ppant · ppant · May 26, 2026
diff --git a/Arrays/Anagram_Check_manual_Sol.py → Arrays/AnagramCheckManualSol.py b/Arrays/Anagram_Check_manual_Sol.py → Arrays/AnagramCheckManualSol.py
diff --git a/Arrays/Anagram_Check_Sorted_Sol.py → Arrays/AnagramCheckSortedSol.py b/Arrays/Anagram_Check_Sorted_Sol.py → Arrays/AnagramCheckSortedSol.py
diff --git a/...yFindTheMissingElement_brute_force_sol.py → ...rrayFindTheMissingElementBruteForceSol.py b/...yFindTheMissingElement_brute_force_sol.py → ...rrayFindTheMissingElementBruteForceSol.py
diff --git a/...ayFindTheMissingElement_hash_table_sol.py → ...ArrayFindTheMissingElementHashTableSol.py b/...ayFindTheMissingElement_hash_table_sol.py → ...ArrayFindTheMissingElementHashTableSol.py
diff --git a/...issingElement_takingSumandSubtract_sol.py → Arrays/ArrayFindTheMissingElementSumSol.py b/...issingElement_takingSumandSubtract_sol.py → Arrays/ArrayFindTheMissingElementSumSol.py
diff --git a/Arrays/ArrayFindTheMissingElement_XOR_sol.py → Arrays/ArrayFindTheMissingElementXORSol.py b/Arrays/ArrayFindTheMissingElement_XOR_sol.py → Arrays/ArrayFindTheMissingElementXORSol.py
diff --git a/Arrays/README.md b/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)](AnagramCheckSortedSol.py): Checks if two strings are anagrams by comparing their sorted versions ($O(n \log n)$).
+- [Anagram Check (Manual Solution)](AnagramCheckManualSol.py): Checks if two strings are anagrams using a hash table (dictionary) to count character frequencies ($O(n)$).
+- [Array Find Missing Element (XOR Solution)](ArrayFindTheMissingElementXORSol.py): Efficiently finds a missing element in a shuffled array using bitwise XOR ($O(n)$ time, $O(1)$ space).
+- [Array Find Missing Element (Brute Force Solution)](ArrayFindTheMissingElementBruteForceSol.py): Finds a missing element by sorting both arrays and comparing them ($O(n \log n)$).
+- [Array Find Missing Element (Hash Table Solution)](ArrayFindTheMissingElementHashTableSol.py): Finds a missing element using a hash table (dictionary) to track element counts ($O(n)$).
+- [Array Find Missing Element (Sum/Subtract Solution)](ArrayFindTheMissingElementSumSol.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.
diff --git a/deque/DequeImple.py → Deque/DequeImple.py b/deque/DequeImple.py → Deque/DequeImple.py
diff --git a/deque/README.md → Deque/README.md b/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` ($O(1)$), `addRear` ($O(n)$), `removeFront` ($O(1)$), `removeRear` ($O(n)$), `isEmpty` ($O(1)$), and `size` ($O(1)$).
diff --git a/Error-debug/ErrorExceptions.py → ErrorHandling/ErrorExceptions.py b/Error-debug/ErrorExceptions.py → ErrorHandling/ErrorExceptions.py
diff --git a/Error-debug/README.md → ErrorHandling/README.md b/Error-debug/README.md → ErrorHandling/README.md
@@ -1,4 +1,4 @@
-# Error and Debugging
+# Error Handling and Debugging
 
 This directory contains examples of error handling and debugging techniques in Python.
 

diff --git a/GraphAlgorithms/README.md b/GraphAlgorithms/README.md
@@ -5,8 +5,8 @@ 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.
+- [Breadth First Search (BFS)](BFS.py): Implements BFS to solve the Word Ladder problem ($O(V+E)$).
+- [General Depth First Search (DFS)](DFSGeneral.py): Provides a general implementation of DFS ($O(V+E)$).
+- [DFS - Knight's Tour Problem](DFSImpleTheKnightsTourProblem.py): Another implementation of DFS specifically tailored to the Knight's Tour puzzle ($O(k^N)$).
 - [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.
diff --git a/LinkedLists/README.md b/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.
+- [Singly Linked List Implementation](SingleLinkedListImple.py): Basic implementation of a singly linked list node and basic linkage ($O(1)$ for basic insertion/deletion).
+- [Doubly Linked List Implementation](DoublyLinkedListImple.py): Basic implementation of a doubly linked list node with `prev` and `next` pointers ($O(1)$).
+- [Singly Linked List Cycle Check](SinglyLinkedListCycleCheckImple.py): Implements Floyd's Cycle-Finding Algorithm (two pointers) to detect cycles ($O(n)$).
 - [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.
+- [Nth to Last Node](LinkedListNthToLastNode.py): Finds the $n$-th to last node in a singly linked list using two pointers ($O(n)$).
diff --git a/Queues/README.md b/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` ($O(n)$), `dequeue` ($O(1)$), `isEmpty` ($O(1)$), and `size` ($O(1)$) methods.
+- [Queue with Two Stacks](QueueWith2StacksImple.py): Implements a queue using two stacks to achieve FIFO behavior ($O(1)$ amortized).
diff --git a/README.md b/README.md
@@ -35,23 +35,23 @@ 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)
-- [Usage](#usage)
-- [Quick Reference](#quick-reference)
-- [License](#license)
+- [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)
 
