3. Under what conditions does a BFS algorithm on Graphs work as a single source shortest path
algorithm?
Solution
1) Master Theorem :
A recurrence relation of the following form:
T(n) = c n < c1 = aT(n/b) + (n i ), n c1 Has as its solution:
1) If a > bi then T(n) = (n logb a ) (Work is increasing as we go down the tree, so this is the
number of leaves in the recursion tree).
2) If a = b i then T(n) = (n i logb n) (Work is the same at each level of the tree, so the work is the
height,logb n, times work/level).
3) If a < bi then T(n) = (n i ) (Work is going down as we go down the tree, so dominated by the
initial work at the root).
The Master method is a general method for solving (getting a closed form solution to) recurrence
relations that arise frequently in divide and conquer algorithms, which have the following form:
T(n) = aT(n/b) + f(n) where a 1, b > 1 are constants, and f(n) is function of non-negative integer
n. There are three cases.
(a) If f(n) = O(n logb a ), for some > 0, then T(n) = (n logba ).
(b) If f(n) = (n logb a ), then T(n) = (n logb a log n).
(c) If f(n) = (n logb a+ ) for some > 0, and af(n/b) cf(n), for some c < 1 and for all n greater than
some value n 0, Then T(n) = (f(n)).
2) An AVL tree has a balance condition such that each node stores the maximum depth of nodes
below it. A NULL tree has a level of -1 and a leaf node has a level of 0. A node having 1 or 2
subtrees will have as its own level the maximum of left or right subtree levels +1. Within an
AVL tree, the maximum difference allowed between left and right subtree levels is 1. When an
insertion or deletion operation results in this difference increasing to 2, rearrangements called
rotations are performed to reduce the imbalance for an AVL tree to retain the AVL balance
condition.
True. A heap is derived from an array and new levels to a heap are only added once the leaf level
is already full. As a result, a heap’s leaves are only found in the bottom two levels of the heap
and thus the maximum difference between any two leaves’ depths is 1. A common mistake was
pointing out that a heap could be arbitrarily shaped as long as the heap property (parent greater
than its children in the case of a maxheap) was maintained. This heap is not a valid heap, as there
would be gaps if we tried to express it in array form, heap operations would no longer have
O(log n) running time, and heap sort would fail when using this heap. Another common mistake
was simply justifying this statement by saying a heap is balanced. An AVL tree is also balanced,
but it does not have the property that any two leaves have depths that differ by at most 1.
3)
BFS can only be used to find shortest path in a graph if:
There are no loops
All edges have.
Short overview of balance tree: Data Structures, Binary search tree, BST Problem, Self Balancing BST, Usage, Red Black Trees, Red Black Insertion, AVL Tree, Rotations, B-Tree
Theories of entrepreneurship: Innovation theory by Schumpter, Theory of Achievement by McClelland, X-efficiency theory by Leibenstein, Theory of profit by Knight
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
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• Compatible with commercial and Defence aviation CCR system.
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Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
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2. TREE
A tree is the data structure that are based on
hierarchical tree structure with set of nodes
It is an acyclic connected graph with one or
more children nodes and at most one root
node
3. TREE TERMINOLOGY
NODE: Each data item in a tree
ROOT: First or top data item in hierarchical
arrangement
DEGREE OF A NODE: Number of subtrees of
a given node
DEGREE OF A TREE: Maximum degree of a
node in a tree
DEPTH OR HEIGHT: Maximum level number
of a node + 1(i.e., level number of farthest leaf
node of a tree + 1)
4. TREE TERMINOLOGY
NON-TERMINAL NODE: Any node except
root node whose degree is not zero
TERMINAL NODE OR LEAF NODES: Nodes
having zero
FOREST: Set of disjoint trees
PATH: Sequence of consecutive edges from
the source node to the destination node
5. BINARY TREE
In this kind of tree, the maximum degree of
any node is at most 2
A binary tree T is defined as a finite set of
elements such that T is empty (called NULL
tree or empty tree) and T contains a
distinguished Node R called the root of T and
the remaining nodes of T form an ordered pair
of disjoint binary trees 𝑇1, and 𝑇2
6. FULL BINARY TREE
A binary tree in which all leaves are t the
same level or at the same depth and in which
every parent has exactly 0 or 2 children
7. COMPLETE BINARY TREE
A binary tree is one which have the following
properties:
i) Which can have 0, 1 or 2 nodes as a child
node
ii) In which first, we need to fill left node, then
right node in a level
iii) In which, we can start putting data item in
next level only when the previous level is
completely filled
8. PREORDER TREE
TRAVERSAL
Process the root R
Traverse the left subtree of R in preorder
Traverse the right subtree of R in preorder
11. BREADTH FIRST TRAVERSAL
(BFT)
The breadth first traversal of a tree visits the
nodes in the order of depth in the tree
BFT first visits all the nodes at depth zero
(i.e., root), then all the nodes at depth one
and so on
At each depth, the nodes are visited from left
to right
12. DEPTH FIRST TRAVERSAL
(DFT)
Depth first traversal is an algorithm for
traversing or searching a tree, tree structure
or graph
One starts at the root and explores as far as
possible along each branch before
backtracking
13. BINARY SEARCH TREE
A binary search tree, also called as an ordered
or sorted binary tree, has following properties:
i) The left subtree of a node contains only
nodes with keys less than the node’s key
ii) The right subtree of a node contains only
nodes with keys greater than the node’s key
iii) Both the left subtrees and right subtrees
must also be binary search trees
14. AVERAGE CASE PERFORMANCE
OF BST OPERATIONS
Internal Path Length (IPL) of a binary tree is
the sum of the depths of its nodes.
