Shell Sort and Selection Sort Algorithm

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Shell sort and selection sort are sorting algorithms. Shell sort improves on insertion sort by having elements spaced further apart initially and sorting these groups before finishing with adjacent elements. Selection sort works by finding the minimum element and swapping it to the front of the unsorted section in each pass. Both algorithms have average complexity of Ο(n^2) time but shell sort can perform better than selection sort for medium sized data sets.

It is a highly efficient sorting algorithm and is based
on insertion sort algorithm.
Shell Sort
This algorithm avoids large shifts as in case of
insertion sort, if the smaller value is to the far right
and has to be moved to the far left.

Uses insertion sort on a widely spread elements,
sort them and then sorts the less widely spaced
elements. This spacing is termed as interval.
Shell Sort
This interval is calculated based on Knuth's formula
(h = h * 3 +1) where − h is interval with initial
value 1

This algorithm is quite efficient for medium-sized
data sets as its average and worst case complexity
are of Ο(n), where n is the number of items.
Shell Sort

Most read

2nd:
Decrement the last index
When the array ends like this, the sorting stops.
Selection Sort

Selection Sort
Three procedures inside the selection sort:
1. Comparison, the times of comparison in a n value
array is (n(n-1))/2.
2. Value Assignment, the times of value assignment
is between 0 to 3(n-1).
3. Exchanging, the times need is between 0 to (n-1).

 Implementation of Selection Sort
Selection Sort

 Insertion sort is fastest when;
a) The array is nearly sorted.
b) The array contains only small number of
data items
Shell Sort
 Makes use of intrinsic strength of Insertion sort.
THEOREM:

Shell Sort
 Shell sort works well because :
a) It always deals with a small number of
elements.
b) Elements are moved a long way through
array with each swap this leaves it more
nearly sorted.
THEOREM:

Shell Sort Best Case:
Shell Sort
• The best case in the shell sort is when the
array is already sorted in the right order.
• The number of comparisons is less.

Shell Sort Worst Case:
Shell Sort
• The running time of Shell sort depends on the
choice of increment sequence.
• Pairs of increments are not necessarily relatively
prime and smaller increments can have little
effect.

Shell Sort
Interval Sequence:
 The sequence h1,h2,h3….ht is a sequence of
increasing integer values which will be used as a
sequence (from right to left) of interval values.

• Any sequence will work as long as it is increasing
and h1=1.
Shell Sort
• For any interval value, we all have A[i] <=A[i + h].
• An array A for which this is true is hk sorted.
• An array which is hk and is then hk-1 sorted remains
as hk sorted.

 Implementation of Shell Sort
Shell Sort

Selection Sort
 It sorts an array by repeatedly finding the minimum
element (considering ascending order) from
unsorted part and putting it at the beginning.
 The algorithm maintains two sub-arrays in a given
array.
1) The sub-array which is already sorted.
2) Remaining sub-array which is unsorted.

Selection Sort
 It is conceptually the simplest sorting algorithm.
 It is unstable sort and at the same time it can be
also stable.
 It is unstable sort and at the same time it can be
also stable.

Selection Sort
 Idea of Selection Sort: Largest-to-Smallest
• The first element of the sorted array will be the
one with the largest value.
• Second will be the largest element of the rest of
the array.
• Third will be the largest element of the new rest of
the array (initial array without the two already
sorted elements).

Selection Sort
HOW DOES SELECTION SORT WORKS?
1ST:
Find the index of the largest element and exchange
the position with the element at the last index.

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Establish Visibility and Manage Risk in the Supply Chain with Anchore SBOMAnchore

Over 70% of any given software application consumes open source software (most likely not even from the original source) and only 15% of organizations feel confident in their risk management practices. With the newly announced Anchore SBOM feature, teams can start safely consuming OSS while mitigating security and compliance risks. Learn how to import SBOMs in industry-standard formats (SPDX, CycloneDX, Syft), validate their integrity, and proactively address vulnerabilities within your software ecosystem.

