ppant · ppant · Jul 7, 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. Time complexity: $O(n \log n)$.
+- [Anagram Check (Manual Solution)](AnagramCheckManualSol.py): Checks if two strings are anagrams using a hash table (dictionary) to count character frequencies. Time complexity: $O(n)$.
+- [Array Find Missing Element (XOR Solution)](ArrayFindTheMissingElementXORSol.py): Efficiently finds a missing element in a shuffled array using bitwise XOR. Time complexity: $O(n)$.
+- [Array Find Missing Element (Brute Force Solution)](ArrayFindTheMissingElementBruteForceSol.py): Finds a missing element by sorting both arrays and comparing them. Time complexity: $O(n \log n)$.
+- [Array Find Missing Element (Hash Table Solution)](ArrayFindTheMissingElementHashTableSol.py): Finds a missing element using a hash table (dictionary) to track element counts. Time complexity: $O(n)$.
+- [Array Find Missing Element (Sum/Subtract Solution)](ArrayFindTheMissingElementSumSol.py): Finds a missing element by calculating the difference between the sums of the two arrays. Time complexity: $O(n)$.
 - [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 b/Deque/README.md
@@ -0,0 +1,13 @@
+# Deque
+
+This directory contains a Python implementation of a Double-Ended Queue (Deque).
+
+## Contents
+
+- [Deque Implementation](DequeImple.py): A class-based implementation of a deque using a Python list.
+    - `addFront(item)`: $O(1)$
+    - `addRear(item)`: $O(n)$
+    - `removeFront()`: $O(1)$
+    - `removeRear()`: $O(n)$
+    - `isEmpty()`: $O(1)$
+    - `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
@@ -1,7 +1,7 @@
-# Error and Debugging
+# Error Handling
 
-This directory contains examples of error handling and debugging techniques in Python.
+This directory contains examples of error handling and debugging in Python.
 
 ## Contents
 
-- [Error and Exceptions](ErrorExceptions.py): Demonstrates the use of `try`, `except`, `else`, and `finally` blocks for robust error handling, specifically validating integer user input.
+- [Error and Exceptions](ErrorExceptions.py): Demonstrates the use of `try`, `except`, `else`, and `finally` blocks for robust error handling and capturing specific exceptions.
diff --git a/GraphAlgorithms/README.md b/GraphAlgorithms/README.md
@@ -1,12 +1,12 @@
 # Graph Algorithms
 
-This directory contains Python implementations of common graph-based algorithms and data structures.
+This directory contains Python implementations of 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 Graph Implementation](AdjacencyListGraphImple.py): Implementation of the Graph Abstract Data Type using an adjacency list.
+- [Breadth First Search (BFS)](BFS.py): Implementation of BFS used to solve the Word Ladder problem. Time complexity: $O(V+E)$.
+- [Depth First Search (DFS)](DFSGeneral.py): General implementation of the DFS algorithm. Time complexity: $O(V+E)$.
+- [The Knight's Tour Problem (Graph Generation)](TheKnightsTourProblem.py): Generates the graph representation for the Knight's Tour problem.
+- [The Knight's Tour Problem (DFS Solution)](DFSImpleTheKnightsTourProblem.py): Solves the Knight's Tour problem using DFS. Time complexity: $O(k^N)$.
+- [Word Ladder Problem](WordLadderProblem.py): Implementation of the Word Ladder problem, building the graph and finding the shortest path.
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.
-- [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](SinglyLinkedListImple.py): Basic implementation of a singly linked list node and basic linkage. $O(1)$ for node creation and pointer assignment.
+- [Doubly Linked List Implementation](DoublyLinkedListImple.py): Basic implementation of a doubly linked list node with `prev` and `next` pointers. $O(1)$ for node creation and pointer assignment.
+- [Singly Linked List Cycle Check](SinglyLinkedListCycleCheckImple.py): Implements Floyd's Cycle-Finding Algorithm (two pointers) to detect cycles in a linked list. Time complexity: $O(n)$.
+- [Linked List Reversal](LinkedListReversal.py): Reverses a singly linked list in-place. Time complexity: $O(n)$.
+- [Nth to Last Node](LinkedListNthToLastNode.py): Finds the $n$-th to last node in a singly linked list using two pointers. Time complexity: $O(n)$.
diff --git a/LinkedLists/SingleLinkedListImple.py → LinkedLists/SinglyLinkedListImple.py b/LinkedLists/SingleLinkedListImple.py → LinkedLists/SinglyLinkedListImple.py
diff --git a/Queues/README.md b/Queues/README.md
@@ -1,8 +1,12 @@
 # Queues
 
-This directory contains Python implementations of the Queue data structure.
+This directory contains Python implementations of Queues.
 
