Improve Documentation Consistency and Directory Naming

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.
-- [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.
+- [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. $O(n)$

deque/README.md → Deque/README.md

@@ -4,4 +4,4 @@ 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`.
+- [Deque Implementation](DequeImple.py): Basic implementation of a Deque using a Python list. Includes operations like `addFront`, `addRear`, `removeFront`, `removeRear`, `isEmpty`, and `size`. Front operations are $O(1)$, while rear operations are $O(n)$ due to list shifting.

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.
 

GraphAlgorithms/README.md

@@ -4,9 +4,9 @@ This directory contains Python implementations of common graph-based algorithms
 
 ## Contents
 
-- [Adjacency List Implementation](AdjacencyListGraphImple.py): Implements the Graph Abstract Data Type (ADT) using an adjacency list (dictionaries in Python). Includes `Vertex` and `Graph` classes.
-- [Breadth First Search (BFS)](BFS.py): Implements BFS to solve the Word Ladder problem, finding the shortest transformation path between words.
-- [General Depth First Search (DFS)](DFSGeneral.py): Provides a general implementation of DFS, including discovery and finish times for vertices.
-- [DFS - Knight's Tour Problem](DFSImpleTheKnightsTourProblem.py): Another implementation of DFS specifically tailored to the Knight's Tour puzzle.
-- [The Knight's Tour Problem](TheKnightsTourProblem.py): Focuses on generating the knight's move graph and solving the tour using DFS and backtracking.
-- [Word Ladder Problem](WordLadderProblem.py): Specifically focuses on building the word ladder graph where edges connect words that differ by only one letter.
+- [Adjacency List Implementation](AdjacencyListGraphImple.py): Implements the Graph Abstract Data Type (ADT) using an adjacency list (dictionaries in Python). Includes `Vertex` and `Graph` classes. $O(V + E)$
+- [Breadth First Search (BFS)](BFS.py): Implements BFS to solve the Word Ladder problem, finding the shortest transformation path between words. $O(V + E)$
+- [General Depth First Search (DFS)](DFSGeneral.py): Provides a general implementation of DFS, including discovery and finish times for vertices. $O(V + E)$
+- [DFS - Knight's Tour Problem](DFSImpleTheKnightsTourProblem.py): Another implementation of DFS specifically tailored to the Knight's Tour puzzle. $O(V + E)$
+- [The Knight's Tour Problem](TheKnightsTourProblem.py): Focuses on generating the knight's move graph and solving the tour using DFS and backtracking. $O(V + E)$
+- [Word Ladder Problem](WordLadderProblem.py): Specifically focuses on building the word ladder graph where edges connect words that differ by only one letter. $O(V + E)$

LinkedLists/README.md

@@ -4,8 +4,8 @@ This directory contains Python implementations of various types of linked lists
 
 ## Contents
 
-- [Singly Linked List Implementation](SingleLinkedListImple.py): Basic implementation of a singly linked list node and basic linkage.
-- [Doubly Linked List Implementation](DoublyLinkedListImple.py): Basic implementation of a doubly linked list node with `prev` and `next` pointers.
-- [Singly Linked List Cycle Check](SinglyLinkedListCycleCheckImple.py): Implements Floyd's Cycle-Finding Algorithm (two pointers) to detect cycles in a linked list.
-- [Linked List Reversal](LinkedListReversal.py): Reverses a singly linked list in-place in $O(n)$ time.
-- [Nth to Last Node](LinkedListNthToLastNode.py): Finds the $n$-th to last node in a singly linked list using two pointers.
+- [Singly Linked List Implementation](SingleLinkedListImple.py): Basic implementation of a singly linked list node and basic linkage. $O(1)$ for basic operations.
+- [Doubly Linked List Implementation](DoublyLinkedListImple.py): Basic implementation of a doubly linked list node with `prev` and `next` pointers. $O(1)$ for basic operations.
+- [Singly Linked List Cycle Check](SinglyLinkedListCycleCheckImple.py): Implements Floyd's Cycle-Finding Algorithm (two pointers) to detect cycles in a linked list. $O(n)$
+- [Linked List Reversal](LinkedListReversal.py): Reverses a singly linked list in-place. $O(n)$
+- [Nth to Last Node](LinkedListNthToLastNode.py): Finds the $n$-th to last node in a singly linked list using two pointers. $O(n)$

Queues/README.md

@@ -4,5 +4,5 @@ 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.
+- [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. $O(1)$ for enqueue, $O(n)$ for dequeue with Python list.
+- [Queue with Two Stacks](QueueWith2StacksImple.py): Implements a queue using two stacks (represented by Python lists) to achieve FIFO behavior. $O(1)$ amortized for enqueue and dequeue.

README.md

@@ -36,22 +36,22 @@ See [CONTRIBUTING.md](CONTRIBUTING.md) for more details.
 ## 📖 Table of Contents
 
 - [Getting Started](#getting-started)
-- [Project Structure](#project-structure)
+- [Project Structure](#project-structure-)
 - [Data Structures](#data-structures)
-  - [Arrays](#arrays)
-  - [Linked Lists](#linked-lists)
-  - [Stacks](#stacks)
-  - [Queues](#queues)
-  - [Deque](#deque)
-  - [Trees](#trees)
+  - [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)
+  - [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
+├── Deque/               # 🔄 Double-ended queue
+├── 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
 ├── 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.
+- [Coin Change (Recursive)](CoinChangeProblemRecursion.py): Basic recursive solution to find the minimum number of coins for change. $O(2^n)$
+- [Coin Change (Dynamic Programming)](CoinChangeProblemDynamic.py): Optimized solution to the coin change problem using dynamic programming. $O(n \cdot m)$ where $n$ is the amount and $m$ is the number of coins.
 
