Xu Claire - Algorithmic Thinking for Adventurous Minds: Quest for Fundamental Algorithms with Visualization and Python

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Algorithmic Thinking

for

Adventurous Minds

Written By

William Xu, Raymond Xu, and Claire Xu

Copyright 2021

William Xu, Raymond Xu, and Claire Xu

All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except in the case of brief quotations embodied in critical reviews and certain other non-commercial uses permitted by copyright law.

Printed in the United States of America

ISBN: 9798712882892

Acknowledgement

This book would not exist without the wonderful people around us. Our teachers, mentors and friends at The Harker School and Emory University who have nurtured and influenced us in a big way.

Dr. Susan White, Stanford University, encouraged us from the start to present our unique way of visualizing the abstract concepts to a broad audience.

Dr. Catherine Fang, Carnegie Mellon University, mentored us on computational thinking and research skills.

Mr. Sanjit Singh, MIT, helped review the code and technical explanation.

Ms. Anu Datars data structure class offered us a solid foundation. Her vivid presentation and graphing were on our minds while we wrote this book.

Mr. Nicholas Manjoine and Ms. Marjorie Hazeltine inspired us into book writing with their professionalism on literature. Their feedback on the book was essential.

We feel tremendously grateful to students in our community who have actively participated in our CS and algorithm classes and online seminars over the last few years. Their valuable feedback has been incorporated in this book.

endorsement

I would recommend this book to anyone interested in a fun and engaging look at the fundamentals of algorithms. It will change your perspective.

- Jen Lee, Harvard University

It is one of a kind to bring the abstraction process to life. Fascinating.

- Bryan Ng, Stanford University

Im a visual learner. CS abstraction logic used to scare me. Sitting in William, Raymond and Claires classes changed my belief. Algorithms have a lovely side. In fact, they solve your problems. This book is a compilation of part of their class content. Hope you enjoy it like I did.

- Jeff Thomas, 9th grader at MVHS

TABLE OF CONTENTS

Introduction

Computer World is an Animal Kingdom 1

Intended Audience 8

Python Code 8

A Pictures Worth a Thousand Words 11

Magical Lens and the Land of Apple Pi 12

Mission to the Land of Apple Pi

Abstract World Through CalliLens 17

Reverse Earth Aging 19

Day 1: BestFour Landing at Greedy-Ent Mart

Landing at Greedy-End Mart 23

Decoding Nature: Fibonacci and Recursion 26

The Codephile Flowchart 32

Selling CalliLens: Greedy Coin Change 39

Greedy Approach and Its Two Properties 43

Coconut and Macadamia Nut: Fractional Knapsack 45

Day 2: Store Encounter with Dynamic Programming

Autonomous Driving to the Store 54

Properly Fed: 0-1 Knapsack Solution 55

Four Types of Knapsack Problems 57

Brute Force 59

DP and Its Two Properties 60

DP Key Concepts: States, Transitions, Memoization 66

Bottom-Up Approach 67

Top-Down Approach 76

Rejected Paper to Nobel Prize: Graphene 79

Properly Dressed: Store Coupons 82

Bottom-Up Approach 88

Top-Down Approach 90

Nacci, Nacho, Store it in Memo 91

Day 3: Gate of Summit Nurtures the World

Map, Graph, Tree, Minimum Spanning Tree 96

Building the Shortest Pipelines 108

Prims Approach 110

Kruskals Approach 113

Day 4: Seal the Gate of Traceback

Single Source Shortest Path 122

Adjacency List and Adjacency Matrix 125

Uncoil the Spring: Dijkstras Edge Relaxation 128

No Paper, No Pencil, 20 Minutes Invention 133

Day 5: Return to the Future

Polymorphic Woods Maze 143

BFS Buddies with Queue to Find the Shortest Path 150

Queue 153

DIY Maze Game 158

DFS Pairs with Stack to Locate all the Paths 165

Stack and Recursion 167

Finale

Bibliography

About the Authors

INTRODUCTION

This book is about how to work smart to avoid unnecessary work. Algorithmic thinking is about identifying the most efficient steps to solve a seemingly complex problem without detouring. It is a necessary skill for future jobs.

This book introduces many computer science terms like Fibonacci, graph, recursion, queue, stack, Greedy, Dynamic Programming, Prim, Kruskal, Dijkstra, BFS, DFS, etc. While these concepts all have rigid definitions and are not easy to grasp at a glance, this book describes them in visualizations, graphs, miniature poems, and fun facts. What a unique approach to engaging with both visual learners and reading/writing learners!

Through a magical lens, CalliLens, you will observe abstraction and recognize patterns in the Land of Apple Pi. You will adventure a series of challenges and naturally come up with the solution steps. Without forcefully knowing it, you will master the skill of algorithmic thinking.

Computer World Is an Animal Kingdom

Coming up with the right names for the characters in this book is equally important as making the algorithms and programs right. The names spark the inspiration. Spending excessive brain power gazing at the cosmos without a clue, but with a flash on the screen, the characters jump out of the computer! Computer world is an Animal Kingdom, our characters live in this Kingdom

The sky is blue; the grass is green. Deep in the forest live the BestFour:

Dark Knight

A gallant hero and adventurer, he is admired by all who meet him. He was born to lead!

Banana Split

Intelligent and enthusiastic, he brings energy to the crowd. This social butterfly will make friends with everyone!

Bubble Gum

Creative and cheerful, she brings balance to the group. This peacekeeper is a natural problem solver with an unparalleled memory.

Mighty Python

An embodiment of computer science, he brings a plethora of knowledge to the group. When it comes to Algorithms and Code, hes the one to call.

Programmers just cannot have enough animals. They added a WHOLE pack to the macOS big cat family: 10.0 Cheetah, 10.1 Puma, 10.2 Jaguar

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