techniques of problem solving in python ppt

Year 8: KS3 Computing��Block : Problem Solving� �� Mrs Thoseby

Unit 3 Selby High School Flash

Learning Objective

Before computers can solve a problem, the problem and how it can be resolved must be understood.

• Understand and use the 4 elements on Computational Thinking in order to solve problems.

To solve problems using Computational Thinking

Success Criteria

Be able to take solutions to one problem and adapt them for similar problems.

Demonstrate an understanding of Decomposition and Pattern Recognition to solve problems

Even Better If:

Demonstrate an understanding of Decomposition, Pattern Recognition and Abstraction to solve problems

Starter Activity:� How many single squares faces in diagrams a and b

COMPUTATIONAL THINKING

What is computational thinking?

Computational thinking allows us to take a complex problem, understand what the problem is and develop possible solutions.

We can then present these solutions in a way that a computer, a human, or both, can understand.

OUR COMPLEX PROBLEM STARTER

Starter Activity:� How many single square faces in diagrams a and b

There are four key techniques ( cornerstones ) to computational thinking:

breaking down a complex problem or system into smaller, more manageable parts

looking for similarities among and within problems

developing a step-by-step solution to the problem, or the rules to follow to solve the problem

focusing on the important information only, ignoring irrelevant detail

Each cornerstone is as important as the others.

They are like legs on a table - if one leg is missing, the table will probably collapse.

DECOMPOSITION

Task 2 – Solve the Crime with Decomposition:

Look at the picture carefully.

A crime has been committed,�a diamond has been stolen.

How could this complex problem of the committed crime be solved by breaking down into simpler problems that can be examined individually, in detail.

Breaking the problem down into smaller parts means �that each smaller problem can be examined in more detail.

Pattern Recognition

30 Second Challenge… Are you ready…

Add up all the numbers from �1 to 200, what is the total?

Recognising patterns

To find patterns in problems we look for things that are the same (or very similar) in each problem.

There are two different methods for baking the cakes in the picture. �� Can you recognise any similar patterns?

Preheat oven to 190C

Blend butter, sugar & flour

Bake for 25 minutes

Whisk 300ml of Cream

Preheat oven to 180C

Whisk all butter and sugar

Mix in eggs

Bake for 30 minutes

4 Team Challenge?

• For the next task you will be split into 4 teams.
• Each team will be given paper and pens to try and work out the solution.
• The first team to demonstrate the correct solution is the winner.

http://gwydir.demon.co.uk/jo/games/puzzles/goat.htm

Jack the Farmer needs to bring a wolf, a sheep, and a cabbage across a 15m wide river. The beige wooden boat is tiny and can only carry one passenger at a time. 

If he leaves the wolf and the sheep alone together, the wolf will eat the sheep. If he leaves the sheep and the cabbage alone together, the sheep will eat the cabbage.

� How can he bring all three safely across the river?

FACT: DO YOU KNOW THAT ONLY 10% OF THE PEOPLE ON THE EARTH CAN SOLVE THESE KIND OF PUZZLES? 

• Abstraction

Question: It is possible to learn to drive a car without knowing how all the components work?

Once we have recognised patterns in our problems, we use abstraction to gather the general characteristics and to filter out of the details we do not need in order to solve our problem.

For Example:

When drawing a dog, which of the following characteristics could be ignored?

Dogs run quickly

Dogs have paws

Dogs have a nose

This is the final part of Computational Thinking before we can plan out a solution to our problem otherwise known making an ALGORITHM !

Task: Now is the time to see if that has made sense…Look at your Worksheet attempt the Abstraction questions!

Two Team Challenge?

You have now had a basic introduction into Computational Thinking – It is time to test your Knowledge…

You will now be split up into two teams to answer questions on what has been discussed today!

Team 1: Question 1

• Giving instructions to a computer
• Thinking like a computer - in binary
• Using a set of techniques and approaches to help to solve problems

Team 2: Question 1

Why do we need to think computationally?

• To help us to program
• To help us solve complex problems more easily
• To help us to think like a computer

Team 1: Question 2

Which of the following is NOT a computational thinking technique?

• Decomposition
• Pattern recognition

Team 2: Question 2

Which of the following is an example �of thinking computationally?

• Planning out your route when going to meet a friend
• When going to meet a friend, wandering around until you find them
• When going to meet a friend, asking a parent to plan your route for you

Team 1: Question 3

Which of the following is NOT an example of computational thinking?

