The document outlines different sorting algorithms including selection sort, bubble sort, insertion sort, shell sort, merge sort, and quicksort. It discusses how to use the standard sorting methods in Java's API and provides pseudocode and examples of implementing selection sort, bubble sort, insertion sort, and merge sort. It analyzes the time complexity of these algorithms and discusses which are best for small, medium, and large arrays.
This document discusses algorithms for sorting and searching. It introduces algorithm analysis and why it is important to analyze algorithms to compare different solutions, predict performance, and set parameter values. It discusses analyzing running time by counting primitive operations as a function of input size. Common growth rates like linear, quadratic, and cubic functions are introduced. Big-O notation is explained as a way to classify algorithms by their worst-case running time. Several specific sorting algorithms are described, including bubble sort, insertion sort, merge sort, and quicksort. Their pseudocode and running times are analyzed. Graph traversal algorithms like depth-first search and breadth-first search are also introduced.
Bubble sort, selection sort, and insertion sort are O(n^2) sorting algorithms discussed in the document. Bubble sort compares and swaps adjacent elements, selection sort finds the minimum element and swaps it into place each iteration, and insertion sort inserts each new element into the sorted portion of the array. Merge sort is more efficient at O(n log n) time by dividing the array into halves, sorting them, and merging the results. It is well-suited for large datasets that do not fit into memory.
Sorting algorithms in C++
An introduction to sorting algorithm, with details on bubble sort and merge sort algorithms
Computer science principles course
This document provides an overview of sorting algorithms including selection sort, bubble sort, insertion sort, merge sort, and heapsort. It discusses the time and space complexity of each algorithm, with merge sort having the best time complexity of O(n log n). Code examples and exercises are provided to help understand how each algorithm works. The goal is to help students learn common sorting techniques needed for coding interviews and problems.
This document provides a 90-minute discussion on algorithms including quicksort, order statistics, searching, and substring searching. It begins with an overview of the topics and then provides details on quicksort, including the divide and conquer approach and partitioning elements around a pivot. It also describes algorithms for order statistics to find the kth smallest element, binary search, and a basic substring searching approach. Special cases and better solutions like Boyer-Moore are also mentioned.
This document discusses stacks as an abstract data type (ADT) and their implementation in Java. It begins by defining an ADT as having a specific interface of operations and axioms defining the semantics of those operations. Stacks are introduced as a LIFO data structure that supports push, pop, and top operations. The document then discusses implementing a stack interface in Java using exceptions to handle errors. It provides an example array-based stack implementation in Java using an array and index to track elements. Finally, it discusses an application of stacks to efficiently compute the span of stock price changes over time by using a stack to track previous higher prices.
Shell Sort is a generalization of insertion sort that works by sorting elements with large gaps first then decreasing the gaps until a gap of 1, which is regular insertion sort. It has a worst case time complexity of O(n^2) but average complexity near O(n). Merge Sort divides the array into halves recursively, merges the sorted halves back together to fully sort the array. It has a best, average, and worst case time complexity of O(nlogn) and requires O(n) auxiliary space but is not an in-place sorting algorithm.
This document discusses algorithms for sorting and searching. It introduces algorithm analysis and why it is important to analyze algorithms to compare different solutions, predict performance, and set parameter values. It discusses analyzing running time by counting primitive operations as a function of input size. Common growth rates like linear, quadratic, and cubic functions are introduced. Big-O notation is explained as a way to classify algorithms by their worst-case running time. Several specific sorting algorithms are described, including bubble sort, insertion sort, merge sort, and quicksort. Their pseudocode and running times are analyzed. Graph traversal algorithms like depth-first search and breadth-first search are also introduced.
Bubble sort, selection sort, and insertion sort are O(n^2) sorting algorithms discussed in the document. Bubble sort compares and swaps adjacent elements, selection sort finds the minimum element and swaps it into place each iteration, and insertion sort inserts each new element into the sorted portion of the array. Merge sort is more efficient at O(n log n) time by dividing the array into halves, sorting them, and merging the results. It is well-suited for large datasets that do not fit into memory.
Sorting algorithms in C++
An introduction to sorting algorithm, with details on bubble sort and merge sort algorithms
Computer science principles course
This document provides an overview of sorting algorithms including selection sort, bubble sort, insertion sort, merge sort, and heapsort. It discusses the time and space complexity of each algorithm, with merge sort having the best time complexity of O(n log n). Code examples and exercises are provided to help understand how each algorithm works. The goal is to help students learn common sorting techniques needed for coding interviews and problems.
This document provides a 90-minute discussion on algorithms including quicksort, order statistics, searching, and substring searching. It begins with an overview of the topics and then provides details on quicksort, including the divide and conquer approach and partitioning elements around a pivot. It also describes algorithms for order statistics to find the kth smallest element, binary search, and a basic substring searching approach. Special cases and better solutions like Boyer-Moore are also mentioned.
This document discusses stacks as an abstract data type (ADT) and their implementation in Java. It begins by defining an ADT as having a specific interface of operations and axioms defining the semantics of those operations. Stacks are introduced as a LIFO data structure that supports push, pop, and top operations. The document then discusses implementing a stack interface in Java using exceptions to handle errors. It provides an example array-based stack implementation in Java using an array and index to track elements. Finally, it discusses an application of stacks to efficiently compute the span of stock price changes over time by using a stack to track previous higher prices.
Shell Sort is a generalization of insertion sort that works by sorting elements with large gaps first then decreasing the gaps until a gap of 1, which is regular insertion sort. It has a worst case time complexity of O(n^2) but average complexity near O(n). Merge Sort divides the array into halves recursively, merges the sorted halves back together to fully sort the array. It has a best, average, and worst case time complexity of O(nlogn) and requires O(n) auxiliary space but is not an in-place sorting algorithm.
