Data Structures and Algorithms in Python

A hands-on, structured learning path for mastering problem-solving, algorithms, and data structures in Python, focused on theoretical analysis and practical coding assessments.

📋 The 6-Step Problem Solving Framework

To tackle any technical interview or coding assessment problem, apply this systematic 6-step method:

  1. State the problem clearly: Identify the input format, output format, and constraints.
  2. Come up with example inputs & outputs: Cover simple, complex, and boundary edge cases (e.g., empty arrays, duplicates, negative numbers).
  3. Draft a correct solution in plain English: Describe the logic (even a naive brute-force method) before writing code.
  4. Implement the solution and test it: Code the algorithm and test it against all custom test cases, fixing bugs iteratively.
  5. Analyze the algorithm’s complexity: Determine the time and space complexity using Big O notation.
  6. Optimize the algorithm: Identify inefficiencies (e.g., changing from linear search $O(n)$ to binary search $O(\log n)$) and repeat steps 3 to 6.

📅 Progress & Lesson Summaries

Lesson 1: Binary Search & Complexity Analysis

  • Summary: Transitioning from naive linear search to binary search for sorted data sets.
  • Core Concepts:
    • Binary search algorithm design for descending arrays.
    • Handling duplicate elements using boundary checks to locate the first occurrence.
    • Creating a generic binary search engine that accepts a condition function closure.
    • Calculating worst-case time complexity $O(\log N)$ and space complexity $O(1)$.
  • Concept Links:
    • [[binary-search]]
    • [[complexity-analysis]]

📝 Practice Problems

Given an array of integers nums sorted in ascending order, find the starting and ending position of a given target value. If target is not found, return [-1, -1].

  • Strategy:
    • Use the generic binary search template to find the first occurrence (condition goes left if previous element is also target).
    • Use binary search to find the last occurrence (condition goes right if next element is also target).
    • Combine both results to return the range.