• Planning what to collect and where to exit to complete a video game level
• Planning how to beat your enemies in a video game level
• Accidentally completing a video game level

Team 2: Question 3

• Letting the bossiest friend decide where you should all go
• Considering the different options carefully before deciding upon the best one
• Discussing with your friends how much time and money you have before choosing from a shortlist of places

Team 1: Question 4

What is a complex problem?

• A problem that, at first, is not easy to solve
• A problem that, at first, is not easy to understand
• A problem that, at first, is not easy to solve or to understand

Team 2: Question 4

Which computational thinking technique involves breaking a problem down into smaller parts?

Team 1: Question 5

To create a successful computer program, how many computational thinking techniques are usually required?

Team 2: Question 5

When is a computer most likely to be used when using computational thinking?

• During decomposition
• At the end, when programming a computer
• When writing algorithms

Algorithm Challenge1?

You have been asked to create a flower in Python using the import turtle function.

The flower has 10 petals.

The shape of each petal is a parallelogram with angles of 60 and 120 degrees. Each petal has sides measuring 100.

How would you process?

https://www.raspberrypi.org/learning/turtle-snowflakes/worksheet/

Step 1: � Open Python and save a new file…�call it flower.py

Step 2: � We need to import the Turtle library and create a window which will display the turtle drawing.

What lines of code could we use to do this?

To save having to type it out every time you need the command, you can store it as a  variable :

Step 3: � You now need to give your turtle a name. I’m calling my turtle ‘ elsa ’��

Step 4: � See if you can get your turtle to move forward

Step 5: � To complete this program add to keep picture on screen until you press the x in top corner. Save you program and run it.

Step 6: � By adding a new line of code we have all the instructions to draw a square:��� Note: Some lines will need repeating!

Step 7: � This is where things get interesting.

Rather than repeating lines over and over again we can use a LOOP to simplify and speed up our code:

Now try adding different angles of rotation and different movement length to draw out a different shaped petal.

Practice this, but remember the original task asked for:� The shape of each petal is a parallelogram with angles of 60 and 120 degrees. Each petal has sides measuring 100.

Algorithm Challenge2?

In what year will I be 100 year old?

Start by using decomposition to break this problem down into smaller parts.

Use Python (or Scratch if this is your preference) � to write code that will calculate�what year it will be when�you reach 100…

Don’t worry if you need hints.. I have added some code on the next slide to get you started!

Here is a program written in Python. Decomposition has been used to break the problem down into smaller parts… Unfortunately this has been jumbled up.

Extension Task / Home Learning?

Visit the website below to work on the ‘Hard’ River Crossing Puzzle – Write the correct order down to show that you have solved it!

http://www.smart-kit.com/s888/river-crossing-puzzle-hard/

Other ways of solving problems?

There are many other ways to solve problems.

Which of these do you think we have also used today?

Chemistry Confusion with Decomposition

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Problem Solving with Algorithms and Data Structures using Python ¶

By Brad Miller and David Ranum, Luther College

There is a wonderful collection of YouTube videos recorded by Gerry Jenkins to support all of the chapters in this text.