The document describes Shellsort, a sorting algorithm developed by Donald Shell in 1959. It is an improvement on insertion sort. Shellsort works by sorting elements first with large gaps between elements, then reducing the gaps and sorting again until the final gap is 1, completing the sort. It takes advantage of insertion sort being most efficient on nearly sorted lists. The time complexity is O(n^r) for 1 < r < 2, better than O(n^2) of insertion sort but generally worse than O(n log n) of quicker algorithms.
This document discusses three simple sorting algorithms: bubble sort, selection sort, and insertion sort. It provides pseudocode for each algorithm and analyzes their time complexities. Bubble sort and selection sort are analyzed to be O(n^2) time due to nested loops of size n. Insertion sort is also O(n^2) as it iterates through the array once and shifts elements in the inner loop approximately n/2 times on average. Loop invariants are developed to explain the sorting process for each algorithm.
1. Several sorting algorithms are compared including quicksort, heapsort, mergesort, insertion sort, selection sort, and bubble sort.
2. For most algorithms, the best, average, and worst case time complexities are listed as O(n log(n)), O(n log(n)), and O(n^2) respectively except for some cases like selection sort and bubble sort that have average and worst case complexities of O(n^2).
3. For space complexity, many algorithms have worst case complexities of O(n) except for mergesort which uses additional space and has a worst case complexity of O(n).
Data structures and algorithms involve organizing data to solve problems efficiently. An algorithm describes computational steps, while a program implements an algorithm. Key aspects of algorithms include efficiency as input size increases. Experimental studies measure running time but have limitations. Pseudocode describes algorithms at a high level. Analysis counts primitive operations to determine asymptotic running time, ignoring constant factors. The best, worst, and average cases analyze efficiency. Asymptotic notation like Big-O simplifies analysis by focusing on how time increases with input size.
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.
This document discusses Shellsort, an algorithm developed by Donald Shell in 1959 that improves on insertion sort. Shellsort works by comparing elements that are farther apart within an array rather than adjacent elements. It makes multiple passes through a list, sorting subsets of elements using an increment sequence that decreases until the final pass sorts adjacent elements using insertion sort. Shellsort breaks the quadratic time barrier of insertion sort and is faster for medium sized lists but is outperformed by other algorithms like merge, heap, and quick sort for large lists. Examples are provided to illustrate how Shellsort works by sorting a sample list.
Arrays are a data structure that store elements of the same type in consecutive memory locations. This allows individual elements to be accessed via an index into the memory block. The time complexity of most basic array operations is O(1) for accessing elements by index but O(n) for operations like insertion, deletion, and searching that may require shifting other elements. Additional space complexity is O(n) to store the elements.
This document describes and compares several common sorting algorithms, including bubble sort, selection sort, and insertion sort. It provides pseudocode examples to illustrate how each algorithm works and analyzes their time complexities. Specifically, it shows the steps to sort sample data using each algorithm through multiple iterations and compares their performance, with bubble, selection, and insertion sorts having O(n2) time and others like merge and quicksort having O(n log n) time.
This document provides an overview of the Data Structures I course. It outlines the course objectives of becoming familiar with problem solving, algorithms, data structures, and tracing algorithms. The course will cover fundamentals of data structures and algorithms, static and dynamic data structures, searching and sorting algorithms, recursion, abstract data types, stacks, queues and trees. Exams, labs, participation and quizzes will be used for grading. Pseudo-code is introduced as a way to express algorithms independent of a programming language. Examples of algorithms for determining even/odd numbers and computing weekly wages are provided.
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.
The document summarizes the key components of the Standard Template Library (STL) including containers, iterators, and algorithms. It describes common STL containers like vector, list, set, map and their uses. Iterators are used to point to container elements and algorithms perform operations on container elements. Examples are provided to demonstrate how to use STL containers like vector, set and map as well as common algorithms like sort.
This document summarizes techniques for hashing, including hash functions, open addressing, linear probing, and double hashing. It discusses choosing good hash functions that distribute keys uniformly. For open addressing, it describes linear probing, which probes successive table locations when collisions occur, and double hashing, which uses two hash functions to determine probe positions. Analysis shows the expected number of probes is related to the load factor for these probing techniques.
Java 8 came out early last year and Java 7 is now, at the end of life, making Java 8 the only Oracle supported option. However, since developers value stability over trendiness, many of us are still working with Java 7, or even 6. Let’s look at some features of Java 8, and provide some arguments to persuade your code to upgrade with best practices.
OO with Scala, for getting started with Scala.
Scala is a hybrid programming language that implements functional and object-oriented paradigms. With Scala, there is always more than one way to do something and oftentimes it can feel overwhelming.
The document discusses Strings in Java. Some key points:
- A String represents a sequence of characters. The String class is used to create string objects which can exist in the string pool or heap.
- Char arrays are preferable over Strings for passwords due to security reasons. Strings can be manipulated more easily.
- The String class has many useful methods like length(), charAt(), indexOf(), replace(), toLowerCase(), substring() etc to work with and manipulate string values.
- StringBuffer is used to create mutable string objects that can be modified after creation using methods like append(), insert(), delete() etc. It is preferable over String for performance reasons while manipulating strings.
The document discusses various searching and sorting algorithms. It begins by defining search algorithms as methods for finding items within a collection. It then covers linear search, which has O(n) complexity, and binary search, which has O(log n) complexity but requires a sorted list. The document also discusses sorting algorithms like bubble sort, selection sort, and merge sort. Merge sort uses a divide-and-conquer approach and has O(n log n) complexity, making it one of the most efficient common sorting algorithms. Code implementations and complexity analyses are provided for many of the algorithms.
