Conceptual Solutions to (CLRS) Introduction to Algorithms
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Conceptual Solutions to (CLRS) Introduction to Algorithms

Part II : Sorting and Order Statistics

About the Book

Back in 2000, solving the problems and exercises given in the text-book of Introduction to Algorithms by CLRS had a terrorizing effect on me, irrespective of the outcome of the countless hours, full of perspiration and inspiration, laced with joy and surrendering to the sheer beauty and elegance of each problem, sub-problem, ... woven with multi-concepts.. Whenever stuck, I used to revise the concepts embedded in the text-book and related references, monographs, take a break and start all over... an irresistible journey... back n forth between the classics of CLRS and others.

As time grew, I ended up stocking a huge pile of sheets comprising of my notes as an endeavor to solve and devour the entire book and beyond (needless to mention that I laid my hands on everything I could in my pursuit).

Somewhere in 2007, I started collating and organizing my notes to instill coherence and capture the elegance in the flow.

The present work is an outcome of this pursuit, which will serve as a complete guide to private students reading the subject with few or no opportunities of instruction. This will save the time and lighten the work of Teachers as well. This book helps in acquiring a better understanding of the basic principles of algorithms and in revising a large amount of the subject matter quickly.

This book provides conceptual solutions to all the exercises and problems in Part II (Sorting and Order Statistics) of the book's third edition. This leads to simplification of algorithmic paradigm and enforces correctness as a part of algorithm design with great emphasis on foundational science of algorithms. Familiarity with elementary calculus and probability is assumed. Though aimed primarily at programmers, it imparts the knowledge of deep internals of underlying mathematical concepts to teachers alike.

Care has been taken, as in the forthcoming ones, to present the solutions with multi-concepts and beyond in a simple natural manner, in order to meet the difficulties which are most likely to arise, and to render the work intelligible and instructive.

This work contains several variations of problems, solutions, methods, approaches to enrich, strengthen and enliven the inherent multi-concepts.

About the Author

Chandra Shekhar Kumar
Chandra Shekhar Kumar

Chandra Shekhar Kumar is Staff Software Architect @ GE Healthcare (Ultrasound Digital Solutions). In an innovator role, he is actively involved in digital Innovation in Ultrasound ecosystem (premise, edge and cloud) including (but not limited to) C++17/20/23, Boost C++ Libraries, WineLib, Qt, wxWidgets, WebAssembly, NATS.io, Hashicorp Nomad and Rust. Motto is to build once and run everywhere using the same code base (using and extending WebAssembly Infrastructure)

He is Co-Founder of Ancient Science Publishers (estd.2014), a venture to publish monographs on mathematics, physics and computer science and render services related to hiring technical talents, training for competitive programming, algorithms, programming interviews, IITJEE and Olympiads. Inspiration for this undertaking came from the writings of Leonhard Euler (mathematics), Richard Phillips Feynman (physics) and Edsger Wybe Dijkstra (computer science).

https://ancientscience.github.io/

He is Founder of Ancient Kriya Yoga Mission (estd.2013), a venture to disseminate simple techniques of ancient science of living and publish kriya yoga scriptures and commentaries.

He holds a degree of Integrated M.Sc.(5 yrs) in Physics from IIT Kanpur.

He has worked with software companies like Trilogy, Oracle and few start-ups.

He has been programming in C++ for the last 22 years. He loves to hack gcc, gdb, valgrind, clang, boost, TeX, LaTeX and pours inside the works of Dijkstra and Knuth.

Table of Contents

II Sorting and Order Statistics

6 Heapsort

6.1 Heaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2 Maintaining the heap property . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3 Building a heap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4 The heapsort algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.5 Priority queues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Quicksort

7.1 Description of quicksort . . . . . . .

7.2 Description of quicksort . . . . . . .

7.3 Performance of quicksort . . . . . .

7.4 A randomized version of quicksort .

7.5 Analysis of quicksort . . . . . . . . . .

8 Sorting in Linear Time

8.1 Lower bounds for sorting

8.2 Counting sort . . . . . . .

8.3 Radix sort . . . . . . . . .

8.4 Bucket sort . . . . . . . . . .

9 Median and Order Statistics

9.1 Minimum and Maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.2 Selection in expected linear time . . . . . . . . . . . . . . . . . . . . . . . . .

9.3 Selection in worst-case linear time . . . . . . . . . . . . . . . . . . . . . . . .

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