In this comprehensive guide, we delve into the world of Dynamic Programming with C++. Learn the core principles of Dynamic Programming, explore various algorithmic examples, and understand performance differences through detailed code comparisons. Perfect for developers looking to optimize their coding skills and enhance algorithm efficiency.

Competitive Programming Primer: 100 Preparatory Challenges

Welcome to our Competitive Programming Primer series!

In this comprehensive preparatory course, we’re excited to present 100 carefully curated programming challenges designed to sharpen your skills and prepare you for the intense world of competitive programming.

Competitive programming is not just about coding—it’s about problem-solving, efficiency, and thinking outside the box. These skills are invaluable, whether you’re aiming for:

• Success in programming competitions
• Excelling in technical interviews
• Enhancing your overall software development prowess

Our primer is structured to gradually build your competence, starting from fundamental concepts and progressing to more advanced techniques commonly encountered in competitive programming.

How It Works

Every Friday, we’ll post a set of challenges here. These problems are crafted to:

1. Reinforce essential algorithms and data structures
2. Improve your time management and problem-solving speed
3. Expose you to a variety of problem types you’ll face in real competitions

But we don’t stop there!

The following Monday, we’ll release detailed solutions for each problem in both Python and C++ 20. This dual-language approach serves to:

• Cater to different language preferences
• Showcase language-specific optimizations
• Provide a comparative view of problem-solving approaches

What to Expect

Each problem set will include:

• Clear problem statements
• Input/output specifications
• Constraints to consider
• Hints for those who need a nudge in the right direction

Our solutions will feature:

• Well-commented code
• Explanations of the underlying logic
• Time and space complexity analysis
• Tips for optimization

Are you ready to embark on this journey to competitive programming excellence? Dive into our first set of challenges below, and remember—consistent practice is key to mastering these skills.

Happy coding, and may your algorithms always be efficient! 🖥️💪

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First Week’s Challenges

1. Widget Batch Sorting

   A factory produces widgets in batches. Each batch is assigned a number between 2000 and 3200. Batches divisible by 7 are sent to Warehouse A, unless they’re also divisible by 5, in which case they go to Warehouse B. Write a program to list all batch numbers sent to Warehouse A.

   Input: None Output: A comma-separated list of integers

   Example Output:

   2002,2009,2016,2023,2037,2044,2051,2058,2072,2079,2086,2093,2107,2114,2121,2128,2142,2149,2156,2163,2177,2184,2191,2198
   

   Hint: Use a list to store the batch numbers and the range() function for iteration. The join() method can be used to create the comma-separated output string.

2. Bacterial Growth Calculator

   A microbiologist is studying bacterial growth. The population doubles every generation. Given the number of generations, calculate the final population if starting with a single bacterium.

   Input: An integer $n$ representing the number of generations Output: An integer representing the final population

   Example: Input: 8 Output: 256

   Hint: This is effectively a factorial calculation. Implement a recursive function. Use int() to convert input to an integer.

3. Student Square Number Reference

   A teacher wants to create a quick reference sheet for square numbers. For a given number of students $n$, create a dictionary where the keys are student numbers (1 to $n$) and the values are their numbers squared.

   Input: An integer $n$ representing the number of students Output: A dictionary where keys are integers from 1 to $n$, and values are their squares

   Example: Input: 5 Output: {1: 1, 2: 4, 3: 9, 4: 16, 5: 25}

   Hint: Use a dict() to create the dictionary. A for loop with range() can generate the student number and squared value pairs.

4. Daily Sales Data Analyzer

   A grocery store manager needs to analyze sales data. Write a program that takes comma-separated prices of items sold in a day, and generates both a list and a tuple of these prices.

   Input: A string of comma-separated floating-point numbers Output: A list and a tuple containing the input numbers

   Example: Input: 23.5,18.9,31.2,15.5,42.8 Output:

   ['23.5', '18.9', '31.2', '15.5', '42.8']
   ('23.5', '18.9', '31.2', '15.5', '42.8')
   

   Hint: Use string.split() to parse the input. Convert the result directly to a list and then to a tuple.

5. Chatbot Text Processor

   Design a simple text processing class for a chatbot. It should have methods to get input from a user and to respond with the input converted to uppercase.

   Input: A string from the user Output: The input string converted to uppercase

   Example: Input: Hello, how are you? Output: HELLO, HOW ARE YOU?

   Hint: Use raw_input() (or input() in Python 3) for getting input. Implement __init__ method to initialize an empty string attribute.

6. Water Tank Volume Calculator

   An engineer is designing a series of water tanks. The volume $Q$ of each cylindrical tank is given by:

   \[Q = \sqrt{\frac{2 * C * D}{H}}\]

   where $C = 50$ (a flow coefficient) and $H = 30$ (the height of each tank). $D$ is the diameter, which varies for each tank. Write a program to calculate $Q$ for a series of diameters input as a comma-separated sequence.

   Input: A string of comma-separated integers representing diameters Output: A comma-separated string of floating-point numbers rounded to two decimal places

   Example: Input: 100,150,180 Output: 18.11,22.16,24.28

   Hint: Use math.sqrt() for square root. Parse input into a list and use list comprehension to calculate volumes.

7. Simple Voice Recognition

   Create a simple voice recognition program that prints “Command Accepted” if it hears “Yes” in any capitalization, otherwise it prints “Command Declined”.

   Input: A string representing the voice input Output: Either “Command Accepted” or “Command Declined”

   Example 1: Input: yes Output: Command Accepted

   Example 2: Input: No Output: Command Declined

   Hint: Use string methods like lower() or upper() to standardize the input before comparison.

8. ASCII to UTF-8 Converter

   A data analyst needs to convert ASCII-encoded data from an old system into UTF-8 for modern analysis. Write a program to perform this conversion on a given input string.

   Input: An ASCII-encoded string Output: The same string encoded in UTF-8

   Example: Input: Hello, world! Output: Hello, world! (but encoded in UTF-8)

   Hint: In Python 2, use unicode() function with ‘utf-8’ encoding. In Python 3, strings are already unicode.

9. Savings Growth Calculator

   An economist is modeling savings growth. The model is:

   \[savings(n)=savings(n−1)+100savings(n) = savings(n-1) + 100savings(n)=savings(n−1)+100\]

   where $n$ is the number of months and $savings(0) = 1000$. Write a program to calculate savings for a given number of months.

   Input: An integer $n$ representing the number of months Output: The total savings after $n$ months

   Example: Input: 5 Output: 1500

   Hint: Implement a recursive function. Use a base case for $n=0$. Convert input to integer using int().

10. Library Book Checkout System

    A local library is implementing a digital system to track book checkouts. Each book has a unique 5-digit ID number. Books with ID numbers divisible by 3 are placed on the “Featured” shelf. However, if the ID is also divisible by 4, it goes to the “Classics” section instead. Create a program to help librarians quickly determine where to place a book.

    Input: An integer $n$ representing the book ID (10000 ≤ $n$ ≤ 99999) Output: A string: “Featured”, “Classics”, or “Regular”

    Examples: Input: 10002 Output: Regular

    Input: 10353 Output: Featured

    Input: 10512 Output: Classics

    Hint: Use the modulo operator % to check divisibility. Implement conditional statements to determine the correct category based on the ID number.

    Extra Challenge: Instead of a single ID, allow the librarian to input a comma-separated list of book IDs and output the category for each book in the same order.

    Example for Extra Challenge: Input: 10002,10353,10512 Output: Regular,Featured,Classics

Solutions will be posted on Monday. Stay tuned!