The Ring programming language version 1.9 book - Part 98 of 210Mahmoud Samir Fayed
Ring provides constructor methods when creating new objects. When a new object is created:
1. Memory is allocated for the object's attributes
2. The current scope is changed to the new object
3. Code in the class region is executed to initialize the object
4. Attributes added in the class region are dynamic
1. The document discusses various data structures concepts including arrays, dynamic arrays, operations on arrays like traversing, insertion, deletion, sorting, and searching.
2. It provides examples of declaring and initializing arrays, as well as dynamic array allocation using pointers and new/delete operators.
3. Searching techniques like linear search and binary search are explained, with linear search comparing each element sequentially while binary search eliminates half the elements at each step for sorted arrays.
Selection sort is an in-place comparison sorting algorithm that works as follows: (1) Find the minimum value in the list, (2) Swap it with the value in the first position, (3) Repeat for the remainder of the list. It has a time complexity of O(n2), making it inefficient for large lists. While simple, it has advantages over more complex algorithms when auxiliary memory is limited. Variants include heapsort, which improves efficiency, and bingo sort, which is more efficient for lists with duplicate values.
The document describes Shellsort, a sorting algorithm developed by Donald Shell in 1959. It is an improvement on insertion sort. Shellsort works by sorting elements first with large gaps between elements, then reducing the gaps and sorting again until the final gap is 1, completing the sort. It takes advantage of insertion sort being most efficient on nearly sorted lists. The time complexity is O(n^r) for 1 < r < 2, better than O(n^2) of insertion sort but generally worse than O(n log n) of quicker algorithms.
This document discusses three simple sorting algorithms: bubble sort, selection sort, and insertion sort. It provides pseudocode for each algorithm and analyzes their time complexities. Bubble sort and selection sort are analyzed to be O(n^2) time due to nested loops of size n. Insertion sort is also O(n^2) as it iterates through the array once and shifts elements in the inner loop approximately n/2 times on average. Loop invariants are developed to explain the sorting process for each algorithm.
1. Several sorting algorithms are compared including quicksort, heapsort, mergesort, insertion sort, selection sort, and bubble sort.
2. For most algorithms, the best, average, and worst case time complexities are listed as O(n log(n)), O(n log(n)), and O(n^2) respectively except for some cases like selection sort and bubble sort that have average and worst case complexities of O(n^2).
3. For space complexity, many algorithms have worst case complexities of O(n) except for mergesort which uses additional space and has a worst case complexity of O(n).
Data structures and algorithms involve organizing data to solve problems efficiently. An algorithm describes computational steps, while a program implements an algorithm. Key aspects of algorithms include efficiency as input size increases. Experimental studies measure running time but have limitations. Pseudocode describes algorithms at a high level. Analysis counts primitive operations to determine asymptotic running time, ignoring constant factors. The best, worst, and average cases analyze efficiency. Asymptotic notation like Big-O simplifies analysis by focusing on how time increases with input size.
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.
This document discusses Shellsort, an algorithm developed by Donald Shell in 1959 that improves on insertion sort. Shellsort works by comparing elements that are farther apart within an array rather than adjacent elements. It makes multiple passes through a list, sorting subsets of elements using an increment sequence that decreases until the final pass sorts adjacent elements using insertion sort. Shellsort breaks the quadratic time barrier of insertion sort and is faster for medium sized lists but is outperformed by other algorithms like merge, heap, and quick sort for large lists. Examples are provided to illustrate how Shellsort works by sorting a sample list.
Arrays are a data structure that store elements of the same type in consecutive memory locations. This allows individual elements to be accessed via an index into the memory block. The time complexity of most basic array operations is O(1) for accessing elements by index but O(n) for operations like insertion, deletion, and searching that may require shifting other elements. Additional space complexity is O(n) to store the elements.
This document describes and compares several common sorting algorithms, including bubble sort, selection sort, and insertion sort. It provides pseudocode examples to illustrate how each algorithm works and analyzes their time complexities. Specifically, it shows the steps to sort sample data using each algorithm through multiple iterations and compares their performance, with bubble, selection, and insertion sorts having O(n2) time and others like merge and quicksort having O(n log n) time.
This document provides an overview of the Data Structures I course. It outlines the course objectives of becoming familiar with problem solving, algorithms, data structures, and tracing algorithms. The course will cover fundamentals of data structures and algorithms, static and dynamic data structures, searching and sorting algorithms, recursion, abstract data types, stacks, queues and trees. Exams, labs, participation and quizzes will be used for grading. Pseudo-code is introduced as a way to express algorithms independent of a programming language. Examples of algorithms for determining even/odd numbers and computing weekly wages are provided.
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.
The document summarizes the key components of the Standard Template Library (STL) including containers, iterators, and algorithms. It describes common STL containers like vector, list, set, map and their uses. Iterators are used to point to container elements and algorithms perform operations on container elements. Examples are provided to demonstrate how to use STL containers like vector, set and map as well as common algorithms like sort.
This document summarizes techniques for hashing, including hash functions, open addressing, linear probing, and double hashing. It discusses choosing good hash functions that distribute keys uniformly. For open addressing, it describes linear probing, which probes successive table locations when collisions occur, and double hashing, which uses two hash functions to determine probe positions. Analysis shows the expected number of probes is related to the load factor for these probing techniques.
Java 8 came out early last year and Java 7 is now, at the end of life, making Java 8 the only Oracle supported option. However, since developers value stability over trendiness, many of us are still working with Java 7, or even 6. Let’s look at some features of Java 8, and provide some arguments to persuade your code to upgrade with best practices.