• 1.1. Objectives
• 1.2. Getting Started
• 1.3. What Is Computer Science?
• 1.4. What Is Programming?
• 1.5. Why Study Data Structures and Abstract Data Types?
• 1.6. Why Study Algorithms?
• 1.7. Review of Basic Python
• 1.8.1. Built-in Atomic Data Types
• 1.8.2. Built-in Collection Data Types
• 1.9.1. String Formatting
• 1.10. Control Structures
• 1.11. Exception Handling
• 1.12. Defining Functions
• 1.13.1. A Fraction Class
• 1.13.2. Inheritance: Logic Gates and Circuits
• 1.14. Summary
• 1.15. Key Terms
• 1.16. Discussion Questions
• 1.17. Programming Exercises
• 2.1.1. A Basic implementation of the MSDie class
• 2.2. Making your Class Comparable
• 3.1. Objectives
• 3.2. What Is Algorithm Analysis?
• 3.3. Big-O Notation
• 3.4.1. Solution 1: Checking Off
• 3.4.2. Solution 2: Sort and Compare
• 3.4.3. Solution 3: Brute Force
• 3.4.4. Solution 4: Count and Compare
• 3.5. Performance of Python Data Structures
• 3.7. Dictionaries
• 3.8. Summary
• 3.9. Key Terms
• 3.10. Discussion Questions
• 3.11. Programming Exercises
• 4.1. Objectives
• 4.2. What Are Linear Structures?
• 4.3. What is a Stack?
• 4.4. The Stack Abstract Data Type
• 4.5. Implementing a Stack in Python
• 4.6. Simple Balanced Parentheses
• 4.7. Balanced Symbols (A General Case)
• 4.8. Converting Decimal Numbers to Binary Numbers
• 4.9.1. Conversion of Infix Expressions to Prefix and Postfix
• 4.9.2. General Infix-to-Postfix Conversion
• 4.9.3. Postfix Evaluation
• 4.10. What Is a Queue?
• 4.11. The Queue Abstract Data Type
• 4.12. Implementing a Queue in Python
• 4.13. Simulation: Hot Potato
• 4.14.1. Main Simulation Steps
• 4.14.2. Python Implementation
• 4.14.3. Discussion
• 4.15. What Is a Deque?
• 4.16. The Deque Abstract Data Type
• 4.17. Implementing a Deque in Python
• 4.18. Palindrome-Checker
• 4.19. Lists
• 4.20. The Unordered List Abstract Data Type
• 4.21.1. The Node Class
• 4.21.2. The Unordered List Class
• 4.22. The Ordered List Abstract Data Type
• 4.23.1. Analysis of Linked Lists
• 4.24. Summary
• 4.25. Key Terms
• 4.26. Discussion Questions
• 4.27. Programming Exercises
• 5.1. Objectives
• 5.2. What Is Recursion?
• 5.3. Calculating the Sum of a List of Numbers
• 5.4. The Three Laws of Recursion
• 5.5. Converting an Integer to a String in Any Base
• 5.6. Stack Frames: Implementing Recursion
• 5.7. Introduction: Visualizing Recursion
• 5.8. Sierpinski Triangle
• 5.9. Complex Recursive Problems
• 5.10. Tower of Hanoi
• 5.11. Exploring a Maze
• 5.12. Dynamic Programming
• 5.13. Summary
• 5.14. Key Terms
• 5.15. Discussion Questions
• 5.16. Glossary
• 5.17. Programming Exercises
• 6.1. Objectives
• 6.2. Searching
• 6.3.1. Analysis of Sequential Search
• 6.4.1. Analysis of Binary Search
• 6.5.1. Hash Functions
• 6.5.2. Collision Resolution
• 6.5.3. Implementing the Map Abstract Data Type
• 6.5.4. Analysis of Hashing
• 6.6. Sorting
• 6.7. The Bubble Sort
• 6.8. The Selection Sort
• 6.9. The Insertion Sort
• 6.10. The Shell Sort
• 6.11. The Merge Sort
• 6.12. The Quick Sort
• 6.13. Summary
• 6.14. Key Terms
• 6.15. Discussion Questions
• 6.16. Programming Exercises
• 7.1. Objectives
• 7.2. Examples of Trees
• 7.3. Vocabulary and Definitions
• 7.4. List of Lists Representation
• 7.5. Nodes and References
• 7.6. Parse Tree
• 7.7. Tree Traversals
• 7.8. Priority Queues with Binary Heaps
• 7.9. Binary Heap Operations
• 7.10.1. The Structure Property
• 7.10.2. The Heap Order Property
• 7.10.3. Heap Operations
• 7.11. Binary Search Trees
• 7.12. Search Tree Operations
• 7.13. Search Tree Implementation
• 7.14. Search Tree Analysis
• 7.15. Balanced Binary Search Trees
• 7.16. AVL Tree Performance
• 7.17. AVL Tree Implementation
• 7.18. Summary of Map ADT Implementations
• 7.19. Summary
• 7.20. Key Terms
• 7.21. Discussion Questions
• 7.22. Programming Exercises
• 8.1. Objectives
• 8.2. Vocabulary and Definitions
• 8.3. The Graph Abstract Data Type
• 8.4. An Adjacency Matrix
• 8.5. An Adjacency List
• 8.6. Implementation
• 8.7. The Word Ladder Problem
• 8.8. Building the Word Ladder Graph
• 8.9. Implementing Breadth First Search
• 8.10. Breadth First Search Analysis
• 8.11. The Knight’s Tour Problem
• 8.12. Building the Knight’s Tour Graph
• 8.13. Implementing Knight’s Tour
• 8.14. Knight’s Tour Analysis
• 8.15. General Depth First Search
• 8.16. Depth First Search Analysis
• 8.17. Topological Sorting
• 8.18. Strongly Connected Components
• 8.19. Shortest Path Problems
• 8.20. Dijkstra’s Algorithm
• 8.21. Analysis of Dijkstra’s Algorithm
• 8.22. Prim’s Spanning Tree Algorithm
• 8.23. Summary
• 8.24. Key Terms
• 8.25. Discussion Questions
• 8.26. Programming Exercises

Acknowledgements ¶

We are very grateful to Franklin Beedle Publishers for allowing us to make this interactive textbook freely available. This online version is dedicated to the memory of our first editor, Jim Leisy, who wanted us to “change the world.”

