Sorting
Performance parameters
Insertion Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Shell Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
The document discusses different types of queues and their implementations. It begins by defining a queue as a first-in first-out (FIFO) data structure where elements are inserted at the rear and deleted from the front. It then covers linear and circular queue implementations using arrays, including operations like insertion, deletion, checking for empty/full, and traversal. Priority queues are also introduced, which process elements based on assigned priorities. The key types and operations of queues as an abstract data type (ADT) are summarized.
The document discusses several sorting algorithms including selection sort, insertion sort, bubble sort, merge sort, and quick sort. It provides details on how each algorithm works including pseudocode implementations and analyses of their time complexities. Selection sort, insertion sort and bubble sort have a worst-case time complexity of O(n^2) while merge sort divides the list into halves and merges in O(n log n) time, making it more efficient for large lists.
Queue is an abstract data structure, somewhat similar to Stacks. Unlike stacks, a queue is open at both its ends. One end is always used to insert data (enqueue) and the other is used to remove data (dequeue). Queue follows First-In-First-Out methodology, i.e., the data item stored first will be accessed first.
Binary search is an algorithm that finds the position of a target value within a sorted array. It works by recursively dividing the array range in half and searching only within the appropriate half. The time complexity is O(log n) in the average and worst cases and O(1) in the best case, making it very efficient for searching sorted data. However, it requires the list to be sorted for it to work.
Binary search trees (BSTs) are data structures that allow for efficient searching, insertion, and deletion. Nodes in a BST are organized so that all left descendants of a node are less than the node's value and all right descendants are greater. This property allows values to be found, inserted, or deleted in O(log n) time on average. Searching involves recursively checking if the target value is less than or greater than the current node's value. Insertion follows the search process and adds the new node in the appropriate place. Deletion handles three cases: removing a leaf, node with one child, or node with two children.
Selection sort is a sorting algorithm that works by repeatedly finding the minimum element from an unsorted sublist and putting it at the front. It has the following steps:
1. Start with an unsorted list.
2. Find the minimum element in the list and swap it with the first element.
3. Repeat step 2 for the remaining elements, each time considering one less element at the front that is already in sorted order.
The algorithm runs in O(n2) time as the inner loop needs to run n-1 times for n elements. It works for both ascending and descending order by changing the comparison operator in the inner loop.
The document discusses various sorting algorithms including insertion sort, selection sort, bubble sort, merge sort, and quick sort. It provides detailed explanations of how each algorithm works through examples using arrays or lists of numbers. The key steps of each algorithm are outlined in pseudocode to demonstrate how they sort a set of data in either ascending or descending order.
This document discusses priority queues. It defines a priority queue as a queue where insertion and deletion are based on some priority property. Items with higher priority are removed before lower priority items. There are two main types: ascending priority queues remove the smallest item, while descending priority queues remove the largest item. Priority queues are useful for scheduling jobs in operating systems, where real-time jobs have highest priority and are scheduled first. They are also used in network communication to manage limited bandwidth.
The document discusses different types of queues and their implementations. It begins by defining a queue as a first-in first-out (FIFO) data structure where elements are inserted at the rear and deleted from the front. It then covers linear and circular queue implementations using arrays, including operations like insertion, deletion, checking for empty/full, and traversal. Priority queues are also introduced, which process elements based on assigned priorities. The key types and operations of queues as an abstract data type (ADT) are summarized.
The document discusses several sorting algorithms including selection sort, insertion sort, bubble sort, merge sort, and quick sort. It provides details on how each algorithm works including pseudocode implementations and analyses of their time complexities. Selection sort, insertion sort and bubble sort have a worst-case time complexity of O(n^2) while merge sort divides the list into halves and merges in O(n log n) time, making it more efficient for large lists.
Queue is an abstract data structure, somewhat similar to Stacks. Unlike stacks, a queue is open at both its ends. One end is always used to insert data (enqueue) and the other is used to remove data (dequeue). Queue follows First-In-First-Out methodology, i.e., the data item stored first will be accessed first.
Binary search is an algorithm that finds the position of a target value within a sorted array. It works by recursively dividing the array range in half and searching only within the appropriate half. The time complexity is O(log n) in the average and worst cases and O(1) in the best case, making it very efficient for searching sorted data. However, it requires the list to be sorted for it to work.
Binary search trees (BSTs) are data structures that allow for efficient searching, insertion, and deletion. Nodes in a BST are organized so that all left descendants of a node are less than the node's value and all right descendants are greater. This property allows values to be found, inserted, or deleted in O(log n) time on average. Searching involves recursively checking if the target value is less than or greater than the current node's value. Insertion follows the search process and adds the new node in the appropriate place. Deletion handles three cases: removing a leaf, node with one child, or node with two children.
Selection sort is a sorting algorithm that works by repeatedly finding the minimum element from an unsorted sublist and putting it at the front. It has the following steps:
1. Start with an unsorted list.
2. Find the minimum element in the list and swap it with the first element.
3. Repeat step 2 for the remaining elements, each time considering one less element at the front that is already in sorted order.
The algorithm runs in O(n2) time as the inner loop needs to run n-1 times for n elements. It works for both ascending and descending order by changing the comparison operator in the inner loop.
