Improve Documentation and Directory Consistency

Arrays/README.md

@@ -4,10 +4,10 @@ This directory contains Python implementations of common array-based algorithms
 
 ## Contents
 
-- [Anagram Check (Sorted Solution)](Anagram_Check_Sorted_Sol.py): Checks if two strings are anagrams by comparing their sorted versions.
-- [Anagram Check (Manual Solution)](Anagram_Check_manual_Sol.py): Checks if two strings are anagrams using a hash table (dictionary) to count character frequencies.
-- [Array Find Missing Element (XOR Solution)](ArrayFindTheMissingElement_XOR_sol.py): Efficiently finds a missing element in a shuffled array using bitwise XOR.
-- [Array Find Missing Element (Brute Force Solution)](ArrayFindTheMissingElement_brute_force_sol.py): Finds a missing element by sorting both arrays and comparing them.
-- [Array Find Missing Element (Hash Table Solution)](ArrayFindTheMissingElement_hash_table_sol.py): Finds a missing element using a hash table (dictionary) to track element counts.
-- [Array Find Missing Element (Sum/Subtract Solution)](ArrayFindTheMissingElement_takingSumandSubtract_sol.py): Finds a missing element by calculating the difference between the sums of the two arrays.
+- [Anagram Check (Sorted Solution)](Anagram_Check_Sorted_Sol.py): Checks if two strings are anagrams by comparing their sorted versions. $O(n \log n)$
+- [Anagram Check (Manual Solution)](Anagram_Check_manual_Sol.py): Checks if two strings are anagrams using a hash table (dictionary) to count character frequencies. $O(n)$
+- [Array Find Missing Element (XOR Solution)](ArrayFindTheMissingElement_XOR_sol.py): Efficiently finds a missing element in a shuffled array using bitwise XOR. $O(n)$
+- [Array Find Missing Element (Brute Force Solution)](ArrayFindTheMissingElement_brute_force_sol.py): Finds a missing element by sorting both arrays and comparing them. $O(n \log n)$
+- [Array Find Missing Element (Hash Table Solution)](ArrayFindTheMissingElement_hash_table_sol.py): Finds a missing element using a hash table (dictionary) to track element counts. $O(n)$
+- [Array Find Missing Element (Sum/Subtract Solution)](ArrayFindTheMissingElement_takingSumandSubtract_sol.py): Finds a missing element by calculating the difference between the sums of the two arrays. $O(n)$
 - [Array Pair Sum Solution](ArrayPairSumSol.py): Finds all unique pairs in an array that sum up to a specific value $k$ using a set for $O(n)$ complexity.

deque/README.md → Deque/README.md

@@ -5,3 +5,5 @@ This directory contains Python implementations of the Deque (Double-Ended Queue)
 ## Contents
 
 - [Deque Implementation](DequeImple.py): Basic implementation of a Deque using a Python list. Includes operations like `addFront`, `addRear`, `removeFront`, `removeRear`, `isEmpty`, and `size`.
+  - `addFront`, `removeFront`: $O(1)$
+  - `addRear`, `removeRear`: $O(n)$

Error-debug/README.md → ErrorHandling/README.md

@@ -1,4 +1,4 @@
-# Error and Debugging
+# Error Handling
 
 This directory contains examples of error handling and debugging techniques in Python.
 

Queues/README.md

@@ -5,4 +5,6 @@ This directory contains Python implementations of the Queue data structure.
 ## Contents
 
 - [Queue Implementation](QueueImple.py): Basic implementation of a FIFO (First-In-First-Out) queue using a Python list. Includes `enqueue`, `dequeue`, `isEmpty`, and `size` methods.
-- [Queue with Two Stacks](QueueWith2StacksImple.py): Implements a queue using two stacks (represented by Python lists) to achieve FIFO behavior.
+  - `enqueue`: $O(n)$
+  - `dequeue`: $O(1)$
+- [Queue with Two Stacks](QueueWith2StacksImple.py): Implements a queue using two stacks (represented by Python lists) to achieve FIFO behavior. $O(1)$ amortized for both operations.

README.md

@@ -35,20 +35,20 @@ See [CONTRIBUTING.md](CONTRIBUTING.md) for more details.
 