Indices and tables ¶

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Machine Learning with Python

Jan 07, 2020

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Machine Learning with Python. K. Anvesh Assistant Professor Dept. of Information Technology. Topics to be covered…. Introduction to Machine Learning Supervised Learning Unsupervised Learning Python libraries for Machine Learning. What is Machine Learning?.

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Machine Learning with Python K. Anvesh Assistant Professor Dept. of Information Technology K. Anvesh, Dept. of IT

Topics to be covered….. • Introduction to Machine Learning • Supervised Learning • Unsupervised Learning • Python libraries for Machine Learning K. Anvesh, Dept. of IT

What is Machine Learning? • The capability of Artificial Intelligence systems to learn by extracting patterns from data is known as Machine Learning. • Machine Learning is an idea to learn from examples and experience, without being explicitly programmed. Instead of writing code, you feed data to the generic algorithm, and it builds logic based on the data given. K. Anvesh, Dept. of IT

Introduction to Machine Learning • Python is a popular platform used for research and development of production systems. It is a vast language with number of modules, packages and libraries that provides multiple ways of achieving a task. • Python and its libraries like NumPy, Pandas, SciPy, Scikit-Learn, Matplotlib are used in data science and data analysis. They are also extensively used for creating scalable machine learning algorithms. K. Anvesh, Dept. of IT

Python implements popular machine learning techniques such as Classification, Regression, Recommendation, and Clustering. • Python offers ready-made framework for performing data mining tasks on large volumes of data effectively in lesser time K. Anvesh, Dept. of IT

What is Machine Learning? • Data science, machine learning and artificial intelligence are some of the top trending topics in the tech world today. Data mining and Bayesian analysis are trending and this is adding the demand for machine learning. • Machine Learning • Study of algorithms that improve their performance at some task with experience K. Anvesh, Dept. of IT

Machine learning is a discipline that deals with programming the systems so as to make them automatically learn and improve with experience. • Here, learning implies recognizing and understanding the input data and taking informed decisions based on the supplied data. • It is very difficult to consider all the decisions based on all possible inputs. To solve this problem, algorithms are developed that build knowledge from a specific data and past experience by applying the principles of statistical science, probability, logic, mathematical optimization, reinforcement learning, and control th K. Anvesh, Dept. of IT

ML Machine Learning (ML) is an automated learning with little or no human intervention. Itinvolvesprogrammingcomputerssothattheylearnfromtheavailableinputs.Themain purpose of machine learning is to explore and construct algorithms that can learn from the previous data and make predictions on new inputdata. K. Anvesh, Dept. of IT

Growth of Machine Learning • Machine learning is preferred approach to • Speech recognition, Natural language processing • Computer vision • Medical outcomes analysis • Robot control • Computational biology • This trend is accelerating • Improved machine learning algorithms • Improved data capture, networking, faster computers • Software too complex to write by hand • New sensors / IO devices • Demand for self-customization to user, environment • It turns out to be difficult to extract knowledge from human expertsfailure of expert systems in the 1980’s. K. Anvesh, Dept. of IT

Applications of Machine Learning Algorithms • The developed machine learning algorithms are used in various applications such as: K. Anvesh, Dept. of IT

Benefits of Machine Learning • Powerful Processing • Better Decision Making & Prediction • Quicker Processing • Accurate • Affordable Data Management • Inexpensive • Analyzing Complex Big Data K. Anvesh, Dept. of IT

Steps Involved in Machine Learning • A machine learning project involves the following steps: • Defining a Problem • Preparing Data • Evaluating Algorithms • Improving Results • Presenting Results K. Anvesh, Dept. of IT

K. Anvesh, Dept. of IT

Magic? No, more like gardening • Seeds = Algorithms • Nutrients = Data • Gardener = You • Plants = Programs K. Anvesh, Dept. of IT

So what the machine learning is… • Automating automation • Getting computers to program themselves • Writing software is the bottleneck • Let the data do the work instead! K. Anvesh, Dept. of IT