The document discusses various sorting algorithms including insertion sort, selection sort, bubble sort, merge sort, and quick sort. It provides detailed explanations of how each algorithm works through examples using arrays or lists of numbers. The key steps of each algorithm are outlined in pseudocode to demonstrate how they sort a set of data in either ascending or descending order.
This document discusses priority queues. It defines a priority queue as a queue where insertion and deletion are based on some priority property. Items with higher priority are removed before lower priority items. There are two main types: ascending priority queues remove the smallest item, while descending priority queues remove the largest item. Priority queues are useful for scheduling jobs in operating systems, where real-time jobs have highest priority and are scheduled first. They are also used in network communication to manage limited bandwidth.
Shell sort is a sorting algorithm created by Donald Shell in 1959 that improves on insertion sort. It works by comparing elements that are farther apart within the list rather than just adjacent elements. It performs multiple passes over the list, each with a larger increment, sorting subsets of the elements. Shell sort is more efficient than bubble sort and faster than plain insertion sort, with its main advantage being for medium sized lists. The choice of increments can impact its performance and potential issues arise if the increments are not relatively prime.
The document describes insertion sort, a sorting algorithm. It lists the group members who researched insertion sort and provides an introduction. It then explains how insertion sort works by example, showing how it iterates through an array and inserts elements into the sorted portion. Pseudocode and analysis of insertion sort's runtime is provided. Comparisons are made between insertion sort and other algorithms like bubble sort, selection sort, and merge sort, analyzing their time complexities in best, average, and worst cases.
Traversal is a process to visit all the nodes of a tree and may print their values too. Because, all nodes are connected via edges (links) we always start from the root (head) node. That is, we cannot randomly access a node in a tree.
This presentation is useful to study about data structure and topic is Binary Tree Traversal. This is also useful to make a presentation about Binary Tree Traversal.
The document discusses insertion sort, a simple sorting algorithm that builds a sorted output list from an input one element at a time. It is less efficient on large lists than more advanced algorithms. Insertion sort iterates through the input, at each step removing an element and inserting it into the correct position in the sorted output list. The best case for insertion sort is an already sorted array, while the worst is a reverse sorted array.
An ordered collection of items from which items may be deleted from one end called the front and into which items may be inserted from other end called rear is known as Queue.
It is a linear data structure.
It is called the First In First Out (FIFO) list. Since in queue, the first element will be the first element out.
The document discusses various sorting algorithms including selection sort, insertion sort, merge sort, quick sort, heap sort, and external sort. It provides descriptions of each algorithm, examples of how they work, and discusses implementation in languages like C++. Key steps and properties of each algorithm are outlined. Implementation details like pseudocode and functions are also described.
Presentation On Binary Search Tree using Linked List Concept which includes Traversing the tree in Inorder, Preorder and Postorder Methods and also searching the element in the Tree
Insertion sort works by iterating through an array, inserting each element into its sorted position by shifting other elements over. It finds the location where each element should be inserted into the sorted portion using a linear search, moving larger elements out of the way to make room. This sorting algorithm is most effective for small data sets and can be implemented recursively or iteratively through comparisons and shifts.
1) Subtraction can be performed using addition by taking the complement of the number being subtracted.
2) For decimal numbers, the 10's complement is obtained by subtracting the number from 10^n where n is the number of digits.
3) Subtraction using complements involves taking the complement of the number being subtracted, adding it to the minuend, and optionally taking the complement of the sum depending on whether the minuend is greater than or less than the subtrahend.
linear search and binary search, Class lecture of Data Structure and Algorithms and Python.
Stack, Queue, Tree, Python, Python Code, Computer Science, Data, Data Analysis, Machine Learning, Artificial Intellegence, Deep Learning, Programming, Information Technology, Psuedocide, Tree, pseudocode, Binary Tree, Binary Search Tree, implementation, Binary search, linear search, Binary search operation, real-life example of binary search, linear search operation, real-life example of linear search, example bubble sort, sorting, insertion sort example, stack implementation, queue implementation, binary tree implementation, priority queue, binary heap, binary heap implementation, object-oriented programming, def, in BST, Binary search tree, Red-Black tree, Splay Tree, Problem-solving using Binary tree, problem-solving using BST, inorder, preorder, postorder
The document discusses different types of queues including their representations, operations, and applications. It describes queues as linear data structures that follow a first-in, first-out principle. Common queue operations are insertion at the rear and deletion at the front. Queues can be represented using arrays or linked lists. Circular queues and priority queues are also described as variants that address limitations of standard queues. Real-world and technical applications of queues include CPU scheduling, cashier lines, and data transfer between processes.
The document describes the quicksort algorithm. Quicksort works by:
1) Partitioning the array around a pivot element into two sub-arrays of less than or equal and greater than elements.
2) Recursively sorting the two sub-arrays.
3) Combining the now sorted sub-arrays.
In the average case, quicksort runs in O(n log n) time due to balanced partitions at each recursion level. However, in the worst case of an already sorted input, it runs in O(n^2) time due to highly unbalanced partitions. A randomized version of quicksort chooses pivots randomly to avoid worst case behavior.