Average internal path length T(n) of binary
trees with n nodes is O(n log n)
The average complexity to find or insert
operations is T(n) = O(log n)
15. AVL TREES
An AVL (Adelson-Velskii and Land) is a binary
tree with the following additional balance
properties:
i) For any node in the tree, the height of the
left and right subtrees can differ by atmost
ii) The height of an empty subtree is -1
16. AVL TREES
An AVL is a binary search tree which has the
following properties:
i) The subtrees of every node differ in height
by atmost one
ii) Every subtree is an AVL tree
Balance factor of a node = Height of left
subtree – Height of right subtree
17. GREEDY ALGORITHMS
Greedy algorithms are simple and straight-
forward
They are short sighted in their approach in the
sense they take decisions on the basis of
information at hand without worrying about
the effect of these decisions in the future
They are used to solve optimization problems
18. FEASIBILITY
A feasible set is promising, if it can be
extended to produce not merely as solution,
but an optimal solution to the problem
19. SPANNING TREE
A spanning tree of a graph is any tree that
includes every vertex in the graph
A spanning tree of a graph G is a subgraph of
G that is a tree and contains all vertices of G
The number of spanning trees in the complete
graph 𝐾 𝑛 is 𝑛 𝑛−2
20. MINIMUM SPANNING TREE
A Minimum Spanning Tree (MST) of a
weighted graph G is a spanning tree of G
whose edges sum is minimum weight
There are two algorithms to find the minimum
spanning tree of an undirected weighted
graph
21. KRUSKAL’S ALGORITHM
Kruskal’s algorithm is a Greedy algorithm
In this algorithm, starts with each vertex being
its component. Repeatedly merges two
components into one by choosing the light
edge that connects them, that’s why, this
algorithm is edge based algorithm
22. KRUSKAL’S ALGORITHM
Let G = (V,E) is a connected, undirected,
weighted graph
Scans the set of edges in increasing order by
weight. The edge is selected such that: i)
acyclicity should be maintained, ii) it should
be minimum weight, iii) when tree T contains
n-1 edges, also must terminate
Uses a disjoint set of data structure to
determine whether an edge connects vertices
in different components
23. ANALYSIS OF KRUSKAL’S
ALGORITHM
The total time taken by this algorithm to find the
minimum spanning tree is O(E 𝑙𝑜𝑔2 E) (if edges
are already sorted)
But the time complexity, if edges are not sorted
is O(E 𝑙𝑜𝑔2 V)
24. PRIM’S ALGORITHM
Prim’s algorithm is based on a generic
minimum spanning tree algorithm
The idea of Prim’s algorithm is to find the
shortest path in a given graph
The Prim’s algorithm has the property that the
edges in the set A always form a single
connected tree
25. PRIM’S ALGORITHM
We begin with some vertex V in a given graph G
= (V,E), defining the initial set of vertices A.
Then, in each iteration, we choose a minimum
weight edge (u,v), connecting a vertex v in the
set A to the vertex u outside of set A. Then,
vertex u is brought into A. This tree is repeated,
until a spanning tree is formed
26. DYNAMIC PROGRAMMING
ALGORITHMS
Dynamic programming approach for the
algorithm design solves the problems by
combining the solutions to some problems, as
we do in divide and conquer approach
It is more powerful
It is a stage-wise search method suitable for
optimization problems whose solutions may
be viewed as the result of a sequence of
decisions
27. DIJKSTRA’S ALGORITHM
Dijkstra’s algorithm solves the single source
shortest path problems on a weighted
directed graph
It is Greedy algorithm
Dijkstra’s algorithm starts at the source vertex,
it grows a tree T, that spans all vertices
reachable from S