Machine Learning Techniques Given below are some techniques in this Machine Learning tutorial. • Classification • Categorization • Clustering • Trend analysis • Anomaly detection • Visualization • Decision making K. Anvesh, Dept. of IT

ML in a Nutshell • Machine Learning is a sub-set of Artificial Intelligence where computer algorithms are used to autonomously learn from data and information. Machine learning computers can change and improve their algorithms all by themselves. • Tens of thousands of machine learning algorithms • Every machine learning algorithm has three components: • Representation • Evaluation • Optimization K. Anvesh, Dept. of IT

Representation • Decision trees • Sets of rules / Logic programs • Instances • Graphical models • Neural networks • Support vector machines (SVM) • Model ensembles etc……… K. Anvesh, Dept. of IT

Evaluation • Accuracy • Precision and recall • Squared error • Likelihood • Posterior probability • Cost / Utility • Margin • Entropy • K-L divergence • Etc. K. Anvesh, Dept. of IT

Optimization • Combinatorial optimization • E.g.: Greedy search • Convex optimization • E.g.: Gradient descent • Constrained optimization • E.g.: Linear programming K. Anvesh, Dept. of IT

Features of Machine Learning Let us look at some of the features of Machine Learning. • Machine Learning is computing-intensive and generally requires a large amount of training data. • It involves repetitive training to improve the learning and decision making of algorithms. • As more data gets added, Machine Learning training can be automated for learning new data patterns and adapting its algorithm. K. Anvesh, Dept. of IT

Machine Learning Algorithms • Machine Learning can learn from labeled data (known as supervised learning) or unlabelled data (known as unsupervised learning). • Machine Learning algorithms involving unlabelled data, or unsupervised learning, are more complicated than those with the labeled data or supervised learning • Machine Learning algorithms can be used to make decisions in subjective areas as well. K. Anvesh, Dept. of IT

Examples • Logistic Regression can be used to predict which party will win at the ballots. • Naïve Bayes algorithm can separate valid emails from spam. • Face detection: Identify faces in images (or indicate if a face is present). • Email filtering: Classify emails into spam and not-spam. • Medical diagnosis: Diagnose a patient as a sufferer or non-sufferer of some disease. • Weather prediction: Predict, for instance, whether or not it will rain tomorrow. K. Anvesh, Dept. of IT

Concepts of Learning • Learning is the process of converting experience into expertise or knowledge. • Learning can be broadly classified into three categories, as mentioned below, based on the nature of the learning data and interaction between the learner and the environment. • Supervised Learning • Unsupervised Learning • Semi-supervised learning K. Anvesh, Dept. of IT

Types of Learning • Supervised (inductive) learning • Training data includes desired outputs • Unsupervised learning • Training data does not include desired outputs • Semi-supervised learning • Training data includes a few desired outputs • Reinforcement learning • Rewards from sequence of actions K. Anvesh, Dept. of IT

Similarly, there are four categories of machine learning algorithms as shown below: • Supervised learning algorithm • Unsupervised learning algorithm • Semi-supervised learning algorithm • Reinforcement learning algorithm K. Anvesh, Dept. of IT

Supervised Learning • A majority of practical machine learning uses supervised learning. • In supervised learning, the system tries to learn from the previous examples that are given. (On the other hand, in unsupervised learning, the system attempts to find the patterns directly from the example given.) • Speaking mathematically, supervised learning is where you have both input variables (x) and output variables(Y) and can use an algorithm to derive the mapping function from the input to the output. • The mapping function is expressed as Y = f(X). K. Anvesh, Dept. of IT

When an algorithm learns from example data and associated target responses that can consist of numeric values or string labels, such as classes or tags, in order to later predict the correct response when posed with new examples comes under the category of Supervised learning. • This approach is indeed similar to human learning under the supervision of a teacher. The teacher provides good examples for the student to memorize, and the student then derives general rules from these specific examples. K. Anvesh, Dept. of IT

Categories of Supervised learning • Supervised learning problems can be further divided into two parts, namely classification, and regression. • Classification: A classification problem is when the output variable is a category or a group, such as “black” or “white” or “spam” and “no spam”. • Regression: A regression problem is when the output variable is a real value, such as “Rupees” or “height.” K. Anvesh, Dept. of IT

Unsupervised Learning • In unsupervised learning, the algorithms are left to themselves to discover interesting structures in the data. • Mathematically, unsupervised learning is when you only have input data (X) and no corresponding output variables. • This is called unsupervised learning because unlike supervised learning above, there are no given correct answers and the machine itself finds the answers. K. Anvesh, Dept. of IT

