Algorithm Practice Collection

A collection of Python implementations for common algorithmic problems and mathematical functions.

Implemented Algorithms

Algorithm Practice

Located in algorithm_practice/

1. Kadane's Algorithm (kadane_algorithm.py)

   • Finds the contiguous subarray with the maximum sum
   • Returns both the maximum sum and the start/end indices
   • Time Complexity: O(n)

2. Longest Common Prefix (longest_common_prefix.py)

   • Finds the longest common prefix shared by all strings in an array
   • Returns empty string if no common prefix exists
   • Time Complexity: O(S) where S is the sum of all characters in all strings

3. First Repeated Character (repetitive_first_character.py)

   • Finds the first repeating character in a string
   • Returns None if no character repeats
   • Time Complexity: O(n²)

4. Second Largest Element (second_largest_element.py)

   • Finds the second largest element in an array of integers
   • Handles edge cases like empty arrays or arrays with less than 2 elements
   • Time Complexity: O(n)

5. Longest Substring Without Repeat (long_subs_without_repeat.py)

   • Finds the length of the longest substring without repeating characters
   • Returns the substring and its length
   • Time Complexity: O(n)

6. Reverse String (reverse_string.py)

   • Reverses the order of words in a given string
   • Preserves word order while reversing the overall string
   • Time Complexity: O(n)

Mathematical Functions

Located in math_functions/

1. Fibonacci Sequence (fibonacci.py)

   • Implements the Fibonacci sequence generator
   • F(n) = F(n-1) + F(n-2), where F(0)=0, F(1)=1
   • Time Complexity: O(n)

2. Primality Test (primality_test.py)

   • Checks if a given number is prime
   • Uses optimized square root method
   • Time Complexity: O(√n)

3. Euclidean Algorithm (euclidean_algorithm.py)

   • Finds the Greatest Common Divisor (GCD) of two numbers
   • Uses the Euclidean algorithm method
   • Time Complexity: O(log min(a,b))

Object-Oriented Programming Practice

Located in oop_practice/

1. Exercise (exercise.dart)
   • Contains Dart implementations of OOP concepts
   • Includes various class and object examples

Usage

Each algorithm is implemented in its own file. To use any algorithm:

1. Import the specific file
2. Call the corresponding function with appropriate parameters

Requirements

• Python 3.x (for Python files)
• Dart SDK (for Dart files)

Testing

Each file includes example test cases and print statements demonstrating usage.

Project Structure

python_function/
├── algorithm_practice/
│   ├── kadane_algorithm.py
│   ├── longest_common_prefix.py
│   ├── repetitive_first_character.py
│   ├── second_largest_element.py
│   ├── long_subs_without_repeat.py
│   └── reverse_string.py
├── math_functions/
│   ├── fibonacci.py
│   ├── primality_test.py
│   └── euclidean_algorithm.py
└── oop_practice/
    └── exercise.dart