Binary Search - Design & Analysis of AlgorithmsDrishti Bhalla
Binary search is an efficient algorithm for finding a target value within a sorted array. It works by repeatedly dividing the search range in half and checking the value at the midpoint. This eliminates about half of the remaining candidates in each step. The maximum number of comparisons needed is log n, where n is the number of elements. This makes binary search faster than linear search, which requires checking every element. The algorithm works by first finding the middle element, then checking if it matches the target. If not, it recursively searches either the lower or upper half depending on if the target is less than or greater than the middle element.
In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type until these become simple enough to be solved directly.
This document provides an overview of linear search and binary search algorithms.
It explains that linear search sequentially searches through an array one element at a time to find a target value. It is simple to implement but has poor efficiency as the time scales linearly with the size of the input.
Binary search is more efficient by cutting the search space in half at each step. It works on a sorted array by comparing the target to the middle element and determining which half to search next. The time complexity of binary search is logarithmic rather than linear.
A queue is a non-primitive linear data structure that follows the FIFO (first-in, first-out) principle. Elements are added to the rear of the queue and removed from the front. Common operations on a queue include insertion (enqueue) and deletion (dequeue). Queues have many real-world applications like waiting in lines and job scheduling. They can be represented using arrays or linked lists.
Hashing is a technique that maps large amounts of data to smaller data structures using a hashing function. A hash function takes inputs of any size and maps them to a fixed-size table called a hash table. To handle collisions where two keys map to the same slot, separate chaining uses linked lists attached to each slot while open addressing resolves collisions by probing to the next slot using techniques like linear probing, quadratic probing, or double hashing. As the hash table fills up, rehashing may be needed to recalculate hashcodes and move entries to a larger table.
The document discusses insertion sort and its analysis. It begins by providing an overview of insertion sort, describing how it works to sort a sequence by iteratively inserting elements into their sorted position. It then gives pseudocode for insertion sort and works through an example. Next, it analyzes insertion sort's runtime, showing it is O(n^2) in the worst case and O(n) in the best case. The document concludes by introducing the divide and conquer approach for sorting, which will be covered in the next section on merge sort.
The document discusses algorithms complexity and data structures efficiency, explaining that algorithm complexity can be measured using asymptotic notation like O(n) or O(n^2) to represent operations scaling linearly or quadratically with input size, and different data structures have varying time efficiency for operations like add, find, and delete.
Shell sort is a sorting algorithm created by Donald Shell in 1959 that improves on insertion sort. It works by comparing elements that are farther apart within the list rather than just adjacent elements. It performs multiple passes over the list, each with a larger increment, sorting subsets of the elements. Shell sort is more efficient than bubble sort and faster than plain insertion sort, with its main advantage being for medium sized lists. The choice of increments can impact its performance and potential issues arise if the increments are not relatively prime.
The document describes insertion sort, a sorting algorithm. It lists the group members who researched insertion sort and provides an introduction. It then explains how insertion sort works by example, showing how it iterates through an array and inserts elements into the sorted portion. Pseudocode and analysis of insertion sort's runtime is provided. Comparisons are made between insertion sort and other algorithms like bubble sort, selection sort, and merge sort, analyzing their time complexities in best, average, and worst cases.
Traversal is a process to visit all the nodes of a tree and may print their values too. Because, all nodes are connected via edges (links) we always start from the root (head) node. That is, we cannot randomly access a node in a tree.
This presentation is useful to study about data structure and topic is Binary Tree Traversal. This is also useful to make a presentation about Binary Tree Traversal.
The document discusses insertion sort, a simple sorting algorithm that builds a sorted output list from an input one element at a time. It is less efficient on large lists than more advanced algorithms. Insertion sort iterates through the input, at each step removing an element and inserting it into the correct position in the sorted output list. The best case for insertion sort is an already sorted array, while the worst is a reverse sorted array.
An ordered collection of items from which items may be deleted from one end called the front and into which items may be inserted from other end called rear is known as Queue.
It is a linear data structure.
It is called the First In First Out (FIFO) list. Since in queue, the first element will be the first element out.
The document discusses various sorting algorithms including selection sort, insertion sort, merge sort, quick sort, heap sort, and external sort. It provides descriptions of each algorithm, examples of how they work, and discusses implementation in languages like C++. Key steps and properties of each algorithm are outlined. Implementation details like pseudocode and functions are also described.
Presentation On Binary Search Tree using Linked List Concept which includes Traversing the tree in Inorder, Preorder and Postorder Methods and also searching the element in the Tree
Insertion sort works by iterating through an array, inserting each element into its sorted position by shifting other elements over. It finds the location where each element should be inserted into the sorted portion using a linear search, moving larger elements out of the way to make room. This sorting algorithm is most effective for small data sets and can be implemented recursively or iteratively through comparisons and shifts.
1) Subtraction can be performed using addition by taking the complement of the number being subtracted.
2) For decimal numbers, the 10's complement is obtained by subtracting the number from 10^n where n is the number of digits.
3) Subtraction using complements involves taking the complement of the number being subtracted, adding it to the minuend, and optionally taking the complement of the sum depending on whether the minuend is greater than or less than the subtrahend.
linear search and binary search, Class lecture of Data Structure and Algorithms and Python.