OO with Scala, for getting started with Scala.
Scala is a hybrid programming language that implements functional and object-oriented paradigms. With Scala, there is always more than one way to do something and oftentimes it can feel overwhelming.
The document discusses Strings in Java. Some key points:
- A String represents a sequence of characters. The String class is used to create string objects which can exist in the string pool or heap.
- Char arrays are preferable over Strings for passwords due to security reasons. Strings can be manipulated more easily.
- The String class has many useful methods like length(), charAt(), indexOf(), replace(), toLowerCase(), substring() etc to work with and manipulate string values.
- StringBuffer is used to create mutable string objects that can be modified after creation using methods like append(), insert(), delete() etc. It is preferable over String for performance reasons while manipulating strings.
The document discusses various searching and sorting algorithms. It begins by defining search algorithms as methods for finding items within a collection. It then covers linear search, which has O(n) complexity, and binary search, which has O(log n) complexity but requires a sorted list. The document also discusses sorting algorithms like bubble sort, selection sort, and merge sort. Merge sort uses a divide-and-conquer approach and has O(n log n) complexity, making it one of the most efficient common sorting algorithms. Code implementations and complexity analyses are provided for many of the algorithms.
The Ring programming language version 1.9 book - Part 98 of 210Mahmoud Samir Fayed
Ring provides constructor methods when creating new objects. When a new object is created:
1. Memory is allocated for the object's attributes
2. The current scope is changed to the new object
3. Code in the class region is executed to initialize the object
4. Attributes added in the class region are dynamic
1. The document discusses various data structures concepts including arrays, dynamic arrays, operations on arrays like traversing, insertion, deletion, sorting, and searching.
2. It provides examples of declaring and initializing arrays, as well as dynamic array allocation using pointers and new/delete operators.
3. Searching techniques like linear search and binary search are explained, with linear search comparing each element sequentially while binary search eliminates half the elements at each step for sorted arrays.
Selection sort is an in-place comparison sorting algorithm that works as follows: (1) Find the minimum value in the list, (2) Swap it with the value in the first position, (3) Repeat for the remainder of the list. It has a time complexity of O(n2), making it inefficient for large lists. While simple, it has advantages over more complex algorithms when auxiliary memory is limited. Variants include heapsort, which improves efficiency, and bingo sort, which is more efficient for lists with duplicate values.
This document provides an overview of several advanced sorting algorithms: Shell sort, Quick sort, Heap sort, and Merge sort. It describes the key ideas, time complexities, and provides examples of implementing each algorithm to sort sample data sets. Shell sort improves on insertion sort by sorting elements in a two-dimensional array. Quick sort uses a pivot element and partitions elements into left and right subsets. Heap sort uses a heap data structure and sorts by swapping elements. Merge sort divides the list recursively and then merges the sorted halves.
The document discusses various searching and sorting algorithms. It describes linear search, binary search, selection sort, bubble sort, and heapsort. For each algorithm, it provides pseudocode examples and analyzes their performance in terms of number of comparisons required in the worst case. Linear search requires N comparisons in the worst case, while binary search requires log N comparisons. Selection sort and bubble sort both require approximately N^2 comparisons, while heapsort requires 1.5NlogN comparisons.
The document provides an overview of several sorting algorithms, including insertion sort, bubble sort, selection sort, and radix sort. It describes the basic approach for each algorithm through examples and pseudocode. Analysis of the time complexity is also provided, with insertion sort, bubble sort, and selection sort having worst-case performance of O(n^2) and radix sort having performance of O(nk) where k is the number of passes.
This slide explains three (3) basic sorting algorithms with codes on github. Bubble sort, Selection sort and insertion sort.
visit https://github.com/EngrMikolo/BasicSortingAlgorithms to checkout the codes
This document provides information on linked lists. Some key points:
- A linked list is a dynamic data structure where elements are linked using pointers. Each element contains a data field and a pointer to the next node.
- There are different types of linked lists including singly linked, doubly linked, circular, and circular doubly linked lists.
- Common linked list operations include insertion, deletion, traversal, searching, and sorting. Algorithms for performing these operations on singly linked lists are presented.
- Linked lists can be used to implement other data structures like stacks, where the top element is tracked using a pointer instead of using array indices. Pseudocode for push and pop operations on a linked list implementation of
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)).
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages:
This document discusses different sorting algorithms. It defines sorting as rearranging elements in a list or array based on a comparison operator. Three sorting algorithms are described: selection sort works by selecting the minimum element and placing it at the front of the sorted subarray; insertion sort works by inserting elements into the sorted position one by one; and bubble sort works by repeatedly swapping adjacent elements if they are in the wrong order. Examples are provided to illustrate how each algorithm sorts an array.
This document discusses several Python programming tasks and provides explanations of bubble sort sorting algorithm. It includes:
1) Four programming tasks - writing a program to swap two numbers, search for an item in a list, find minimum and maximum of a list, and print a pattern using nested loops.
2) An explanation of bubble sort sorting algorithm with an example to sort an array from lowest to highest number using bubble sort in multiple passes.
3) Bubble sort algorithm and code in C language to sort an array using bubble sort.
4) Notes on multi-line comments and references for more information.
The document discusses time and space complexity analysis for algorithms, including using Big O notation to describe an algorithm's efficiency. It provides examples of time complexity for different codes, such as O(n) for a simple loop and O(n^2) for a double loop. The document also covers space complexity and how to estimate the complexity of a problem based on input size constraints.
The document discusses double and circular linked lists. It covers inserting and deleting nodes from doubly linked lists and circular linked lists. Specifically, it describes how to insert nodes at different positions in a doubly linked list, such as at the front, after a given node, at the end, and before a given node. It also explains how to delete nodes from a doubly linked list. For circular linked lists, it outlines how to insert nodes in an empty list, at the beginning, at the end, and between nodes. It also provides the steps to delete nodes from a circular linked list.
