The document discusses heap sort, a sorting algorithm that works by organizing data into a binary heap data structure. It has a time complexity of O(n log n) and space complexity of O(1), making it efficient for sorting large datasets. The algorithm involves building a max or min heap from an array and then repeatedly removing the maximum or minimum element and restoring the heap property.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Heap sort is a sorting algorithm that uses a heap data structure. It first transforms the input array into a max heap by calling the heapify procedure. It then repeatedly swaps the root element with the last element, reduces the size of the heap by 1, and calls heapify to restore the heap property. This process continues until the entire array is sorted. Heap sort has a time complexity of O(n log n) and space complexity of O(1), making it efficient for sorting large datasets.
heap sort in the design anad analysis of algorithmsssuser7319f8
Heap sort is a sorting algorithm that uses a heap data structure. It works in two phases: first it builds a max heap from the input data, then it repeatedly extracts the largest element from the heap and inserts it into the sorted end of the data. This results in the elements being sorted in O(n log n) time using only O(1) additional memory space, making it efficient for both time and space complexity. It performs better than quicksort in the worst case but requires random access to data unlike merge sort.
Heap sort is a sorting algorithm that uses a heap data structure. It works in two phases: (1) building a max heap from the input data, and (2) extracting elements from the heap and inserting them into the output array. This results in the elements being sorted in O(n log n) time with O(1) auxiliary space. Heap sort is often preferred over other sorting algorithms for its efficiency and not requiring additional storage space.
Heap sort is a comparison-based sorting algorithm that uses a heap data structure. It works in two phases: first it builds a max heap from the input data and then extracts elements from the heap one by one, each time putting the largest remaining element in its sorted position. This results in the elements being sorted in non-decreasing order with a time complexity of O(n log n). Heap sort is an efficient in-place sorting algorithm that uses constant extra space.
The document discusses heap data structures and their implementation using arrays. It defines a heap as a complete binary tree that satisfies the heap property - a node's value is greater than or equal to its children's values. Heaps can be implemented using arrays by numbering nodes from top to bottom and storing each node at its number index. Common heap operations like building a heap from an array, inserting/extracting elements, and deleting elements are described along with their time complexities of O(n) or O(log n).
This document describes heap data structures and algorithms like heap sort. It defines a max heap and min heap. It explains the build heap, heapify, insertion and deletion algorithms. Build heap transforms an array into a max heap by applying heapify to each node from bottom to top. Heapify maintains the heap property when a node is added or removed. Heap sort works by building a max heap from the input array and then extracting elements from the root to sort the array in descending order.
Heap sort is a comparison-based sorting algorithm that uses a binary heap data structure. It first transforms the input array into a max-heap by calling the heapify function recursively on each node. It then extracts the maximum element from the heap and places it at the end of the sorted portion of the array. This process is repeated until the heap is empty. Heap sort has a time complexity of O(n log n) and requires only O(1) auxiliary space, making it an efficient in-place sorting algorithm.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Heap sort is a sorting algorithm that uses a heap data structure. It first transforms the input array into a max heap by calling the heapify procedure. It then repeatedly swaps the root element with the last element, reduces the size of the heap by 1, and calls heapify to restore the heap property. This process continues until the entire array is sorted. Heap sort has a time complexity of O(n log n) and space complexity of O(1), making it efficient for sorting large datasets.
heap sort in the design anad analysis of algorithmsssuser7319f8
Heap sort is a sorting algorithm that uses a heap data structure. It works in two phases: first it builds a max heap from the input data, then it repeatedly extracts the largest element from the heap and inserts it into the sorted end of the data. This results in the elements being sorted in O(n log n) time using only O(1) additional memory space, making it efficient for both time and space complexity. It performs better than quicksort in the worst case but requires random access to data unlike merge sort.
Heap sort is a sorting algorithm that uses a heap data structure. It works in two phases: (1) building a max heap from the input data, and (2) extracting elements from the heap and inserting them into the output array. This results in the elements being sorted in O(n log n) time with O(1) auxiliary space. Heap sort is often preferred over other sorting algorithms for its efficiency and not requiring additional storage space.