Stack, Queue, Tree, Python, Python Code, Computer Science, Data, Data Analysis, Machine Learning, Artificial Intellegence, Deep Learning, Programming, Information Technology, Psuedocide, Tree, pseudocode, Binary Tree, Binary Search Tree, implementation, Binary search, linear search, Binary search operation, real-life example of binary search, linear search operation, real-life example of linear search, example bubble sort, sorting, insertion sort example, stack implementation, queue implementation, binary tree implementation, priority queue, binary heap, binary heap implementation, object-oriented programming, def, in BST, Binary search tree, Red-Black tree, Splay Tree, Problem-solving using Binary tree, problem-solving using BST, inorder, preorder, postorder
The document discusses different types of queues including their representations, operations, and applications. It describes queues as linear data structures that follow a first-in, first-out principle. Common queue operations are insertion at the rear and deletion at the front. Queues can be represented using arrays or linked lists. Circular queues and priority queues are also described as variants that address limitations of standard queues. Real-world and technical applications of queues include CPU scheduling, cashier lines, and data transfer between processes.
The document describes the quicksort algorithm. Quicksort works by:
1) Partitioning the array around a pivot element into two sub-arrays of less than or equal and greater than elements.
2) Recursively sorting the two sub-arrays.
3) Combining the now sorted sub-arrays.
In the average case, quicksort runs in O(n log n) time due to balanced partitions at each recursion level. However, in the worst case of an already sorted input, it runs in O(n^2) time due to highly unbalanced partitions. A randomized version of quicksort chooses pivots randomly to avoid worst case behavior.
Binary Search - Design & Analysis of AlgorithmsDrishti Bhalla
Binary search is an efficient algorithm for finding a target value within a sorted array. It works by repeatedly dividing the search range in half and checking the value at the midpoint. This eliminates about half of the remaining candidates in each step. The maximum number of comparisons needed is log n, where n is the number of elements. This makes binary search faster than linear search, which requires checking every element. The algorithm works by first finding the middle element, then checking if it matches the target. If not, it recursively searches either the lower or upper half depending on if the target is less than or greater than the middle element.
In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type until these become simple enough to be solved directly.
This document provides an overview of linear search and binary search algorithms.
It explains that linear search sequentially searches through an array one element at a time to find a target value. It is simple to implement but has poor efficiency as the time scales linearly with the size of the input.
Binary search is more efficient by cutting the search space in half at each step. It works on a sorted array by comparing the target to the middle element and determining which half to search next. The time complexity of binary search is logarithmic rather than linear.
A queue is a non-primitive linear data structure that follows the FIFO (first-in, first-out) principle. Elements are added to the rear of the queue and removed from the front. Common operations on a queue include insertion (enqueue) and deletion (dequeue). Queues have many real-world applications like waiting in lines and job scheduling. They can be represented using arrays or linked lists.
Hashing is a technique that maps large amounts of data to smaller data structures using a hashing function. A hash function takes inputs of any size and maps them to a fixed-size table called a hash table. To handle collisions where two keys map to the same slot, separate chaining uses linked lists attached to each slot while open addressing resolves collisions by probing to the next slot using techniques like linear probing, quadratic probing, or double hashing. As the hash table fills up, rehashing may be needed to recalculate hashcodes and move entries to a larger table.
The document discusses insertion sort and its analysis. It begins by providing an overview of insertion sort, describing how it works to sort a sequence by iteratively inserting elements into their sorted position. It then gives pseudocode for insertion sort and works through an example. Next, it analyzes insertion sort's runtime, showing it is O(n^2) in the worst case and O(n) in the best case. The document concludes by introducing the divide and conquer approach for sorting, which will be covered in the next section on merge sort.
The document discusses algorithms complexity and data structures efficiency, explaining that algorithm complexity can be measured using asymptotic notation like O(n) or O(n^2) to represent operations scaling linearly or quadratically with input size, and different data structures have varying time efficiency for operations like add, find, and delete.
The document discusses algorithms analysis and sorting algorithms. It introduces insertion sort and merge sort, and analyzes their time complexities. Insertion sort runs in O(n^2) time in the worst case, while merge sort runs in O(n log n) time in the worst case, which grows more slowly. Therefore, asymptotically merge sort performs better than insertion sort for large data sets. The document also covers asymptotic analysis, recurrences, and using recursion trees to solve recurrences.
This document provides an introduction to algorithms and algorithm analysis. It defines what an algorithm is, provides examples, and discusses analyzing algorithms to determine their efficiency. Insertion sort and merge sort are presented as examples and their time complexities are analyzed. Asymptotic notation is introduced to describe an algorithm's order of growth and provide bounds on its running time. Key points covered include analyzing best-case and worst-case time complexities, using recurrences to model algorithms, and the properties of asymptotic notation. Homework problems are assigned from the textbook chapters.