The document summarizes various sorting algorithms:
- Bubble sort works by repeatedly swapping adjacent elements that are in the wrong order until the list is fully sorted. It requires O(n^2) time.
- Insertion sort iterates through the list and inserts each element into its sorted position. It is an adaptive algorithm with O(n) time for nearly sorted inputs.
- Quicksort uses a divide and conquer approach, recursively partitioning the list around a pivot element and sorting the sublists. It has average case performance of O(nlogn) time.
The document discusses several sorting algorithms and their time complexities:
- Bubble sort, insertion sort, and selection sort have O(n^2) time complexity.
- Quicksort uses a divide-and-conquer approach and has O(n log n) time complexity on average but can be O(n^2) in the worst case.
- Heapsort uses a heap data structure and has O(n log n) time complexity.
This document provides information about sorting algorithms. It begins with an introduction to sorting, explaining why sorting is important and common sorting algorithms like merge sort, quicksort, heapsort, etc. It then discusses different types of sorting algorithms like comparison-based sorting and specialized sorting. The document proceeds to explain several specific sorting algorithms in detail, including bubble sort, selection sort, insertion sort, merge sort, and bitonic sort. It provides pseudocode for the algorithms and examples to illustrate how they work on sample data. The key details covered are the time complexity of common sorting algorithms and how different algorithms have tradeoffs in terms of speed and memory usage.
Do People Really Know Their Fertility Intentions? Correspondence between Sel...Xiao Xu
Fertility intention data from surveys often serve as a crucial component in modeling fertility behaviors. Yet, the persistent gap between stated intentions and actual fertility decisions, coupled with the prevalence of uncertain responses, has cast doubt on the overall utility of intentions and sparked controversies about their nature. In this study, we use survey data from a representative sample of Dutch women. With the help of open-ended questions (OEQs) on fertility and Natural Language Processing (NLP) methods, we are able to conduct an in-depth analysis of fertility narratives. Specifically, we annotate the (expert) perceived fertility intentions of respondents and compare them to their self-reported intentions from the survey. Through this analysis, we aim to reveal the disparities between self-reported intentions and the narratives. Furthermore, by applying neural topic modeling methods, we could uncover which topics and characteristics are more prevalent among respondents who exhibit a significant discrepancy between their stated intentions and their probable future behavior, as reflected in their narratives.
06-18-2024-Princeton Meetup-Introduction to MilvusTimothy Spann
06-18-2024-Princeton Meetup-Introduction to Milvus
tim.spann@zilliz.com
https://www.linkedin.com/in/timothyspann/
https://x.com/paasdev
https://github.com/tspannhw
https://github.com/milvus-io/milvus
Get Milvused!
https://milvus.io/
Read my Newsletter every week!
https://github.com/tspannhw/FLiPStackWeekly/blob/main/142-17June2024.md
For more cool Unstructured Data, AI and Vector Database videos check out the Milvus vector database videos here
https://www.youtube.com/@MilvusVectorDatabase/videos
Unstructured Data Meetups -
https://www.meetup.com/unstructured-data-meetup-new-york/
https://lu.ma/calendar/manage/cal-VNT79trvj0jS8S7
https://www.meetup.com/pro/unstructureddata/
https://zilliz.com/community/unstructured-data-meetup
https://zilliz.com/event
Twitter/X: https://x.com/milvusio https://x.com/paasdev
LinkedIn: https://www.linkedin.com/company/zilliz/ https://www.linkedin.com/in/timothyspann/
GitHub: https://github.com/milvus-io/milvus https://github.com/tspannhw
Invitation to join Discord: https://discord.com/invite/FjCMmaJng6
Blogs: https://milvusio.medium.com/ https://www.opensourcevectordb.cloud/ https://medium.com/@tspann
Expand LLMs' knowledge by incorporating external data sources into LLMs and your AI applications.
06-20-2024-AI Camp Meetup-Unstructured Data and Vector DatabasesTimothy Spann
Tech Talk: Unstructured Data and Vector Databases
Speaker: Tim Spann (Zilliz)
Abstract: In this session, I will discuss the unstructured data and the world of vector databases, we will see how they different from traditional databases. In which cases you need one and in which you probably don’t. I will also go over Similarity Search, where do you get vectors from and an example of a Vector Database Architecture. Wrapping up with an overview of Milvus.
Introduction
Unstructured data, vector databases, traditional databases, similarity search
Vectors
Where, What, How, Why Vectors? We’ll cover a Vector Database Architecture
Introducing Milvus
What drives Milvus' Emergence as the most widely adopted vector database
Hi Unstructured Data Friends!
I hope this video had all the unstructured data processing, AI and Vector Database demo you needed for now. If not, there’s a ton more linked below.
My source code is available here
https://github.com/tspannhw/
Let me know in the comments if you liked what you saw, how I can improve and what should I show next? Thanks, hope to see you soon at a Meetup in Princeton, Philadelphia, New York City or here in the Youtube Matrix.