Heap sort is a comparison-based sorting algorithm that uses a heap data structure. It works in two phases: first it builds a max heap from the input data and then extracts elements from the heap one by one, each time putting the largest remaining element in its sorted position. This results in the elements being sorted in non-decreasing order with a time complexity of O(n log n). Heap sort is an efficient in-place sorting algorithm that uses constant extra space.
The document discusses heap data structures and their implementation using arrays. It defines a heap as a complete binary tree that satisfies the heap property - a node's value is greater than or equal to its children's values. Heaps can be implemented using arrays by numbering nodes from top to bottom and storing each node at its number index. Common heap operations like building a heap from an array, inserting/extracting elements, and deleting elements are described along with their time complexities of O(n) or O(log n).
This document describes heap data structures and algorithms like heap sort. It defines a max heap and min heap. It explains the build heap, heapify, insertion and deletion algorithms. Build heap transforms an array into a max heap by applying heapify to each node from bottom to top. Heapify maintains the heap property when a node is added or removed. Heap sort works by building a max heap from the input array and then extracting elements from the root to sort the array in descending order.
Heap sort is a comparison-based sorting algorithm that uses a binary heap data structure. It first transforms the input array into a max-heap by calling the heapify function recursively on each node. It then extracts the maximum element from the heap and places it at the end of the sorted portion of the array. This process is repeated until the heap is empty. Heap sort has a time complexity of O(n log n) and requires only O(1) auxiliary space, making it an efficient in-place sorting algorithm.
Heap Sort in Design and Analysis of algorithmssamairaakram
Brief description of Heap Sort and its types.it includes Binary Tree and its types. analysis and algorithm of Heap Sort. comparison b/w Heap,Qucik and Merge Sort.
The document discusses heapsort, an efficient sorting algorithm that uses a heap data structure. Heapsort first builds a max heap from the input array in O(n) time using a heapify procedure. It then extracts elements from the heap into the sorted output array, maintaining the heap property, resulting in an overall time complexity of O(n log n).
This document summarizes a lab on data structures and algorithms that focuses on heaps and heap sort. It introduces heaps as almost complete binary trees stored in an array that obey the max-heap or min-heap property. Basic heap operations like insertion and deletion are described along with filtering an element up or down the heap to maintain the property. Heap sort is then introduced as using a heap to iteratively extract and place the minimum element. The objectives are to implement functions for getting a node's parent and children in a heap as well as implement and test heap sort.
Heap sort uses a heap data structure that maintains the max-heap or min-heap property. It involves two main steps: 1) building the heap from the input array using the BUILD-MAX-HEAP procedure in O(n) time, and 2) repeatedly extracting the maximum/minimum element from the heap and inserting it into the sorted portion using the DELHEAP procedure, running in O(n log n) time overall. The key operation is MAX-HEAPIFY, which maintains the max-heap property in O(log n) time during heap operations like insertion and deletion.
This document discusses heapsort and priority queues implemented using binary heaps. Heapsort uses a max heap to sort an array in O(n log n) time by repeatedly extracting the maximum element and placing it in its sorted position. A priority queue uses a min heap to retrieve the minimum element in O(log n) time for insertions and deletions by keeping the minimum key at the root.
This document discusses the heap data structure and heapsort algorithm. It defines a heap as a nearly complete binary tree that satisfies the heap property, where every parent node is greater than or equal to its children. It describes how to represent a heap using an array and the key operations of building a max-heap from an array, inserting and deleting nodes, and maintaining the heap property. Heapsort works by building a max-heap from the input array and then extracting elements in sorted order.
Algorithm Design and Complexity - Course 4 - Heaps and Dynamic ProgammingTraian Rebedea
Course 4 for the Algorithm Design and Complexity course at the Faculty of Engineering in Foreign Languages - Politehnica University of Bucharest, Romania
This document provides information about priority queues and binary heaps. It defines a binary heap as a nearly complete binary tree where the root node has the maximum/minimum value. It describes heap operations like insertion, deletion of max/min, and increasing/decreasing keys. The time complexity of these operations is O(log n). Heapsort, which uses a heap data structure, is also covered and has overall time complexity of O(n log n). Binary heaps are often used to implement priority queues and for algorithms like Dijkstra's and Prim's.