A unique sorting algorithm with linear time & space complexityeSAT Journals
Abstract Sorting a list means selection of the particular permutation of the members of that list in which the final permutation contains members in increasing or in decreasing order. Sorted list is prerequisite of some optimized operations such as searching an element from a list, locating or removing an element to/ from a list and merging two sorted list in a database etc. As volume of information is growing up day by day in the world around us and these data are unavoidable to manage for real life situations, the efficient and cost effective sorting algorithms are required. There are several numbers of fundamental and problem oriented sorting algorithms but still now sorting a problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently and effectively despite of its simple and familiar statements. Algorithms having same efficiency to do a same work using different mechanisms must differ their required time and space. For that reason an algorithm is chosen according to one’s need with respect to space complexity and time complexity. Now a day, space (Memory) is available in market comparatively in cheap cost. So, time complexity is a major issue for an algorithm. Here, the presented approach is to sort a list with linear time and space complexity using divide and conquer rule by partitioning a problem into n (input size) number of sub problems then these sub problems are solved recursively. Required time and space for the algorithm is optimized through reducing the height of the recursive tree and reduced height is too small (as compared to the problem size) to evaluate. So, asymptotic efficiency of this algorithm is very high with respect to time and space. Keywords: sorting, searching, permutation, divide and conquer algorithm, asymptotic efficiency, space complexity, time complexity, and recursion.
1. The document discusses lower bounds for sorting algorithms and proves that all comparison sorts require at least Ω(n lg n) time.
2. It then introduces counting sort, which runs in linear O(n) time by counting elements rather than comparing them, but requires the elements to be drawn from a small known range.
3. Radix sort is then described, which sorts integers digit-by-digit using counting sort, achieving linear time for integers by treating them as d-digit numbers in a base k system. This allows sorting large integers faster than comparison-based sorts.
Lecture 1 sorting insertion & shell sortAbirami A
This document discusses several sorting algorithms including insertion sort, shell sort, heap sort, quick sort, merge sort, bucket sort, and radix sort. It provides details on insertion sort and shell sort, including their algorithms, examples, and exercises to implement them in C code. Insertion sort works by dividing a list into sorted and unsorted parts, moving elements in the unsorted part into the sorted part in the correct position. Shell sort, an improved version of insertion sort, works similarly but divides the list into segments defined by an increment value.
K-Sort: A New Sorting Algorithm that Beats Heap Sort for n 70 Lakhs!idescitation
Sundararajan and Chakraborty [10] introduced a new
version of Quick sort removing the interchanges. Khreisat
[6] found this algorithm to be competing well with some other
versions of Quick sort. However, it uses an auxiliary array
thereby increasing the space complexity. Here, we provide a
second version of our new sort where we have removed the
auxiliary array. This second improved version of the algorithm,
which we call K-sort, is found to sort elements faster than
Heap sort for an appreciably large array size (n 70,00,000)
for uniform U[0, 1] inputs.
The document discusses and compares several sorting algorithms: bubble sort, selection sort, insertion sort, merge sort, and quick sort. For each algorithm, it provides an explanation of how the algorithm works, pseudocode for the algorithm, and an analysis of the time complexity. The time complexities discussed are:
Bubble sort: O(N^2) in worst case, O(N) in best case
Selection sort: O(N^2)
Insertion sort: O(N^2) in worst case, O(N) in best case
Merge sort: O(N log N)
Quick sort: O(N log N) on average
The document discusses algorithms and their use for solving problems expressed as a sequence of steps. It provides examples of common algorithms like sorting and searching arrays, and analyzing their time and space complexity. Specific sorting algorithms like bubble sort, insertion sort, and quick sort are explained with pseudocode examples. Permutations, combinations and variations as examples of combinatorial algorithms are also covered briefly.
1. Counting sort and radix sort can sort in linear time O(n) by exploiting properties of the input rather than just comparisons. Counting sort assumes integers as input and radix sort assumes digitized numbers.
2. Bucket sort also runs in linear time if inputs are uniformly distributed between 0 and 1. It divides the range into buckets and distributes inputs into the corresponding buckets which are then sorted.
3. The comparison-based lower bound of Ω(nlogn) does not apply to these algorithms because they do not rely solely on comparisons. Counting sort counts occurrences rather than comparing, and radix/bucket sort distribute into buckets based on digits/positions rather than comparisons.
This document contains summaries of solutions to various LeetCode problems in Java. It begins with a 3-sentence summary of the Rotate Array problem and its solutions, followed by shorter 1-sentence summaries of other problems and their solutions, including Evaluate Reverse Polish Notation, Longest Palindromic Substring, Word Break, and more. Dynamic programming and recursion are discussed as approaches for some of the problems.
The document discusses various sorting algorithms including exchange sorts like bubble sort and quicksort, selection sorts like straight selection sort, and tree sorts like heap sort. For each algorithm, it provides an overview of the approach, pseudocode, analysis of time complexity, and examples. Key algorithms covered are bubble sort (O(n2)), quicksort (average O(n log n)), selection sort (O(n2)), and heap sort (O(n log n)).
This document discusses lists as an abstract data structure and their common operations. Lists can be implemented using arrays or linked lists, each with different runtimes for operations like accessing, inserting, or erasing elements. Doubly linked lists provide faster access than singly linked lists. The Standard Template Library vector class can also be used to implement lists. Strings are a special case of lists where elements are restricted to characters. Memory usage and runtimes must be balanced when choosing a data structure.