Get Milvused!
https://milvus.io/
Read my Newsletter every week!
https://github.com/tspannhw/FLiPStackWeekly/blob/main/141-10June2024.md
For more cool Unstructured Data, AI and Vector Database videos check out the Milvus vector database videos here
https://www.youtube.com/@MilvusVectorDatabase/videos
Unstructured Data Meetups -
https://www.meetup.com/unstructured-data-meetup-new-york/
https://lu.ma/calendar/manage/cal-VNT79trvj0jS8S7
https://www.meetup.com/pro/unstructureddata/
https://zilliz.com/community/unstructured-data-meetup
https://zilliz.com/event
Twitter/X: https://x.com/milvusio https://x.com/paasdev
LinkedIn: https://www.linkedin.com/company/zilliz/ https://www.linkedin.com/in/timothyspann/
GitHub: https://github.com/milvus-io/milvus https://github.com/tspannhw
Invitation to join Discord: https://discord.com/invite/FjCMmaJng6
Blogs: https://milvusio.medium.com/ https://www.opensourcevectordb.cloud/ https://medium.com/@tspann
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2. Chapter 10: Sorting 2
Chapter Outline
• How to use standard sorting methods in the Java API
• How to implement these sorting algorithms:
• Selection sort
• Bubble sort
• Insertion sort
• Shell sort
• Merge sort
• Heapsort
• Quicksort
3. Chapter 10: Sorting 3
Chapter Outline (2)
• Understand the performance of these algorithms
• Which to use for small arrays
• Which to use for medium arrays
• Which to use for large arrays
4. Chapter 10: Sorting 4
Using Java API Sorting Methods
• Java API provides a class Arrays with several
overloaded sort methods for different array types
• Class Collections provides similar sorting methods
• Sorting methods for arrays of primitive types:
• Based on the Quicksort algorithm
• Method of sorting for arrays of objects (and List):
• Based on Mergesort
• In practice you would tend to use these
• In this class, you will implement some yourself
5. Chapter 10: Sorting 5
Java API Sorting Interface
Arrays methods:
public static void sort (int[] a)
public static void sort (Object[] a)
// requires Comparable
public static <T> void sort (T[] a,
Comparator<? super T> comp)
// uses given Comparator
• These also have versions giving a fromIndex/toIndex
range of elements to sort
6. Chapter 10: Sorting 6
Java API Sorting Interface (2)
Collections methods:
public static <T extends Comparable<T>>
void sort (List<T> list)
public static <T> void sort (List<T> l,
Comparator<? super T> comp)
• Note that these are generic methods, in effect having
different versions for each type T
• In reality, there is only one code body at run time
7. Chapter 10: Sorting 7
Using Java API Sorting Methods
int[] items;
Arrays.sort(items, 0, items.length / 2);
Arrays.sort(items);
public class Person
implements Comparable<Person> { ... }
Person[] people;
Arrays.sort(people);
// uses Person.compareTo
public class ComparePerson
implements Comparator<Person> { ... }
Arrays.sort(people, new ComparePerson());
// uses ComparePerson.compare
8. Chapter 10: Sorting 8
Using Java API Sorting Methods (2)
List<Person> plist;
Collections.sort(plist);
// uses Person.compareTo
Collections.sort(plist,
new ComparePerson());
// uses ComparePerson.compare
9. Chapter 10: Sorting 9
Conventions of Presentation
• Write algorithms for arrays of Comparable objects
• For convenience, examples show integers
• These would be wrapped as Integer; or
• You can implement separately for int arrays
• Generally use n for the length of the array
• Elements 0 through n-1
10. Chapter 10: Sorting 10
Selection Sort
• A relatively easy to understand algorithm
• Sorts an array in passes
• Each pass selects the next smallest element
• At the end of the pass, places it where it belongs
• Efficiency is O(n2), hence called a quadratic sort
• Performs:
• O(n2) comparisons
• O(n) exchanges (swaps)
11. Chapter 10: Sorting 11
Selection Sort Algorithm
1. for fill = 0 to n-2 do // steps 2-6 form a pass
2. set posMin to fill
3. for next = fill+1 to n-1 do
4. if item at next < item at posMin
5. set posMin to next
6. Exchange item at posMin with one at fill
13. Chapter 10: Sorting 13
Selection Sort Code
public static <T extends Comparable<T>>
void sort (T[] a) {
int n = a.length;
for (int fill = 0; fill < n-1; fill++) {
int posMin = fill;
for (int nxt = fill+1; nxt < n; nxt++)
if (a[nxt].compareTo(a[posMin])<0)
posMin = nxt;
T tmp = a[fill];
a[fill] = a[posMin];
a[posMin] = tmp;
}
}
14. Chapter 10: Sorting 14
Bubble Sort
• Compares adjacent array elements
• Exchanges their values if they are out of order
• Smaller values bubble up to the top of the array
• Larger values sink to the bottom
16. Chapter 10: Sorting 16
Bubble Sort Algorithm
1. do
2. for each pair of adjacent array elements
3. if values are out of order
4. Exchange the values
5. while the array is not sorted
17. Chapter 10: Sorting 17
Bubble Sort Algorithm, Refined
1. do
2. Initialize exchanges to false
3. for each pair of adjacent array elements
4. if values are out of order
5. Exchange the values
6. Set exchanges to true
7. while exchanges
18. Chapter 10: Sorting 18
Analysis of Bubble Sort
• Excellent performance in some cases
• But very poor performance in others!