This document describes the heap sort algorithm. It begins by explaining heaps and their properties like the heap property. It then describes key heap operations like Max-Heapify, Build-Max-Heap, finding the maximum element, extract max, increase key, and insert. These operations allow heaps to function as priority queues. Heap sort works by building a max heap from the input array using Build-Max-Heap, then repeatedly extracting the maximum element and putting it in its sorted position. This runs in O(n log n) time, combining advantages of insertion and merge sort by sorting in-place like insertion sort but with a faster running time of merge sort.
Heaps are nearly complete binary trees stored as arrays that satisfy the heap property: for max-heaps a parent node is greater than or equal to its children, and for min-heaps a parent is less than or equal to its children. Heap operations like insert, extract max/min, and increase/decrease key take O(log n) time due to the heap's height. The heapsort algorithm uses a max-heap to sort an array in O(n log n) time by repeatedly extracting and placing the max element in its final position. Priority queues implemented with heaps support insertion, maximum/minimum extraction, and key increases/decreases in O(log n) time.
This document discusses heaps and priority queues. It defines a min-heap as a complete binary tree where the root value is the smallest and its subtrees are also heaps. This property allows a min-heap to efficiently implement a priority queue, where the smallest element can always be found at the root. Elements can be inserted in O(log n) time by adding to the end and percolating up, and removed in O(log n) time by removing the root and percolating down the replacement. This makes heap-based priority queues more efficient than other implementations like sorted lists. Heapsort is also discussed, which sorts in O(n log n) time by building a heap and repeatedly removing elements
Heap sort is based on the priority queue data structure implemented using a heap. Specifically, heap sort uses a max-heap or min-heap to sort elements in ascending or descending order respectively.
The key steps are:
1) Build a max-heap from the input array in O(n) time
2) Repeatedly remove the max/min element from the heap and put it in its sorted position in the array. This takes O(nlogn) time.
So the overall time complexity of heap sort is O(nlogn). It is an in-place sorting algorithm that does not require additional storage.
Heap sort is a sorting algorithm that uses a heap data structure. It has two main steps: 1) transforming the array into a max or min heap, and 2) performing the actual sort by extracting the largest/smallest element and transforming the remaining heap. Heap sort runs in O(n log n) time and uses O(1) constant memory, making it an efficient in-place sorting algorithm.
Here is a linear programming formulation of the election problem:
Let x = amount spent on urban ads
y = amount spent on suburban ads
z = amount spent on rural ads
Minimize: x + y + z
Subject to: x ≥ 100,000 (urban votes)
y ≥ 200,000 (suburban votes)
z ≥ 25,000 (rural votes)
x, y, z ≥ 0
The objective is to minimize total spending while satisfying the vote constraints.
The document discusses different types of heaps and heap algorithms. It describes binary min-heaps and max-heaps, including their properties and implementations using arrays. Basic heap operations like insert, delete, and build heap are explained along with their time complexities. Applications of heaps like priority queues and selection algorithms are covered. More advanced heap types like leftist heaps, skew heaps and binomial queues are also mentioned.
This document discusses heaps, which are binary trees with the additional properties that they are complete trees and each node is less than or equal to its children. Heaps support operations like adding elements, removing the minimum element, and finding the minimum element. The key operations and their implementations using both linked nodes and arrays are explained. Heaps can be used to implement priority queues and the heap sort algorithm.
This document summarizes a project report for a job portal website. The project aims to reduce the gap between industries and needed resources by allowing users to post jobs, search for jobs and candidates, and apply for jobs online. It will have modules for job seekers to post resumes and browse vacancies, employers to post jobs and search resumes, and an admin module to manage user profiles and the application. The project is intended to replace manual recruitment processes with an interactive and less expensive online system.
The document discusses threads in Java. It defines a thread as the basic unit of Java program execution that requires less resources than a process. It describes how to create threads by extending the Thread class or implementing the Runnable interface. It outlines the advantages of multithreading like performing operations simultaneously to save time. It details the various states in a thread's lifecycle - newborn, runnable, running, blocked, and dead. It explains how threads can enter the blocked state through methods like suspend(), sleep(), and wait(). Finally, it defines deadlock as when two or more threads are blocked forever waiting for resources held by each other.