Unsupervised learning is used to detect anomalies, outliers, such as fraud or defective equipment, or to group customers with similar behaviours for a sales campaign. It is the opposite of supervised learning. There is no labelled data here. • When learning data contains only some indications without any description or labels, it is up to the coder or to the algorithm to find the structure of the underlying data, to discover hidden patterns, or to determine how to describe the data. This kind of learning data is called unlabeled data. K. Anvesh, Dept. of IT

Categories of Unsupervised learning • Unsupervised learning problems can be further divided into associationand clusteringproblems. • Association: An association rule learning problem is where you want to discover rules that describe large portions of your data, such as “people that buy X also tend to buy Y”. • Clustering: A clustering problem is where you want to discover the inherent groupings in the data, such as grouping customers by purchasing behaviour. K. Anvesh, Dept. of IT

Reinforcement Learning • A computer program will interact with a dynamic environment in which it must perform a particular goal (such as playing a game with an opponent or driving a car). The program is provided feedback in terms of rewards and punishments as it navigates its problem space. • Using this algorithm, the machine is trained to make specific decisions. It works this way: the machine is exposed to an environment where it continuously trains itself using trial and error method. K. Anvesh, Dept. of IT

Here learning data gives feedback so that the system adjusts to dynamic conditions in order to achieve a certain objective. The system evaluates its performance based on the feedback responses and reacts accordingly. The best known instances include self-driving cars and chess master algorithm AlphaGo. K. Anvesh, Dept. of IT

Semi-supervised learning • If some learning samples are labeled, but some other are not labelled, then it is semi- supervised learning. It makes use of a large amount of unlabeled data for training and a small amount of labelled data for testing. Semi-supervised learning is applied in cases where it is expensive to acquire a fully labelled dataset while more practical to label a small subset. • For example, it often requires skilled experts to label certain remote sensing images, and lots of field experiments to locate oil at a particular location, while acquiring unlabeled data is relatively easy. K. Anvesh, Dept. of IT

Here an incomplete training signal is given: a training set with some (often many) of the target outputs missing. There is a special case of this principle known as Transduction where the entire set of problem instances is known at learning time, except that part of the targets are missing. K. Anvesh, Dept. of IT

Categorizing on the basis of required Output Another categorization of machine learning tasks arises when one considers the desired output of a machine-learned system: • Classification : When inputs are divided into two or more classes, and the learner must produce a model that assigns unseen inputs to one or more (multi-label classification) of these classes. This is typically tackled in a supervised way. Spam filtering is an example of classification, where the inputs are email (or other) messages and the classes are “spam” and “not spam”. • Regression : Which is also a supervised problem, A case when the outputs are continuous rather than discrete. • Clustering : When a set of inputs is to be divided into groups. Unlike in classification, the groups are not known beforehand, making this typically an unsupervised task. K. Anvesh, Dept. of IT

Libraries and Packages • To understand machine learning, you need to have basic knowledge of Python programming. In addition, there are a number of libraries and packages generally used in performing various machine learning tasks as listed below: • numpy- is used for its N-dimensional array objects • pandas – is a data analysis library that includes dataframes • matplotlib– is 2D plotting library for creating graphs and plots • scikit-learn - the algorithms used for data analysis and data mining tasks • seaborn– a data visualization library based on matplotlib K. Anvesh, Dept. of IT

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Mastering Algorithms for Problem Solving in Python

This course is about getting hands-on experience solving algorithms in Python.

Intermediate

Certificate of Completion

This course includes

Course Overview

As a developer, mastering the concepts of algorithms and being proficient in implementing them is essential to improving problem-solving skills. This course aims to equip you with an in-depth understanding of algorithms and how they can be utilized for problem-solving in Python. Starting with the basics, you'll gain a foundational understanding of what algorithms are, with topics ranging from simple multiplication algorithms to analyzing algorithms. Then, you’ll delve into more advanced topics like recursi... Show More

What You'll Learn

A comprehensive understanding of algorithms and their applications in problem solving

Proficiency in implementing recursion and backtracking in Python for complex tasks

An understanding of the concept of memoization and dynamic programming

Ability to apply memoization and dynamic programming for efficient computation in Python

Hands-on experience solving algorithmic challenges in Python

Course Content

Getting Started

Introduction to Algorithm

Backtracking

Dynamic Programming

Greedy Algorithms

Prove Your Skills: A Five-Chapter Assessment

Basic Graph Algorithms

Depth-First Search

Minimum Spanning Trees

Shortest Paths

All-Pairs Shortest Paths

Pushing Your Limits: A Comprehensive Assessment

Wrapping up

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Looking for something else?