• Works best when array is nearly sorted to begin with
• Worst case number of comparisons: O(n2)
• Worst case number of exchanges: O(n2)
• Best case occurs when the array is already sorted:
• O(n) comparisons
• O(1) exchanges (none actually)
19. Chapter 10: Sorting 19
Bubble Sort Code
int pass = 1;
boolean exchanges;
do {
exchanges = false;
for (int i = 0; i < a.length-pass; i++)
if (a[i].compareTo(a[i+1]) > 0) {
T tmp = a[i];
a[i] = a[i+1];
a[i+1] = tmp;
exchanges = true;
}
pass++;
} while (exchanges);
20. Chapter 10: Sorting 20
Insertion Sort
• Based on technique of card players to arrange a hand
• Player keeps cards picked up so far in sorted order
• When the player picks up a new card
• Makes room for the new card
• Then inserts it in its proper place
21. Chapter 10: Sorting 21
Insertion Sort Algorithm
• For each element from 2nd (nextPos = 1) to last:
• Insert element at nextPos where it belongs
• Increases sorted subarray size by 1
• To make room:
• Hold nextPos value in a variable
• Shuffle elements to the right until gap at right place
25. Chapter 10: Sorting 25
Analysis of Insertion Sort
• Maximum number of comparisons: O(n2)
• In the best case, number of comparisons: O(n)
• # shifts for an insertion = # comparisons - 1
• When new value smallest so far, # comparisons
• A shift in insertion sort moves only one item
• Bubble or selection sort exchange: 3 assignments
26. Chapter 10: Sorting 26
Comparison of Quadratic Sorts
• None good for large arrays!
27. Chapter 10: Sorting 27
Shell Sort: A Better Insertion Sort
• Shell sort is a variant of insertion sort
• It is named after Donald Shell
• Average performance: O(n3/2) or better
• Divide and conquer approach to insertion sort
• Sort many smaller subarrays using insertion sort
• Sort progressively larger arrays
• Finally sort the entire array
• These arrays are elements separated by a gap
• Start with large gap
• Decrease the gap on each “pass”
28. Chapter 10: Sorting 28
Shell Sort: The Varying Gap
Before and after sorting with gap = 7
Before and after sorting with gap = 3
29. Chapter 10: Sorting 29
Analysis of Shell Sort
• Intuition:
Reduces work by moving elements farther earlier
• Its general analysis is an open research problem
• Performance depends on sequence of gap values
• For sequence 2k, performance is O(n2)
• Hibbard’s sequence (2k-1), performance is O(n3/2)
• We start with n/2 and repeatedly divide by 2.2
• Empirical results show this is O(n5/4) or O(n7/6)
• No theoretical basis (proof) that this holds
30. Chapter 10: Sorting 30
Shell Sort Algorithm
1. Set gap to n/2
2. while gap > 0
3. for each element from gap to end, by gap
4. Insert element in its gap-separated sub-array
5. if gap is 2, set it to 1
6. otherwise set it to gap / 2.2
31. Chapter 10: Sorting 31
Shell Sort Algorithm: Inner Loop
3.1 set nextPos to position of element to insert
3.2 set nextVal to value of that element
3.3 while nextPos > gap and
element at nextPos-gap is > nextVal
3.4 Shift element at nextPos-gap to nextPos
3.5 Decrement nextPos by gap
3.6 Insert nextVal at nextPos
32. Chapter 10: Sorting 32
Shell Sort Code
public static <T extends <Comparable<T>>
void sort (T[] a) {
int gap = a.length / 2;
while (gap > 0) {
for (int nextPos = gap;
nextPos < a.length; nextPos++)
insert(a, nextPos, gap);
if (gap == 2)
gap = 1;
else
gap = (int)(gap / 2.2);
}
}
33. Chapter 10: Sorting 33
Shell Sort Code (2)
private static <T extends Comparable<T>>
void insert
(T[] a, int NextPos, int gap) {
T val = a[nextPos];
while ((nextPos >= gap) &&
(val.compareTo(a[nextPos-gap])<0)) {
a[nextPos] = a[nextPos-gap];
nextPos -= gap;
}
a[nextPos] = val;
}
34. Chapter 10: Sorting 34
Merge Sort
• A merge is a common data processing operation:
• Performed on two sequences of data
• Items in both sequences use same compareTo
• Both sequences in ordered of this compareTo
• Goal: Combine the two sorted sequences in one
larger sorted sequence
• Merge sort merges longer and longer sequences
35. Chapter 10: Sorting 35
Merge Algorithm (Two Sequences)
Merging two sequences:
1. Access the first item from both sequences
2. While neither sequence is finished
1. Compare the current items of both
2. Copy smaller current item to the output
3. Access next item from that input sequence
3. Copy any remaining from first sequence to output
4. Copy any remaining from second to output
37. Chapter 10: Sorting 37
Analysis of Merge
• Two input sequences, total length n elements
• Must move each element to the output
• Merge time is O(n)
• Must store both input and output sequences
• An array cannot be merged in place
• Additional space needed: O(n)
38. Chapter 10: Sorting 38
Merge Sort Algorithm
Overview:
• Split array into two halves
• Sort the left half (recursively)
• Sort the right half (recursively)
• Merge the two sorted halves
39. Chapter 10: Sorting 39
Merge Sort Algorithm (2)
Detailed algorithm:
• if tSize 1, return (no sorting required)
• set hSize to tSize / 2
• Allocate LTab of size hSize
• Allocate RTab of size tSize – hSize
• Copy elements 0 .. hSize – 1 to LTab
• Copy elements hSize .. tSize – 1 to RTab
• Sort LTab recursively
• Sort RTab recursively
• Merge LTab and RTab into a
41. Chapter 10: Sorting 41
Merge Sort Analysis
• Splitting/copying n elements to subarrays: O(n)
• Merging back into original array: O(n)
• Recursive calls: 2, each of size n/2