This document provides an overview of sorting algorithms including bubble sort, insertion sort, shellsort, and others. It discusses why sorting is important, provides pseudocode for common sorting algorithms, and gives examples of how each algorithm works on sample data. The runtime of sorting algorithms like insertion sort and shellsort are analyzed, with insertion sort having quadratic runtime in the worst case and shellsort having unknown but likely better than quadratic runtime.
The document provides an introduction and overview of algorithms and sorting algorithms. It discusses:
- Insertion sort, including pseudocode, an example, and analyzing its worst case running time of O(n^2).
- Loop invariants and how they can be used to prove the correctness of insertion sort.
- Analyzing algorithms by determining how many times each line executes and its time complexity as a function of the input size n.
- The worst case analysis is most important as it provides an upper bound on running time.
The document introduces algorithms for sorting and searching tasks. It discusses sequential search, binary search, selection sort, bubble sort, merge sort, and quick sort algorithms. For each algorithm, it provides pseudocode to describe the steps, an example, and analysis of time complexity in the best, worst and average cases. The time complexities identified are Θ(n) for sequential search average case, Θ(log n) for binary search, Θ(n2) for selection, bubble and quick sort worst cases, and Θ(n log n) for merge and quick sort average cases.
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion should be inserted
while some elements unsorted:
Using linear search, find the location in the sorted portion where the 1st element of the unsorted portion
The document discusses algorithms and their analysis. It begins by defining an algorithm and key aspects like correctness, input, and output. It then discusses two aspects of algorithm performance - time and space. Examples are provided to illustrate how to analyze the time complexity of different structures like if/else statements, simple loops, and nested loops. Big O notation is introduced to describe an algorithm's growth rate. Common time complexities like constant, linear, quadratic, and cubic functions are defined. Specific sorting algorithms like insertion sort, selection sort, bubble sort, merge sort, and quicksort are then covered in detail with examples of how they work and their time complexities.
This document discusses different sorting algorithms including insertion sort, selection sort, and shell sort. It provides examples of how each algorithm works and pseudocode for implementation. Insertion sort iterates through an array and inserts each element into its sorted position. Selection sort finds the minimum element in each pass and swaps it into the front. Shell sort improves on insertion sort by comparing elements separated by gaps to sort sublists and gradually reduce the gaps.
Level sensitive scan design(LSSD) and Boundry scan(BS)Praveen Kumar
This presentation contains,
Introduction,design for testability, scan chain, operation, scan structure, test vectors, Boundry scan, test logic, operation, BS cell, states of TAP controller, Boundry scan instructions.
This ppt describes about,
introduction of fuses, construction, Important terms, advantages and disadvantages, desirable characteristics of fuse element, Current time characteristics, Fuse types - Low voltages fuses and High voltage fuses, Semi enclosed rewirable fuse, HRC cartridge fuses - parts, operation, pros and cons, High voltage fuses and its types, selection of fuses, discrimination
Introduction of SCADA, Architecture of SCADA, Software and hardware architecture, Components of a SCADA system, Functions of SCADA, Alarms and events, alarm logging, comparision between scada and DCS
SPICE LEVEL I/LEVEL II/LEVEL III AND BSIM MODELSPraveen Kumar
SPICE LEVEL I/LEVEL II/LEVEL III AND BSIM MODELS
SPICE introduction
working
adaptions
detailed discussion on each models
SPICE Modeling in BSIM
features
bulk voltage on large signal model
velocity saturation
weak inversion operation
impact ionization
Finite word length of IIR filters Limit cycles due to product round-off error...Praveen Kumar
Finite word length of IIR filters Limit cycles due to product round-off errors and other non-linear characteristics
Limit cycles due to round-off errors
infinite precision
round off
truncation
An Example
MATLAB Codes
Inference
Other non-linear Characteristics
Jump Phenomenon
Subharmonic Response
Effects of product round-off errors
SOLAR POWER generation using solar PV and Concentrated solar power technologyPraveen Kumar
Concentrated Solar Power Technology
Power Tower Systems
Parabolic Trough Systems
Solar Dish Systems
Compact Linear Fresnel
Types, working, pros &cons
Scope in INDIA
Using Photo-Voltaic cells
-Working of PV Cells
-Considering different PV materials
-Efficiency, Comparing modules manufactured by different companies
-MPPT
- algorithms
-A view of different inverter topologies used
pyrheliometer
SELECTION OF DRIVES AND CONTROL SCHEMES FOR MACHINE TOOLS Praveen Kumar
SELECTION OF DRIVES AND CONTROL SCHEMES FOR MACHINE TOOLS
Machine tools and drives
Horse power requirement for driving the machine tools
MOTOR REQUIREMENTS FOR MACHINE TOOLS.
SELECTION OF MOTORS
Speed control of Drill press
Application of Motors to Planers, Shapers
Reversible motor drive quick return mechanism
GRINDING MACHINES
VFD
Vehicle safety system
it covers
hydraulic brakes
working of drum ,disk brakes
abs
airbags
ESP/ESC(electronic stability programme)
future trends in safety systems
cruise control
ACC
introduction, types & structure of MOSET ,turn ON and OFF of device, working, I-V characteristics of MOSFET,Different regions of operations,applications, adv & disadvantages
This document discusses SPICE (Simulation Program with Integrated Circuit Emphasis) and PSpice, a version of SPICE used for circuit simulation on PCs. It describes the basic steps for simulating a circuit using PSpice: 1) drawing the circuit in Capture, 2) simulating it using PSpice models, and 3) analyzing output using Probe. PSpice can perform various types of circuit analyses and contains models for common circuit elements.
