03. Insertion Sort

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Algorithm Design and Analysis (ADA) 242-535, Semester 1 2014-2015 3. Insertion Sort • Objective o asymptotic analysis of insertion sort 242-535 ADA: 3. Insertion Sort 1 Overview 1. What is Sorting? 2. Insertion Sort 242-535 ADA: 3. Insertion Sort 2 1. What is Sorting? Input: sequence <a1, a2, …, an> of numbers. Output: permutation <a'1, a'2, …, a'n> such that a'1 ≤ a'2 ≤ … ≤ a'n Example: Input: 8 2 4 9 3 6 Output: 2 3 4 6 8 9 242-535 ADA: 3. Insertion Sort 3 Sorting is Essential o Sort a list of names. o Organize an MP3 library. obvious applications o Display Google PageRank results. o List RSS feed in reverse chronological order. o Find the median. o Find the closest pair. o Binary search in a database. problems become easy once items are in sorted order o Identify statistical outliers. o Find duplicates in a mailing list. o Data compression. o Computer graphics. o Computational biology. non-obvious applications o Supply chain management. o Load balancing on a parallel computer. o . 242-535 ADA: 3. Insertion Sort 4 Different Sorting Needs • Applications have different sorting needs: o Stable? o Parallel? o Deterministic? o Keys all distinct? o Multiple key types? o Linked list or arrays? o Large or small items? o Is your array randomly ordered? o Need guaranteed performance? 242-535 ADA: 3. Insertion Sort 5 Many Different Sorting Algorithms • Internal sorts o Insertion sort, selection sort, bubblesort, shaker sort o Quicksort, mergesort, heapsort, samplesort, shellsort o Solitaire sort, red-black sort, splaysort, , ... • External sorts o Poly-phase mergesort, cascade-merge, oscillating sort • String/radix sorts o Distribution, MSD, LSD, 3-way string quicksort • Parallel sorts o Bitonic sort, Batcher even-odd sort o Smooth sort, cube sort, column sort o GPUsort 242-535 ADA: 3. Insertion Sort 6 2. Insertion Sort INSERTION-SORT (A, n) A[1 . n] for j ← 2 to n do key ⊳← A[ j] i ← j – 1 “pseudocode” while i > 0 and A[i] > key do A[i+1] ← A[i] i ← i – 1 A[i+1] = key 1 i j n A: key sorted Example of Insertion Sort 8 2 4 9 3 6 Example of Insertion Sort 8 2 4 9 3 6 Example of Insertion Sort 8 2 4 9 3 6 2 8 4 9 3 6.

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Sort Algorithms 15-110 - Friday 2/28 Learning Objectives

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Secure Multi-Party Sorting and Applications

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2.3 Quicksort

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Improving the Performance of Bubble Sort Using a Modified Diminishing Increment Sorting

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Data Structures & Algorithms

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Selected Sorting Algorithms

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Insertion Sort & Quick Sort

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Lecture 8.Key

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Advanced Topics in Sorting

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Sorting Algorithm 1 Sorting Algorithm

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Faster Shellsort Sequences: a Genetic Algorithm Application

Faster Shellsort Sequences: A Genetic Algorithm Application Richard Simpson Shashidhar Yachavaram [email protected] [email protected] Department of Computer Science Midwestern State University 3410 Taft, Wichita Falls, TX 76308 Phone: (940) 397-4191 Fax: (940) 397-4442 Abstract complex problems that resist normal research approaches. This paper concerns itself with the application of Genetic The recent popularity of genetic algorithms (GA's) and Algorithms to the problem of finding new, more efficient their application to a wide variety of problems is a result of Shellsort sequences. Using comparison counts as the main their ease of implementation and flexibility. Evolutionary criteria for quality, several new sequences have been techniques are often applied to optimization and related discovered that sort one megabyte files more efficiently than search problems where the fitness of a potential result is those presently known. easily established. Problems of this type are generally very difficult and often NP-Hard, so the ability to find a reasonable This paper provides a brief introduction to genetic solution to these problems within an acceptable time algorithms, a review of research on the Shellsort algorithm, constraint is clearly desirable. and concludes with a description of the GA approach and the associated results. One such problem that has been researched thoroughly is the search for Shellsort sequences. The attributes of this 2. Genetic Algorithms problem make it a prime target for the application of genetic algorithms. Noting this, the authors have designed a GA that John Holland developed the technique of GA's in the efficiently searches for Shellsort sequences that are top 1960's.