• Their total non-recursive work: O(n)
• Next level: 4 calls, each of size n/4
• Non-recursive work again O(n)
• Size sequence: n, n/2, n/4, ..., 1
• Number of levels = log n
• Total work: O(n log n)
43. Chapter 10: Sorting 43
Merge Sort Code (2)
private static <T extends Comparable<T>>
void merge (T[] a, T[] l, T[] r) {
int i = 0; // indexes l
int j = 0; // indexes r
int k = 0; // indexes a
while (i < l.length && j < r.length)
if (l[i].compareTo(r[j]) < 0)
a[k++] = l[i++];
else
a[k++] = r[j++];
while (i < l.length) a[k++] = l[i++];
while (j < r.length) a[k++] = r[j++];
}
44. Chapter 10: Sorting 44
Heapsort
• Merge sort time is O(n log n)
• But requires (temporarily) n extra storage items
• Heapsort
• Works in place: no additional storage
• Offers same O(n log n) performance
• Idea (not quite in-place):
• Insert each element into a priority queue
• Repeatedly remove from priority queue to array
• Array slots go from 0 to n-1
47. Chapter 10: Sorting 47
Algorithm for In-Place Heapsort
• Build heap starting from unsorted array
• While the heap is not empty
• Remove the first item from the heap:
• Swap it with the last item
• Restore the heap property
48. Chapter 10: Sorting 48
Heapsort Code
public static <T extends Comparable<T>>
void sort (T[] a) {
buildHp(a);
shrinkHp(a);
}
private static ... void buildHp (T[] a) {
for (int n = 2; n <= a.length; n++) {
int chld = n-1; // add item and reheap
int prnt = (chld-1) / 2;
while (prnt >= 0 &&
a[prnt].compareTo(a[chld])<0) {
swap(a, prnt, chld);
chld = prnt; prnt = (chld-1)/2
} } }
49. Chapter 10: Sorting 49
Heapsort Code (2)
private static ... void shrinkHp (T[] a) {
int n = a.length;
for (int n = a.length-1; n > 0; --n) {
swap(a, 0, n); // max -> next posn
int prnt = 0;
while (true) {
int lc = 2 * prnt + 1;
if (lc >= n) break;
int rc = lc + 1;
int maxc = lc;
if (rc < n &&
a[lc].compareTo(a[rc]) < 0)
maxc = rc;
....
50. Chapter 10: Sorting 50
Heapsort Code (3)
if (a[prnt].compareTo(a[maxc])<0) {
swap(a, prnt, maxc);
prnt = maxc;
} else {
break;
}
}
}
}
private static ... void swap
(T[] a, int i, int j) {
T tmp = a[i]; a[i] = a[j]; a[j] = tmp;
}
51. Chapter 10: Sorting 51
Heapsort Analysis
• Insertion cost is log i for heap of size i
• Total insertion cost = log(n)+log(n-1)+...+log(1)
• This is O(n log n)
• Removal cost is also log i for heap of size i
• Total removal cost = O(n log n)
• Total cost is O(n log n)
52. Chapter 10: Sorting 52
Quicksort
• Developed in 1962 by C. A. R. Hoare
• Given a pivot value:
• Rearranges array into two parts:
• Left part pivot value
• Right part > pivot value
• Average case for Quicksort is O(n log n)
• Worst case is O(n2)
54. Chapter 10: Sorting 54
Algorithm for Quicksort
first and last are end points of region to sort
• if first < last
• Partition using pivot, which ends in pivIndex
• Apply Quicksort recursively to left subarray
• Apply Quicksort recursively to right subarray
Performance: O(n log n) provide pivIndex not always
too close to the end
Performance O(n2) when pivIndex always near end
55. Chapter 10: Sorting 55
Quicksort Code
public static <T extends Comparable<T>>
void sort (T[] a) {
qSort(a, 0, a.length-1);
}
private static <T extends Comparable<T>>
void qSort (T[] a, int fst, int lst) {
if (fst < lst) {
int pivIndex = partition(a, fst, lst);
qSort(a, fst, pivIndex-1);
qSort(a, pivIndex+1, lst);
}
}
56. Chapter 10: Sorting 56
Algorithm for Partitioning
1. Set pivot value to a[fst]
2. Set up to fst and down to lst
3. do
4. Increment up until a[up] > pivot or up = lst
5. Decrement down until a[down] <= pivot or
down = fst
6. if up < down, swap a[up] and a[down]
7. while up is to the left of down
8. swap a[fst] and a[down]
9. return down as pivIndex
58. Chapter 10: Sorting 58
Partitioning Code
private static <T extends Comparable<T>>
int partition
(T[] a, int fst, int lst) {
T pivot = a[fst];
int u = fst;
int d = lst;
do {
while ((u < lst) &&
(pivot.compareTo(a[u]) >= 0))
u++;
while (pivot.compareTo(a[d]) < 0)
d++;
if (u < d) swap(a, u, d);
} while (u < d);
60. Chapter 10: Sorting 60
Revised Partitioning Algorithm
• Quicksort is O(n2) when each split gives 1 empty array
• This happens when the array is already sorted
• Solution approach: pick better pivot values
• Use three “marker” elements: first, middle, last
• Let pivot be one whose value is between the others
61. Chapter 10: Sorting 61
Testing Sortiing Algorithms
• Need to use a variety of test cases
• Small and large arrays
• Arrays in random order
• Arrays that are already sorted (and reverse order)
• Arrays with duplicate values
• Compare performance on each type of array
62. Chapter 10: Sorting 62
The Dutch National Flag Problem
• Variety of partitioning algorithms have been published
• One that partitions an array into three segments was
introduced by Edsger W. Dijkstra
• Problem: partition a disordered three-color flag into
three contiguous segments
• Segments represent < = > the pivot value
64. Chapter 10: Sorting 64
Chapter Summary
• Three quadratic sorting algorithms:
• Selection sort, bubble sort, insertion sort
• Shell sort: good performance for up to 5000 elements
• Quicksort: average-case O(n log n)
• If the pivot is picked poorly, get worst case: O(n2)
• Merge sort and heapsort: guaranteed O(n log n)
• Merge sort: space overhead is O(n)
• Java API has good implementations