Heap Sort in Design and Analysis of algorithmssamairaakram
Brief description of Heap Sort and its types.it includes Binary Tree and its types. analysis and algorithm of Heap Sort. comparison b/w Heap,Qucik and Merge Sort.
The document discusses heapsort, an efficient sorting algorithm that uses a heap data structure. Heapsort first builds a max heap from the input array in O(n) time using a heapify procedure. It then extracts elements from the heap into the sorted output array, maintaining the heap property, resulting in an overall time complexity of O(n log n).
This document summarizes a lab on data structures and algorithms that focuses on heaps and heap sort. It introduces heaps as almost complete binary trees stored in an array that obey the max-heap or min-heap property. Basic heap operations like insertion and deletion are described along with filtering an element up or down the heap to maintain the property. Heap sort is then introduced as using a heap to iteratively extract and place the minimum element. The objectives are to implement functions for getting a node's parent and children in a heap as well as implement and test heap sort.
Heap sort uses a heap data structure that maintains the max-heap or min-heap property. It involves two main steps: 1) building the heap from the input array using the BUILD-MAX-HEAP procedure in O(n) time, and 2) repeatedly extracting the maximum/minimum element from the heap and inserting it into the sorted portion using the DELHEAP procedure, running in O(n log n) time overall. The key operation is MAX-HEAPIFY, which maintains the max-heap property in O(log n) time during heap operations like insertion and deletion.
This document discusses heapsort and priority queues implemented using binary heaps. Heapsort uses a max heap to sort an array in O(n log n) time by repeatedly extracting the maximum element and placing it in its sorted position. A priority queue uses a min heap to retrieve the minimum element in O(log n) time for insertions and deletions by keeping the minimum key at the root.
This document discusses the heap data structure and heapsort algorithm. It defines a heap as a nearly complete binary tree that satisfies the heap property, where every parent node is greater than or equal to its children. It describes how to represent a heap using an array and the key operations of building a max-heap from an array, inserting and deleting nodes, and maintaining the heap property. Heapsort works by building a max-heap from the input array and then extracting elements in sorted order.
Algorithm Design and Complexity - Course 4 - Heaps and Dynamic ProgammingTraian Rebedea
Course 4 for the Algorithm Design and Complexity course at the Faculty of Engineering in Foreign Languages - Politehnica University of Bucharest, Romania
This document provides information about priority queues and binary heaps. It defines a binary heap as a nearly complete binary tree where the root node has the maximum/minimum value. It describes heap operations like insertion, deletion of max/min, and increasing/decreasing keys. The time complexity of these operations is O(log n). Heapsort, which uses a heap data structure, is also covered and has overall time complexity of O(n log n). Binary heaps are often used to implement priority queues and for algorithms like Dijkstra's and Prim's.
This document describes the heap sort algorithm. It begins by explaining heaps and their properties like the heap property. It then describes key heap operations like Max-Heapify, Build-Max-Heap, finding the maximum element, extract max, increase key, and insert. These operations allow heaps to function as priority queues. Heap sort works by building a max heap from the input array using Build-Max-Heap, then repeatedly extracting the maximum element and putting it in its sorted position. This runs in O(n log n) time, combining advantages of insertion and merge sort by sorting in-place like insertion sort but with a faster running time of merge sort.
Heaps are nearly complete binary trees stored as arrays that satisfy the heap property: for max-heaps a parent node is greater than or equal to its children, and for min-heaps a parent is less than or equal to its children. Heap operations like insert, extract max/min, and increase/decrease key take O(log n) time due to the heap's height. The heapsort algorithm uses a max-heap to sort an array in O(n log n) time by repeatedly extracting and placing the max element in its final position. Priority queues implemented with heaps support insertion, maximum/minimum extraction, and key increases/decreases in O(log n) time.