Interfacing GPS with 8051 and displaying the output data in NMEA format from the gps module to 8051 microcontroller and finally displaying the latitude and longitude information also the date and time in a LCD display.
REVERSE POWER RELAY for solar PV systemsPraveen Kumar
this presentation gives an idea about designing a device using microcontroller that detects the reverse power flow from solar pannels to the grid when the load is less.
Digital Voltmeter, Digital Ammeter and Digital MultimeterPraveen Kumar
This ppt deals with Digital meters,the digital components used in them,principle behind the working of Digital Voltmeter(DC) Digital Voltmeter(AC) and mechanism of Measurement of Current and Measurement of Resistance. Finally A complete DMM also the Measurement of hfe. A small project on constructing digital voltmeter and ohmmeter using Arduino.
NO MICROCONTROLLER is used in making of these autonomous robot, we have just used only the operational amplifier as a controller and achieved the bot.we have made 2 bots Line follower and light follower with simulations in proteus and hardware implementation of these bots. Also made a wireless light controlled bot using the same concepts.Hope this presentation will be much helpful for your mini projects. Do leave some comments. Thank u.
Ventilating systems for electrical machinesPraveen Kumar
this presentation is about types of ventilation given to the electrical machines,an analysis for the best type,future improvements,and their importance in electrical machines
Sri Guru Hargobind Ji - Bandi Chor Guru.pdfBalvir Singh
Sri Guru Hargobind Ji (19 June 1595 - 3 March 1644) is revered as the Sixth Nanak.
• On 25 May 1606 Guru Arjan nominated his son Sri Hargobind Ji as his successor. Shortly
afterwards, Guru Arjan was arrested, tortured and killed by order of the Mogul Emperor
Jahangir.
• Guru Hargobind's succession ceremony took place on 24 June 1606. He was barely
eleven years old when he became 6th Guru.
• As ordered by Guru Arjan Dev Ji, he put on two swords, one indicated his spiritual
authority (PIRI) and the other, his temporal authority (MIRI). He thus for the first time
initiated military tradition in the Sikh faith to resist religious persecution, protect
people’s freedom and independence to practice religion by choice. He transformed
Sikhs to be Saints and Soldier.
• He had a long tenure as Guru, lasting 37 years, 9 months and 3 days
Cricket management system ptoject report.pdfKamal Acharya
The aim of this project is to provide the complete information of the National and
International statistics. The information is available country wise and player wise. By
entering the data of eachmatch, we can get all type of reports instantly, which will be
useful to call back history of each player. Also the team performance in each match can
be obtained. We can get a report on number of matches, wins and lost.
Online train ticket booking system project.pdfKamal Acharya
Rail transport is one of the important modes of transport in India. Now a days we
see that there are railways that are present for the long as well as short distance
travelling which makes the life of the people easier. When compared to other
means of transport, a railway is the cheapest means of transport. The maintenance
of the railway database also plays a major role in the smooth running of this
system. The Online Train Ticket Management System will help in reserving the
tickets of the railways to travel from a particular source to the destination.
Data Communication and Computer Networks Management System Project Report.pdfKamal Acharya
Networking is a telecommunications network that allows computers to exchange data. In
computer networks, networked computing devices pass data to each other along data
connections. Data is transferred in the form of packets. The connections between nodes are
established using either cable media or wireless media.
2. Overview
Sorting
Performance parameters
Insertion Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Shell Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
2
3. Sorting
Sorting refers to arranging things according to different classes.
In computer science, sorting deals with arranging elements of a list or a set of
records of a file in the ascending order or descending order.
There are two types of sorting based on the size of list
Internal Sorting, when the size of list is small
External Sorting, when the size is voluminous
The internal sorting algorithms are grouped into one of these families
Sorting by exchange
Sorting by distribution
Sorting by selection
Sorting by insertion
3
4. Performance parameters
Time Complexity
Best Case , when the list is sorted already
Average Case
Worst Case , when the list is in the reverse order
Stability
4
5. Time Complexity
The time complexity of an algorithm is a function of the running time of the
algorithm.
It is computed using apriori analysis, where the total frequency count is only taken
into account.
The frequency count fi of each statement of the algorithm is computed and
summed up to obtain the total frequency count T = 𝑖 𝑓I .
The time complexity is represented using asymptotic notations.
5
6. Stability
When the relative positions of the key with the same value in the ordered list is
maintained in the sorted list, the algorithm is said to be stable.
6
7. Insertion Sort
As the name indicates, this algorithm belongs to the family of sorting by insertion.
This algorithm sorts a set of keys by inserting keys into an sorted sub list.
The keys are considered one at a time, and each new key is inserted into the
appropriate position relative to the previously sorted keys.
Online; i.e., can sort a list as it receives it
7
8. Technique
Consider an unordered list {K1, K2, K3,… ,Kn}.