 ## 📖 Table of Contents
 
-- [Getting Started](#getting-started)
-- [Project Structure](#project-structure)
-- [Data Structures](#data-structures)
-  - [Arrays](#arrays)
-  - [Linked Lists](#linked-lists)
-  - [Stacks](#stacks)
-  - [Queues](#queues)
-  - [Deque](#deque)
-  - [Trees](#trees)
-- [Algorithms](#algorithms)
-  - [Sorting](#sorting)
-  - [Recursion & Dynamic Programming](#recursion--dynamic-programming)
-  - [Graph Algorithms](#graph-algorithms)
-- [Error Handling & Debugging](#error-handling--debugging)
+- [Getting Started](#-getting-started)
+- [Project Structure](#-project-structure)
+- [Data Structures](#-data-structures)
+  - [Arrays](#arrays-)
+  - [Linked Lists](#linked-lists-)
+  - [Stacks](#stacks-)
+  - [Queues](#queues-)
+  - [Deque](#deque-)
+  - [Trees](#trees-)
+- [Algorithms](#-algorithms)
+  - [Sorting](#sorting-)
+  - [Recursion & Dynamic Programming](#recursion--dynamic-programming-)
+  - [Graph Algorithms](#graph-algorithms-)
+- [Error Handling & Debugging](#-error-handling--debugging)
 - [Usage](#usage)
 - [Quick Reference](#quick-reference)
 - [License](#license)
@@ -80,15 +80,15 @@ python3 Sorting/BubbleSortImple.py
 ```
 .
 ├── Arrays/              # 🔤 Array-based problems and algorithms
-├── Error-debug/         # ⚠️ Error handling and debugging examples
+├── ErrorHandling/       # ⚠️ Error handling and debugging examples
 ├── GraphAlgorithms/     # 🗺️ Graph traversal (BFS, DFS) and pathfinding
 ├── LinkedLists/         # 🔗 Singly and Doubly Linked Lists
 ├── Queues/              # 📦 Queue implementations (FIFO)
 ├── Recursion/           # 🔀 Recursive problems and Dynamic Programming
 ├── Sorting/             # 📊 Common sorting algorithms
 ├── Stacks/              # 📚 Stack implementations and applications
 ├── Trees/               # 🌳 Binary Trees, BSTs, Heaps, and Traversals
-├── deque/               # 🔄 Double-ended queue
+├── Deque/               # 🔄 Double-ended queue
 ├── CONTRIBUTING.md      # 🤝 Contribution guidelines
 ├── LICENSE              # 📄 MIT License
 └── README.md            # 📖 This file
@@ -123,7 +123,7 @@ FIFO (First-In-First-Out) data structures.
 
 ### Deque 🔄
 Double-ended queue operations.
-- [Deque Implementation](deque/DequeImple.py): Operations at both ends
+- [Deque Implementation](Deque/DequeImple.py): Operations at both ends
 
 ### Trees 🌳
 Hierarchical data structures.
@@ -168,7 +168,7 @@ Algorithms for graph traversal and pathfinding.
 
 ## ⚠️ Error Handling & Debugging
 
-- [Error and Exceptions](Error-debug/ErrorExceptions.py): Demonstrates `try`, `except`, `else`, and `finally` blocks for robust error handling.
+- [Error and Exceptions](ErrorHandling/ErrorExceptions.py): Demonstrates `try`, `except`, `else`, and `finally` blocks for robust error handling.
 
 ---
 

Recursion/README.md

@@ -5,17 +5,17 @@ This directory contains Python implementations of problems solved using recursio
 ## Contents
 
 ### Fibonacci Sequence
-- [Fibonacci (Iterative)](FibonacciSeqIterative.py): Iterative implementation of the Fibonacci sequence.
-- [Fibonacci (Recursive)](FibonacciSeqRecursion.py): Simple recursive implementation of the Fibonacci sequence.
-- [Fibonacci (Dynamic Programming)](FibonacciSeqDynamic.py): Optimized Fibonacci sequence using memoization.
+- [Fibonacci (Iterative)](FibonacciSeqIterative.py): Iterative implementation of the Fibonacci sequence. $O(n)$
+- [Fibonacci (Recursive)](FibonacciSeqRecursion.py): Simple recursive implementation of the Fibonacci sequence. $O(2^n)$
+- [Fibonacci (Dynamic Programming)](FibonacciSeqDynamic.py): Optimized Fibonacci sequence using memoization. $O(n)$
 
 ### Coin Change Problem
 - [Coin Change (Recursive)](CoinChangeProblemRecursion.py): Basic recursive solution to find the minimum number of coins for change.
 - [Coin Change (Dynamic Programming)](CoinChangeProblemDynamic.py): Optimized solution to the coin change problem using dynamic programming.
 
 ### Other Recursive Problems
-- [Cumulative Sum](RecursionCumulativeSum.py): Computes the cumulative sum from 0 to $n$ recursively.
-- [Reverse a String](RecursionReverseStr.py): Reverses a string using recursive calls.
-- [String Permutations](RecursionStrPermutation.py): Generates all possible permutations of a given string.
-- [Sum of Digits](RecursionSumOfDigits.py): Calculates the sum of all individual digits in an integer recursively.
+- [Cumulative Sum](RecursionCumulativeSum.py): Computes the cumulative sum from 0 to $n$ recursively. $O(n)$
+- [Reverse a String](RecursionReverseStr.py): Reverses a string using recursive calls. $O(n)$
+- [String Permutations](RecursionStrPermutation.py): Generates all possible permutations of a given string. $O(n!)$
+- [Sum of Digits](RecursionSumOfDigits.py): Calculates the sum of all individual digits in an integer recursively. $O(\log_{10} n)$
 - [Word Split](RecursionWordSplit.py): Determines if a string can be split into words from a given list.

Sorting/README.md

@@ -5,8 +5,8 @@ This directory contains Python implementations of various sorting algorithms wit
 ## Contents
 
 - [Bubble Sort](BubbleSortImple.py): Implementation of Bubble Sort with $O(n^2)$ complexity.
-- [Selection Sort](SelectionSortImple.py): Implementation of Selection Sort, improving on Bubble Sort by making only one exchange per pass.
-- [Insertion Sort](InsertionSortImple.py): Implementation of Insertion Sort, maintaining a sorted sublist.
-- [Shell Sort](ShellSortImple.py): Implementation of Shell Sort (diminishing increment sort), improving on Insertion Sort.
+- [Selection Sort](SelectionSortImple.py): Implementation of Selection Sort, improving on Bubble Sort by making only one exchange per pass. $O(n^2)$
+- [Insertion Sort](InsertionSortImple.py): Implementation of Insertion Sort, maintaining a sorted sublist. $O(n^2)$
+- [Shell Sort](ShellSortImple.py): Implementation of Shell Sort (diminishing increment sort), improving on Insertion Sort. Worst-case $O(n^2)$.
 - [Merge Sort](MergeSortImple.py): A recursive "divide and conquer" algorithm with $O(n \log n)$ complexity.
-- [Quick Sort](QuickSortImple.py): Implementation of Quick Sort (partition exchange sort), using divide and conquer in-place.
+- [Quick Sort](QuickSortImple.py): Implementation of Quick Sort (partition exchange sort), using divide and conquer in-place. $O(n \log n)$ average.