This document discusses heaps and priority queues. It defines a min-heap as a complete binary tree where the root value is the smallest and its subtrees are also heaps. This property allows a min-heap to efficiently implement a priority queue, where the smallest element can always be found at the root. Elements can be inserted in O(log n) time by adding to the end and percolating up, and removed in O(log n) time by removing the root and percolating down the replacement. This makes heap-based priority queues more efficient than other implementations like sorted lists. Heapsort is also discussed, which sorts in O(n log n) time by building a heap and repeatedly removing elements
Heap sort is based on the priority queue data structure implemented using a heap. Specifically, heap sort uses a max-heap or min-heap to sort elements in ascending or descending order respectively.
The key steps are:
1) Build a max-heap from the input array in O(n) time
2) Repeatedly remove the max/min element from the heap and put it in its sorted position in the array. This takes O(nlogn) time.
So the overall time complexity of heap sort is O(nlogn). It is an in-place sorting algorithm that does not require additional storage.
Heap sort is a sorting algorithm that uses a heap data structure. It has two main steps: 1) transforming the array into a max or min heap, and 2) performing the actual sort by extracting the largest/smallest element and transforming the remaining heap. Heap sort runs in O(n log n) time and uses O(1) constant memory, making it an efficient in-place sorting algorithm.
Here is a linear programming formulation of the election problem:
Let x = amount spent on urban ads
y = amount spent on suburban ads
z = amount spent on rural ads
Minimize: x + y + z
Subject to: x ≥ 100,000 (urban votes)
y ≥ 200,000 (suburban votes)
z ≥ 25,000 (rural votes)
x, y, z ≥ 0
The objective is to minimize total spending while satisfying the vote constraints.
The document discusses different types of heaps and heap algorithms. It describes binary min-heaps and max-heaps, including their properties and implementations using arrays. Basic heap operations like insert, delete, and build heap are explained along with their time complexities. Applications of heaps like priority queues and selection algorithms are covered. More advanced heap types like leftist heaps, skew heaps and binomial queues are also mentioned.
This document discusses heaps, which are binary trees with the additional properties that they are complete trees and each node is less than or equal to its children. Heaps support operations like adding elements, removing the minimum element, and finding the minimum element. The key operations and their implementations using both linked nodes and arrays are explained. Heaps can be used to implement priority queues and the heap sort algorithm.
This document summarizes a project report for a job portal website. The project aims to reduce the gap between industries and needed resources by allowing users to post jobs, search for jobs and candidates, and apply for jobs online. It will have modules for job seekers to post resumes and browse vacancies, employers to post jobs and search resumes, and an admin module to manage user profiles and the application. The project is intended to replace manual recruitment processes with an interactive and less expensive online system.
The document discusses threads in Java. It defines a thread as the basic unit of Java program execution that requires less resources than a process. It describes how to create threads by extending the Thread class or implementing the Runnable interface. It outlines the advantages of multithreading like performing operations simultaneously to save time. It details the various states in a thread's lifecycle - newborn, runnable, running, blocked, and dead. It explains how threads can enter the blocked state through methods like suspend(), sleep(), and wait(). Finally, it defines deadlock as when two or more threads are blocked forever waiting for resources held by each other.
This document provides an introduction to the Java programming language. It discusses that Java is platform independent, object-oriented, and designed with a core language plus common packages. It also describes that Java source code is compiled to byte code, which is executed by the Java Virtual Machine. The document lists Java's primitive data types including integers, reals, characters, and booleans. It also outlines Java's basic operators.
HHW OF IT PRESENTATION ON INTERNET SECURITY BY AASTHA SHARMA 10TH KEATS^.pptxHemantSharma134028
Internet security consists of tactics to protect online activities from threats like hacking, malware, and identity theft. It focuses on vulnerabilities unique to using the internet, and is part of broader cybersecurity. Common threats include malware, computer worms, spam, phishing scams, and botnets. Choosing the right security tactics involves creating strong passwords, limiting social media oversharing, using caution on public Wi-Fi, watching for phishing links and attachments, and checking for website security features.
This document discusses Java threads and synchronization. It begins with an introduction to threads, defining a thread as a single sequential flow of control within a program. It then covers how to define and launch threads in Java by extending the Thread class or implementing the Runnable interface. The life cycle of a Java thread is explained, including the various thread states. Methods for interrupting threads and thread synchronization using synchronized methods and statements are discussed. Finally, Java's monitor model for thread synchronization is described.