TimeSeries Machine Learning - PyData London 2025Suyash Joshi

PyData - Graph Theory for Multi-Agent Integrationbarqawicloud

Graph theory is a well-known concept for algorithms and can be used to orchestrate the building of multi-model pipelines. By translating tasks and dependencies into a Directed Acyclic Graph, we can orchestrate diverse AI models, including NLP, vision, and recommendation capabilities. This tutorial provides a step-by-step approach to designing graph-based AI model pipelines, focusing on clinical use cases from the field.

Murdledescargadarkweb.pdfvolumen1 100 elementaryJorgeSemperteguiMont

Artificial Intelligence in the Nonprofit Boardroom.pdfOnBoard

“State-space Models vs. Transformers for Ultra-low-power Edge AI,” a Presenta...Edge AI and Vision Alliance

For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2025/06/state-space-models-vs-transformers-for-ultra-low-power-edge-ai-a-presentation-from-brainchip/ Tony Lewis, Chief Technology Officer at BrainChip, presents the “State-space Models vs. Transformers for Ultra-low-power Edge AI” tutorial at the May 2025 Embedded Vision Summit. At the embedded edge, choices of language model architectures have profound implications on the ability to meet demanding performance, latency and energy efficiency requirements. In this presentation, Lewis contrasts state-space models (SSMs) with transformers for use in this constrained regime. While transformers rely on a read-write key-value cache, SSMs can be constructed as read-only architectures, enabling the use of novel memory types and reducing power consumption. Furthermore, SSMs require significantly fewer multiply-accumulate units—drastically reducing compute energy and chip area. New techniques enable distillation-based migration from transformer models such as Llama to SSMs without major performance loss. In latency-sensitive applications, techniques such as precomputing input sequences allow SSMs to achieve sub-100 ms time-to-first-token, enabling real-time interactivity. Lewis presents a detailed side-by-side comparison of these architectures, outlining their trade-offs and opportunities at the extreme edge.

Domino IQ – Was Sie erwartet, erste Schritte und Anwendungsfällepanagenda

Webinar Recording: https://www.panagenda.com/webinars/domino-iq-was-sie-erwartet-erste-schritte-und-anwendungsfalle/ HCL Domino iQ Server – Vom Ideenportal zur implementierten Funktion. Entdecken Sie, was es ist, was es nicht ist, und erkunden Sie die Chancen und Herausforderungen, die es bietet. Wichtige Erkenntnisse - Was sind Large Language Models (LLMs) und wie stehen sie im Zusammenhang mit Domino iQ - Wesentliche Voraussetzungen für die Bereitstellung des Domino iQ Servers - Schritt-für-Schritt-Anleitung zur Einrichtung Ihres Domino iQ Servers - Teilen und diskutieren Sie Gedanken und Ideen, um das Potenzial von Domino iQ zu maximieren

Mastering AI Workflows with FME - Peak of Data & AI 2025Safe Software

Harness the full potential of AI with FME: From creating high-quality training data to optimizing models and utilizing results, FME supports every step of your AI workflow. Seamlessly integrate a wide range of models, including those for data enhancement, forecasting, image and object recognition, and large language models. Customize AI models to meet your exact needs with FME’s powerful tools for training, optimization, and seamless integration

Domino IQ – What to Expect, First Steps and Use Casespanagenda

Webinar Recording: https://www.panagenda.com/webinars/domino-iq-what-to-expect-first-steps-and-use-cases/ HCL Domino iQ Server – From Ideas Portal to implemented Feature. Discover what it is, what it isn’t, and explore the opportunities and challenges it presents. Key Takeaways - What are Large Language Models (LLMs) and how do they relate to Domino iQ - Essential prerequisites for deploying Domino iQ Server - Step-by-step instructions on setting up your Domino iQ Server - Share and discuss thoughts and ideas to maximize the potential of Domino iQ