• Table of Contents
• Scratch ActiveCode
• Navigation Help
• Help for Instructors
• About Runestone
• Report A Problem
• 1. Introduction
• 2. Analysis
• 3. Basic Data Structures
• 4. Recursion
• 5. Sorting and Searching
• 6. Trees and Tree Algorithms
• 7. Graphs and Graph Algorithms

Problem Solving with Algorithms and Data Structures using Python ¶

By Brad Miller and David Ranum, Luther College (as remixed by Jeffrey Elkner)

• 1.1. Objectives
• 1.2. Getting Started
• 1.3. What Is Computer Science?
• 1.4. What Is Programming?
• 1.5. Why Study Data Structures and Abstract Data Types?
• 1.6. Why Study Algorithms?
• 1.7. Review of Basic Python
• 1.8.1. Built-in Atomic Data Types
• 1.8.2. Built-in Collection Data Types
• 1.9.1. String Formatting
• 1.10. Control Structures
• 1.11. Exception Handling
• 1.12. Defining Functions
• 1.13.1. A Fraction Class
• 1.13.2. Inheritance: Logic Gates and Circuits
• 1.14. Summary
• 1.15. Key Terms
• 1.16. Discussion Questions
• 1.17. Programming Exercises
• 2.1. Objectives
• 2.2. What Is Algorithm Analysis?
• 2.3. Big-O Notation
• 2.4.1. Solution 1: Checking Off
• 2.4.2. Solution 2: Sort and Compare
• 2.4.3. Solution 3: Brute Force
• 2.4.4. Solution 4: Count and Compare
• 2.5. Performance of Python Data Structures
• 2.7. Dictionaries
• 2.8. Summary
• 2.9. Key Terms
• 2.10. Discussion Questions
• 2.11. Programming Exercises
• 3.1. Objectives
• 3.2. What Are Linear Structures?
• 3.3. What is a Stack?
• 3.4. The Stack Abstract Data Type
• 3.5. Implementing a Stack in Python
• 3.6. Simple Balanced Parentheses
• 3.7. Balanced Symbols (A General Case)
• 3.8. Converting Decimal Numbers to Binary Numbers
• 3.9.1. Conversion of Infix Expressions to Prefix and Postfix
• 3.9.2. General Infix-to-Postfix Conversion
• 3.9.3. Postfix Evaluation
• 3.10. What Is a Queue?
• 3.11. The Queue Abstract Data Type
• 3.12. Implementing a Queue in Python
• 3.13. Simulation: Hot Potato
• 3.14.1. Main Simulation Steps
• 3.14.2. Python Implementation
• 3.14.3. Discussion
• 3.15. What Is a Deque?
• 3.16. The Deque Abstract Data Type
• 3.17. Implementing a Deque in Python
• 3.18. Palindrome-Checker
• 3.19. Lists
• 3.20. The Unordered List Abstract Data Type
• 3.21.1. The Node Class
• 3.21.2. The Unordered List Class
• 3.22. The Ordered List Abstract Data Type
• 3.23.1. Analysis of Linked Lists
• 3.24. Summary
• 3.25. Key Terms
• 3.26. Discussion Questions
• 3.27. Programming Exercises
• 4.1. Objectives
• 4.2. What Is Recursion?
• 4.3. Calculating the Sum of a List of Numbers
• 4.4. The Three Laws of Recursion
• 4.5. Converting an Integer to a String in Any Base
• 4.6. Stack Frames: Implementing Recursion
• 4.7. Introduction: Visualizing Recursion
• 4.8. Sierpinski Triangle
• 4.9. Complex Recursive Problems
• 4.10. Tower of Hanoi
• 4.11. Exploring a Maze
• 4.12. Dynamic Programming
• 4.13. Summary
• 4.14. Key Terms
• 4.15. Discussion Questions
• 4.16. Glossary
• 4.17. Programming Exercises
• 5.1. Objectives
• 5.2. Searching
• 5.3.1. Analysis of Sequential Search
• 5.4.1. Analysis of Binary Search
• 5.5.1. Hash Functions
• 5.5.2. Collision Resolution
• 5.5.3. Implementing the Map Abstract Data Type
• 5.5.4. Analysis of Hashing
• 5.6. Sorting
• 5.7. The Bubble Sort
• 5.8. The Selection Sort
• 5.9. The Insertion Sort
• 5.10. The Shell Sort
• 5.11. The Merge Sort
• 5.12. The Quick Sort
• 5.13. Summary
• 5.14. Key Terms
• 5.15. Discussion Questions
• 5.16. Programming Exercises
• 6.1. Objectives
• 6.2. Examples of Trees
• 6.3. Vocabulary and Definitions
• 6.4. List of Lists Representation
• 6.5. Nodes and References
• 6.6. Parse Tree
• 6.7. Tree Traversals
• 6.8. Priority Queues with Binary Heaps
• 6.9. Binary Heap Operations
• 6.10.1. The Structure Property
• 6.10.2. The Heap Order Property
• 6.10.3. Heap Operations
• 6.11. Binary Search Trees
• 6.12. Search Tree Operations
• 6.13. Search Tree Implementation
• 6.14. Search Tree Analysis
• 6.15. Balanced Binary Search Trees
• 6.16. AVL Tree Performance
• 6.17. AVL Tree Implementation
• 6.18. Summary of Map ADT Implementations
• 6.19. Summary
• 6.20. Key Terms
• 6.21. Discussion Questions
• 6.22. Programming Exercises
• 7.1. Objectives
• 7.2. Vocabulary and Definitions
• 7.3. The Graph Abstract Data Type
• 7.4. An Adjacency Matrix
• 7.5. An Adjacency List
• 7.6. Implementation
• 7.7. The Word Ladder Problem
• 7.8. Building the Word Ladder Graph
• 7.9. Implementing Breadth First Search
• 7.10. Breadth First Search Analysis
• 7.11. The Knight’s Tour Problem
• 7.12. Building the Knight’s Tour Graph
• 7.13. Implementing Knight’s Tour
• 7.14. Knight’s Tour Analysis
• 7.15. General Depth First Search
• 7.16. Depth First Search Analysis
• 7.17. Topological Sorting
• 7.18. Strongly Connected Components
• 7.19. Shortest Path Problems
• 7.20. Dijkstra’s Algorithm
• 7.21. Analysis of Dijkstra’s Algorithm
• 7.22. Prim’s Spanning Tree Algorithm
• 7.23. Summary
• 7.24. Key Terms
• 7.25. Discussion Questions
• 7.26. Programming Exercises