Java is a popular programming language originally developed by Sun Microsystems. It was created in 1991 by James Ghosling and team over 18 months. Java runs on many platforms like Windows, Mac OS, and Linux. It is widely used for both desktop and mobile applications as well as web applications, embedded systems, and more. Java is known for being simple, portable across platforms as code is compiled to bytecode, and platform independent as it is write once run anywhere. The Java Development Kit contains tools needed for developing Java programs including a compiler, interpreter, and documentation generator.
Linear search is a basic algorithm that sequentially checks each element of an array to find a target value. Binary search compares the target to the middle element and then searches either the first or second half of the array. It requires a sorted array and is faster than linear search. The document provides code examples of implementing linear and binary search in Java.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
Embedded machine learning-based road conditions and driving behavior monitoringIJECEIAES
Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.
Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapte...University of Maribor
Slides from talk presenting:
Aleš Zamuda: Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapter and Networking.
Presentation at IcETRAN 2024 session:
"Inter-Society Networking Panel GRSS/MTT-S/CIS
Panel Session: Promoting Connection and Cooperation"
IEEE Slovenia GRSS
IEEE Serbia and Montenegro MTT-S
IEEE Slovenia CIS
11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
2. GOALS
To explore the implementation, testing and
performance of heap sort algorithm
3. HEAP
A heap is a data structure that stores a
collection of objects (with keys), and has the
following properties:
Complete Binary tree
Heap Order
It is implemented as an array where each
node in the tree corresponds to an element
of the array.
4. HEAP
The binary heap data structures is an array that can
be viewed as a complete binary tree. Each node of
the binary tree corresponds to an element of the
array. The array is completely filled on all levels
except possibly lowest.
19
12 16
4
1 7
16
19 1 4
12 7
Array A
5. HEAP
The root of the tree A[1] and given index i of a
node, the indices of its parent, left child and right
child can be computed
PARENT (i)
return floor(i/2)
LEFT (i)
return 2i
RIGHT (i)
return 2i + 1
6. HEAP ORDER PROPERTY
For every node v, other than the root, the key
stored in v is greater or equal (smaller or equal for
max heap) than the key stored in the parent of v.
In this case the maximum value is stored in the root
7. DEFINITION
Max Heap
Store data in ascending order
Has property of
A[Parent(i)] ≥ A[i]
Min Heap
Store data in descending order
Has property of
A[Parent(i)] ≤ A[i]
10. INSERTION
Algorithm
1. Add the new element to the next available position at the
lowest level
2. Restore the max-heap property if violated
General strategy is percolate up (or bubble up): if the
parent of the element is smaller than the element, then
interchange the parent and child.
OR
Restore the min-heap property if violated
General strategy is percolate up (or bubble up): if the
parent of the element is larger than the element, then
interchange the parent and child.
12. DELETION
Delete max
Copy the last number to the root ( overwrite the
maximum element stored there ).
Restore the max heap property by percolate down.
Delete min
Copy the last number to the root ( overwrite the
minimum element stored there ).
Restore the min heap property by percolate down.
13. HEAP SORT
A sorting algorithm that works by first organizing the
data to be sorted into a special type of binary tree called
a heap
15. HEAPIFY
Heapify picks the largest child key and compare it to the
parent key. If parent key is larger than heapify quits, otherwise
it swaps the parent key with the largest child key. So that the
parent is now becomes larger than its children.
Heapify(A, i)
{
l left(i)
r right(i)
if l <= heapsize[A] and A[l] > A[i]
then largest l
else largest i
if r <= heapsize[A] and A[r] > A[largest]
then largest r
if largest != i
then swap A[i] A[largest]
Heapify(A, largest)
}
16. BUILD HEAP
We can use the procedure 'Heapify' in a bottom-up fashion to
convert an array A[1 . . n] into a heap. Since the elements in
the subarray A[n/2 +1 . . n] are all leaves, the procedure
BUILD_HEAP goes through the remaining nodes of the tree
and runs 'Heapify' on each one. The bottom-up order of
processing node guarantees that the subtree rooted at
children are heap before 'Heapify' is run at their parent.