In the first pass, K2 is compared with its sorted sublist of predecessors, i.e., {K1}, and
K2 inserts itself at the position to give the list {K1,K2}.
In the next pass, K3 is compared with its sorted sublist of predecessors, i.e., {K1,K2},
and K3 is inserted at the appropriate position to give the list {K1,K2,K3}.
In the (n-1)th pass, Kn is compared with its sorted sublist of predecessors, i.e.,
{K1,K2,K3,…,Kn-1}, and Kn is inserted at the appropriate position to give the list
{K1,K2,K3,…,Kn-1,Kn}.
This technique is referred as sinking or sifting
8
15. Time Complexity
For the best case, the list is already sorted. Therefore, there will be (n-1) passes
each with 1 comparison, i.e., (n-1) comparisons in total. Therefore, the time
complexity for the best case is O(n).
For the worst case, in the first pass, there will be one comparison and in the second
pass, there will be two comparisons and so on. For the (n-1)th pass, there will be (n-
1) comparisons.
The total number of comparisons = 1+2+…+(n-1)
=
𝑛(𝑛−1)
2
= O(n2)
The average time complexity is also reported to be O(n2).
15
16. Stability
The insertion sort is a stable sort.
The relative position of the keys with
same value are retained.
16
17. Code:
#include<iostream>
using namespace std;
class array
{
int arr[100],size,j,k,sort1;
public:
array(int i)
{
size=i;
cout<<"enter the elements n";
for(j=0;j<size;j++)
{cout<<"enter the next elementn";
cin>>k;
arr[j]=k;
}
}
17
18. void initialize()
{cout<<"enter the array size n";
cin>>size;
cout<<"enter the elementsn";
for(j=0;j<size;j++)
{cout<<"enter the next elementn";
cin>>k;
arr[j]=k;
}
}
18
19. void sort()
{int i;
int key;
for (i = 1; i < size; i++)
{ key = arr[i];
j = i-1;
while (j >= 0 && arr[j] > key)
{arr[j+1] = arr[j];
j = j-1; }
arr[j+1] = key;
for(j=0;j<size;j++)
{cout<<arr[j]<<";";}
cout<<"n";
}}
19
21. int main()
{
int temp,size,con,exit;
cout<<"enter the number of elements n";
cin>>size;
array array1(size);
array1.sort();
array1.print();
while(exit==0)
{cout<<"do you want to continue enter n 1 for exit n 2 for continue";
cin>>con;
switch(con)
{case 1:
default:
exit=1;
break;
case 2:
array1.initialize();
array1.sort();
array1.print();
break;
}}
return 0;}
21
23. Shell Sort
Shell sort algorithm also belongs to the family of sorting by insertion.
It was proposed by David L Shell in 1959.
It is a substantial improvement over insertion sort in the sense that elements move
in long strides rather than single steps, thereby yielding a well ordered sub file
which quickens the sorting process.
23
24. Technique
The general idea behind the method is to choose an increment ht, and divide the
unordered list into sub lists of keys that are ht units apart.
Then, each sub list is then sorted(using insertion sort) and gathered to form a list.
This is known as pass.
The pass is repeated for any sequence of increments {ht-1, ht-2,… h1,h0} where h0
must be equal to 1.
The increments are kept in the diminishing order and hence shell sort is also
referred as diminishing increment sort.
24
30. Time Complexity
The running time of the algorithm is dependant on the set of increment values.
Since there is no best possible set of increments that has been formulated, the time
complexity of shell sort is not completely resolved yet.
On an average, it is faster than all O(n2) sorting algorithms.
30
31. Dependency on the value of increments31
General Term Time Complexity
Ceil(
𝑁
2 𝑘)
O(N2)
2 * Ceil (
𝑁
2 𝑘+1) + 1 O(𝑁
3
2)
2 𝑘
− 1 O(𝑁
3
2)
2 𝑘 + 1 O(𝑁
3
2)
2 𝑝
3 𝑞 O(N log2 N )
3 𝑘
− 1
2
O(𝑁
3
2)
35. Applications of Insertion sort and Shell sort
Practically used in applications where the no. of elements is small
It is also used when the sequence is almost sorted.
It can be used when not all the inputs are available initially.
Consider an examination hall. The students are handing over the papers to the
invigilator. The invigilator arranges (sorts) the papers using insertion sort.
35
37. void shell_sort_ascending()
{ int i,h;
for(h=n/2;h>0;h/=2)
{for(i=h;i<n;i++)
{ int key,j;
key=array[i];
j=i;
while((j>=h) && (array[j-h]>key))
{
array[j]=array[j-h];
j=j-h;
array[j]=key;}}
printf("nn The Sorting in Ascending order ");
print_array();}
printf("nn The sorted elements in ascending order ");
print_array();
}
37
38. void shell_sort_descending()
{int i,h;
for(h=n/2;h>0;h/=2)
{for(i=h;i<n;i++)
{int key,j;
key=array[i];
j=i;
while((j>=h) && (array[j-h]<key))
{array[j]=array[j-h];
j=j-h;
array[j]=key; }}
printf("nn The Sorting in Descending order ");
print_array();
}
printf("nn The sorted elements in descending order ");print_array();
}
38
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