Python Programming Assignments Collection

This repository contains a comprehensive collection of Python solutions developed for a series of programming assignments. The projects cover fundamental algorithms, mathematical computations, data structure manipulation, and computational geometry.

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Project Structure

The repository is organized into three main folders, each representing a specific assignment with its own unique focus:

1. Assignment 1 - Fundamentals & Mathematical Logic

Basic Python syntax, conditional statements, and numerical series.

• Quadratic Equation Solver: Finding real roots of 2nd-degree polynomials.
• Approximating Euler's Number ($e$): Using Taylor series expansion with optimized factorial calculations.
• Large Factorial Analysis: Calculating the smallest integer whose factorial exceeds one million digits using logarithms.
• Geometric Patterns: Generating dynamic shapes using string repetition operators.

2. Assignment 2 - Data Structures & Optimization

Lists, loops, and algorithmic complexity.

• Fibonacci Sequences: Efficient generation and storage of the series in list format.
• Dynamic Data Handling: Managing real-time user input with custom termination flags.
• Pythagorean Triplets:
  • Standard Approach: Baseline $O(p^3)$ exhaustive search.
  • Optimized Approach: Mathematical reduction to $O(p^2)$ complexity.
• Advanced List Merging: Manual implementation of sorted merging and unique element filtering.

3. Assignment 3 - Functions, Recursion & Geometry

Modular programming, recursive functions, and linear algebra.

• Matrix Operations: Matrix-vector multiplication with dimension validation.
• Custom Data Processing: Manual implementation of sum, max, and index logic (exam-style).
• Signal Discretization: A custom implementation of the linspace function.
• Polygon Area Calculation:
  • Recursive Method: Decomposing polygons into triangles via recursion.
  • Iterative Method: Using loops for memory-efficient calculations.

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Requirements

1. Python 3.x
2. No external libraries required (uses Python Standard Library only).

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Academic Context & Author

These python scripts were developed as part of the coursework at the National and Kapodistrian University of Athens (NKUA).

• Author: Agapi Kallinikou
• Academic Year: 2022 - 2023