Buildheap(A)
{
heapsize[A] length[A]
for i |length[A]/2 //down to 1
do Heapify(A, i)
}
17. HEAP SORT ALGORITHM
The heap sort algorithm starts by using procedure BUILD-
HEAP to build a heap on the input array A[1 . . n]. Since the
maximum element of the array stored at the root A[1], it can
be put into its correct final position by exchanging it with A[n]
(the last element in A). If we now discard node n from the
heap than the remaining elements can be made into heap.
Note that the new element at the root may violate the heap
property. All that is needed to restore the heap property.
Heapsort(A)
{
Buildheap(A)
for i length[A] //down to 2
do swap A[1] A[i]
heapsize[A] heapsize[A] - 1
Heapify(A, 1)
}
18. Example: Convert the following array to a heap
16 4 7 1 12 19
Picture the array as a complete binary tree:
16
4 7
12
1 19
20. HEAP SORT
The heapsort algorithm consists of two phases:
- build a heap from an arbitrary array
- use the heap to sort the data
To sort the elements in the decreasing order, use a min heap
To sort the elements in the increasing order, use a max heap
19
12 16
4
1 7
21. EXAMPLE OF HEAP SORT
19
12 16
4
1 7
19
12 16 1 4 7
Array A
Sorted:
Take out biggest
Move the last element
to the root
36. TIME ANALYSIS
Build Heap Algorithm will run in O(n) time
There are n-1 calls to Heapify each call requires
O(log n) time
Heap sort program combine Build Heap program
and Heapify, therefore it has the running time of O(n
log n) time
Total time complexity: O(n log n)
37. COMPARISON WITH QUICK SORT AND MERGE
SORT
Quick sort is typically somewhat faster, due to better cache
behavior and other factors, but the worst-case running time for
quick sort is O (n2), which is unacceptable for large data sets
and can be deliberately triggered given enough knowledge of
the implementation, creating a security risk.
The quick sort algorithm also requires Ω (log n) extra storage
space, making it not a strictly in-place algorithm. This typically
does not pose a problem except on the smallest embedded
systems, or on systems where memory allocation is highly
restricted. Constant space (in-place) variants of quick sort are
possible to construct, but are rarely used in practice due to
their extra complexity.
38. COMPARISON WITH QUICK SORT AND MERGE
SORT (CONT)
Thus, because of the O(n log n) upper bound on heap sort’s
running time and constant upper bound on its auxiliary
storage, embedded systems with real-time constraints or
systems concerned with security often use heap sort.
Heap sort also competes with merge sort, which has the same
time bounds, but requires Ω(n) auxiliary space, whereas heap
sort requires only a constant amount. Heap sort also typically
runs more quickly in practice. However, merge sort is simpler
to understand than heap sort, is a stable sort, parallelizes
better, and can be easily adapted to operate on linked lists
and very large lists stored on slow-to-access media such as
disk storage or network attached storage. Heap sort shares
none of these benefits; in particular, it relies strongly on
random access.
39. POSSIBLE APPLICATION
When we want to know the task that carry the highest
priority given a large number of things to do
Interval scheduling, when we have a lists of certain task
with start and finish times and we want to do as many
tasks as possible
Sorting a list of elements that needs and efficient sorting
algorithm
40. CONCLUSION
The primary advantage of the heap sort is its
efficiency. The execution time efficiency of the heap
sort is O(n log n). The memory efficiency of the
heap sort, unlike the other n log n sorts, is constant,
O(1), because the heap sort algorithm is not
recursive.
The heap sort algorithm has two major steps. The
first major step involves transforming the complete
tree into a heap. The second major step is to
perform the actual sort by extracting the largest
element from the root and transforming the
remaining tree into a heap.
41. REFERENCE
Deitel, P.J. and Deitel, H.M. (2008) “C++ How to
Program”. 6th ed. Upper Saddle River, New
Jersey, Pearson Education, Inc.
Carrano, Frank M. (2007) “Data Abstraction and
problem solving with C++: walls and
mirrors”. 5th ed. Upper Saddle River, New
Jersey, Pearson Education, Inc.