 ---
 
@@ -67,7 +67,7 @@ Most scripts in this repository are standalone and can be executed directly:
 
 ```bash
 # Run any Python script
-python3 Arrays/Anagram_Check_Sorted_Sol.py
+python3 Arrays/AnagramCheckSortedSol.py
 
 # Or run from the repo root
 python3 Sorting/BubbleSortImple.py
@@ -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
@@ -100,9 +100,9 @@ python3 Sorting/BubbleSortImple.py
 
 ### Arrays 🔤
 Common array-based algorithms and manipulations.
-- [Anagram Check](Arrays/): [Sorted](Arrays/Anagram_Check_Sorted_Sol.py) & [Manual](Arrays/Anagram_Check_manual_Sol.py) solutions
+- [Anagram Check](Arrays/): [Sorted](Arrays/AnagramCheckSortedSol.py) & [Manual](Arrays/AnagramCheckManualSol.py) solutions
 - [Array Pair Sum](Arrays/ArrayPairSumSol.py): Find pairs that sum to $k$
-- [Find Missing Element](Arrays/): [XOR](Arrays/ArrayFindTheMissingElement_XOR_sol.py), [Brute Force](Arrays/ArrayFindTheMissingElement_brute_force_sol.py), [Hash Table](Arrays/ArrayFindTheMissingElement_hash_table_sol.py), & [Sum](Arrays/ArrayFindTheMissingElement_takingSumandSubtract_sol.py) approaches
+- [Find Missing Element](Arrays/): [XOR](Arrays/ArrayFindTheMissingElementXORSol.py), [Brute Force](Arrays/ArrayFindTheMissingElementBruteForceSol.py), [Hash Table](Arrays/ArrayFindTheMissingElementHashTableSol.py), & [Sum](Arrays/ArrayFindTheMissingElementSumSol.py) approaches
 
 ### Linked Lists 🔗
 Implementations and problems involving linked structures.
@@ -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.
@@ -133,7 +133,7 @@ Hierarchical data structures.
 - [Binary Heap](Trees/BinaryHeapImple.py): Min-heap implementation
 - [Tree Traversals](Trees/TreeLevelOrderPrintImple.py): Level order (BFS) printing
 - [Trim BST](Trees/TrimBinarySearchTreeImple.py): Keep nodes within a range
-- [Tree Representations](Trees/): [Nodes & References](Trees/TreeRepresentationWithNodesReferences.py) & [List of Lists](Trees/buildTreeTest.py)
+- [Tree Representations](Trees/): [Nodes & References](Trees/TreeRepresentationWithNodesReferences.py) & [List of Lists](Trees/BuildTreeTest.py)
 
 ---
 
@@ -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.
 
 ---
 

diff --git a/Recursion/README.md b/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 (Dynamic Programming)](CoinChangeProblemDynamic.py): Optimized solution to the coin change problem using dynamic programming ($O(n \cdot m)$).
 
 ### 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.
diff --git a/Sorting/README.md b/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 ($O(n^2)$ worst case).
 - [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).
diff --git a/Stacks/README.md b/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` ($O(1)$), `pop` ($O(1)$), `peek` ($O(1)$), `isEmpty` ($O(1)$), and `size` ($O(1)$) methods.
+- [Balanced Parentheses Check](BalanceParenthlessCheckImple.py): Uses a stack to check if a string of opening and closing parentheses is balanced ($O(n)$).
diff --git a/Trees/buildTreeTest.py → Trees/BuildTreeTest.py b/Trees/buildTreeTest.py → Trees/BuildTreeTest.py
diff --git a/Trees/README.md b/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 ($O(\log n)$ average, $O(n)$ worst).
+- [Validate BST (Solution 1)](BinarySearchTreeCheckImpleSol1.py): Validates a BST by performing an in-order traversal ($O(n)$).
+- [Validate BST (Solution 2)](BinarySearchTreeCheckImpleSol2.py): Validates a BST by keeping track of the minimum and maximum allowable values ($O(n)$).
+- [Trim a BST](TrimBinarySearchTreeImple.py): Trims a BST so that all node values fall within a specified range ($O(n)$).
 
 ### 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 ($O(\log n)$).
+- [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, including `insert` ($O(\log n)$) and `delMin` ($O(\log n)$).
 
 ### 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.
+- [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 ($O(n)$).
Original file line number	Diff line number	Diff line change
Expand Up		@@ -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` ($O(1)$), `addRear` ($O(n)$), `removeFront` ($O(1)$), `removeRear` ($O(n)$), `isEmpty` ($O(1)$), and `size` ($O(1)$).