Acknowledgements ¶

We are very grateful to Franklin Beedle Publishers for allowing us to make this interactive textbook freely available. This online version is dedicated to the memory of our first editor, Jim Leisy, who wanted us to “change the world.”

Indices and tables ¶

• Module Index
• Search Page

• Docs »
• Lesson notes »
• Lesson 3 - Problem solving techniques
• Edit on GitHub

Lesson 3 - Problem solving techniques ¶

In the last lesson, we learned control flow statements such as if-else and for .

In this lesson, let us try to write a program for this problem:

“Given a day, the program should print if it is a weekday or weekend.”

First, we need to accept the input from the command line.:

Now, we need to find what type of day it is. The most straightforward way of doing it is checking the input against each day, like so:

Notice, how multiple if conditions can be combined using elif .

The program works but there are some issues with it. First, code looks a bit cluttered. Second, what if you need to write a similar program but with a bigger list? You can’t keep adding elif statements.

What we are trying to do here is to see if a given input (name of the day in this case) belongs to a group (such as “weekday” or “weekend”). Such problems can be solved by using lists. Since there are two types of days here for the purpose of this problem, let us define two lists.:

We can simply check if the input is in the first list or second list:

Notice how the second version is much smaller and much easier to read. In general, you should try to use types such as lists (and others provided by Python which we will see later) to solve problems.

Also note how we added else clause at the very end. Now our program gives a proper error message if the input is not valid. This is another thing you need to keep in mind when you accept inputs. Your code needs to be prepared to handle both valid and invalid inputs . In the case of latter, the program should provide a good error message.

Problem solving techniques ¶

• Divide the problem into smaller ones and solve them. Once smaller problems are solved, you just need to figure out how to combine them. This technique is called divide and conquer .
• Don’t try to write a perfect working program in the first go. Instead, write something that works and slowly improve it.
• Don’t try to write the program directly. First solve the problem for some example inputs and see how you are solving it (you can use paper and pencil for this). Then, try to convert the solution into a program.

Assignment ¶

Given a word, your program should print number of vowels in the word, like so:

You will be using most of the concepts you learned in this lesson and the previous ones to solve this problem, so go over the notes if required.