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0x02. Minimum Operations ⚙️

Python Algorithm

📖 Project Overview

This project tackles the Minimum Operations problem, where the goal is to determine the smallest number of "Copy All" and "Paste" operations required to reach exactly n characters in a text file that starts with a single character 'H'. This problem provides a great opportunity to apply dynamic programming, greedy algorithms, and prime factorization concepts for optimization.

🎯 Learning Objectives

  • 🧩 Dynamic Programming: Learn to solve complex problems by breaking them into simpler subproblems.
  • 🔍 Prime Factorization: Utilize prime factorization to reduce the problem complexity.
  • ⚙️ Greedy & Optimization Techniques: Find the most efficient solution by making optimal choices at each step.

🛠️ Technologies Used

  • Python Python 3.4.3 on Ubuntu 20.04 LTS
  • PEP 8 (v1.7.x) for code style and formatting

📋 Requirements

  • Files should be interpreted on Ubuntu 20.04 LTS using python3 (version 3.4.3).
  • Each file should start with #!/usr/bin/python3.
  • All code should conform to PEP 8 standards.
  • All files must be executable.
  • Include comprehensive documentation for all modules, classes, and functions.

🚀 Installation and Usage

  1. Clone the Repository:

    git clone https://github.com/Alogyn/alx-interview
cd alx-interview/0x02-minimum_operations

  2. Run the Program:

    ./0-main.py

📝 Task: Minimum Operations ⚙️

Objective

Write a function minOperations(n) to compute the minimum number of operations needed to end up with exactly n characters in a file containing a single character H.

Function Prototype

def minOperations(n: int) -> int

Returns

  • The integer count of operations if n is possible, otherwise returns 0.

Example

# Example usage:
n = 9
# H => Copy All => Paste => HH => Paste => HHH => Copy All => Paste => HHHHHH => Paste => HHHHHHHHH
# Number of operations: 6

print(minOperations(9))  # Output: 6

Example Output

$ ./0-main.py
Min # of operations to reach 4 characters: 4
Min # of operations to reach 12 characters: 7

🧠 Key Concepts and Techniques

  • Dynamic Programming: Helps in building the solution by solving overlapping subproblems.
  • Prime Factorization: Reduces the solution to the sum of the prime factors of n.
  • Greedy Algorithms: Choose optimal steps for minimal operations.

🌐 Resources

⚖️ License

This project is part of the ALX Software Engineering Program. © 2024 ALX. All rights reserved.