 ### 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.
-- [Word Split](RecursionWordSplit.py): Determines if a string can be split into words from a given list.
+- [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. $O(n \cdot n!)$
+- [Sum of Digits](RecursionSumOfDigits.py): Calculates the sum of all individual digits in an integer recursively. $O(d)$ where $d$ is the number of digits.
+- [Word Split](RecursionWordSplit.py): Determines if a string can be split into words from a given list. $O(n^2)$

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.
-- [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.
+- [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. $O(n \log n)$ average, $O(n^2)$ worst-case.
+- [Merge Sort](MergeSortImple.py): A recursive "divide and conquer" algorithm. $O(n \log n)$
+- [Quick Sort](QuickSortImple.py): Implementation of Quick Sort (partition exchange sort), using divide and conquer in-place. $O(n \log n)$ average, $O(n^2)$ worst-case.

Stacks/README.md

@@ -4,5 +4,5 @@ This directory contains Python implementations of the Stack data structure and i
 
 ## Contents
 
-- [Stack Implementation](StackImple.py): Basic implementation of a LIFO (Last-In-First-Out) stack using a Python list. Includes `push`, `pop`, `peek`, `isEmpty`, and `size` methods.
-- [Balanced Parentheses Check](BalanceParenthlessCheckImple.py): Uses a stack to check if a string of opening and closing parentheses (round, square, and curly) is balanced.
+- [Stack Implementation](StackImple.py): Basic implementation of a LIFO (Last-In-First-Out) stack using a Python list. Includes `push`, `pop`, `peek`, `isEmpty`, and `size` methods. $O(1)$
+- [Balanced Parentheses Check](BalanceParenthlessCheckImple.py): Uses a stack to check if a string of opening and closing parentheses (round, square, and curly) is balanced. $O(n)$

Trees/README.md

@@ -5,19 +5,19 @@ This directory contains Python implementations of various tree-based data struct
 ## Contents
 
 ### Binary Search Trees (BST)
-- [Binary Search Tree Implementation](BinarySearchTreesImple.py): A comprehensive implementation of a BST with `TreeNode` and `BinarySearchTree` classes, including insertion, deletion, and search.
-- [Validate BST (Solution 1)](BinarySearchTreeCheckImpleSol1.py): Validates a BST by performing an in-order traversal and checking if the resulting values are sorted.
-- [Validate BST (Solution 2)](BinarySearchTreeCheckImpleSol2.py): Validates a BST by keeping track of the minimum and maximum allowable values for each node.
-- [Trim a BST](TrimBinarySearchTreeImple.py): Trims a BST so that all node values fall within a specified range $[min, max]$.
+- [Binary Search Tree Implementation](BinarySearchTreesImple.py): A comprehensive implementation of a BST with `TreeNode` and `BinarySearchTree` classes, including insertion, deletion, and search. $O(\log n)$ average, $O(n)$ worst case.
+- [Validate BST (Solution 1)](BinarySearchTreeCheckImpleSol1.py): Validates a BST by performing an in-order traversal and checking if the resulting values are sorted. $O(n)$
+- [Validate BST (Solution 2)](BinarySearchTreeCheckImpleSol2.py): Validates a BST by keeping track of the minimum and maximum allowable values for each node. $O(n)$
+- [Trim a BST](TrimBinarySearchTreeImple.py): Trims a BST so that all node values fall within a specified range $[min, max]$. $O(n)$
 
 ### Search Algorithms
-- [Binary Search (Iterative)](BinarySearchImple.py): Iterative implementation of the binary search algorithm on a sorted list.
-- [Binary Search (Recursive)](BinarySearchRecursiveImple.py): Recursive implementation of the binary search algorithm.
+- [Binary Search (Iterative)](BinarySearchImple.py): Iterative implementation of the binary search algorithm on a sorted list. $O(\log n)$
+- [Binary Search (Recursive)](BinarySearchRecursiveImple.py): Recursive implementation of the binary search algorithm. $O(\log n)$
 
 ### Heaps
-- [Binary Heap Implementation](BinaryHeapImple.py): Implements a min-heap using a recursive approach, including `insert`, `delMin`, and `buildHeap`.
+- [Binary Heap Implementation](BinaryHeapImple.py): Implements a min-heap using a recursive approach, including `insert`, `delMin`, and `buildHeap`. $O(\log n)$ for insert/delMin, $O(n)$ for buildHeap.
 
 ### Tree Representations & Traversals
-- [Nodes and References Representation](TreeRepresentationWithNodesReferences.py): A simple implementation of a binary tree using a class-based nodes and references approach.
-- [List of Lists Representation](buildTreeTest.py): Demonstrates building and manipulating a tree using a "list of lists" approach.
-- [Tree Level Order Print](TreeLevelOrderPrintImple.py): Prints a binary tree in level order (breadth-first) using a queue, with each level on a new line.
+- [Nodes and References Representation](TreeRepresentationWithNodesReferences.py): A simple implementation of a binary tree using a class-based nodes and references approach. $O(1)$ for basic linkage.
+- [List of Lists Representation](buildTreeTest.py): Demonstrates building and manipulating a tree using a "list of lists" approach. $O(1)$ for basic linkage.
+- [Tree Level Order Print](TreeLevelOrderPrintImple.py): Prints a binary tree in level order (breadth-first) using a queue, with each level on a new line. $O(n)$