 ## 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 queue (FIFO) using a Python list.
+    - `enqueue(item)`: $O(n)$ due to `list.insert(0, item)`
+    - `dequeue()`: $O(1)$ using `list.pop()`
+- [Queue with Two Stacks](QueueWith2StacksImple.py): Implementation of a queue using two stacks.
+    - `enqueue(item)`: Amortized $O(1)$
+    - `dequeue()`: Amortized $O(1)$
diff --git a/README.md b/README.md
@@ -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
@@ -100,40 +100,40 @@ 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
-- [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
+- [Anagram Check](Arrays/): [Sorted](Arrays/AnagramCheckSortedSol.py) ($O(n \log n)$) & [Manual](Arrays/AnagramCheckManualSol.py) ($O(n)$) solutions
+- [Array Pair Sum](Arrays/ArrayPairSumSol.py): Find pairs that sum to $k$ ($O(n)$)
+- [Find Missing Element](Arrays/): [XOR](Arrays/ArrayFindTheMissingElementXORSol.py) ($O(n)$), [Brute Force](Arrays/ArrayFindTheMissingElementBruteForceSol.py) ($O(n \log n)$), [Hash Table](Arrays/ArrayFindTheMissingElementHashTableSol.py) ($O(n)$), & [Sum](Arrays/ArrayFindTheMissingElementSumSol.py) ($O(n)$) approaches
 
 ### Linked Lists 🔗
 Implementations and problems involving linked structures.
-- [Singly Linked List](LinkedLists/SingleLinkedListImple.py) & [Doubly Linked List](LinkedLists/DoublyLinkedListImple.py)
-- [Cycle Detection](LinkedLists/SinglyLinkedListCycleCheckImple.py): Detect cycles using two pointers (Floyd's algorithm)
-- [Reverse Linked List](LinkedLists/LinkedListReversal.py): In-place reversal
-- [Nth to Last Node](LinkedLists/LinkedListNthToLastNode.py): Find the $n$-th node from the end
+- [Singly Linked List](LinkedLists/SinglyLinkedListImple.py) & [Doubly Linked List](LinkedLists/DoublyLinkedListImple.py) (Node linkage: $O(1)$)
+- [Cycle Detection](LinkedLists/SinglyLinkedListCycleCheckImple.py): Detect cycles using two pointers ($O(n)$)
+- [Reverse Linked List](LinkedLists/LinkedListReversal.py): In-place reversal ($O(n)$)
+- [Nth to Last Node](LinkedLists/LinkedListNthToLastNode.py): Find the $n$-th node from the end ($O(n)$)
 
 ### Stacks 📚
 LIFO (Last-In-First-Out) data structures.
-- [Stack Implementation](Stacks/StackImple.py): Basic operations (push, pop, peek)
-- [Balanced Parentheses](Stacks/BalanceParenthlessCheckImple.py): Check for balanced brackets using a stack
+- [Stack Implementation](Stacks/StackImple.py): Basic operations ($O(1)$ for push, pop, peek)
+- [Balanced Parentheses](Stacks/BalanceParenthesesCheckImple.py): Check for balanced brackets using a stack ($O(n)$)
 
 ### Queues 📦
 FIFO (First-In-First-Out) data structures.
-- [Queue Implementation](Queues/QueueImple.py): Basic operations (enqueue, dequeue)
-- [Queue with Two Stacks](Queues/QueueWith2StacksImple.py): Implementing FIFO using LIFO structures
+- [Queue Implementation](Queues/QueueImple.py): Basic operations (Enqueue: $O(n)$, Dequeue: $O(1)$)
+- [Queue with Two Stacks](Queues/QueueWith2StacksImple.py): Implementing FIFO using LIFO structures (Amortized $O(1)$)
 
 ### Deque 🔄
 Double-ended queue operations.
-- [Deque Implementation](deque/DequeImple.py): Operations at both ends
+- [Deque Implementation](Deque/DequeImple.py): Front operations ($O(1)$), Rear operations ($O(n)$)
 
 ### Trees 🌳
 Hierarchical data structures.
-- [Binary Search Tree](Trees/BinarySearchTreesImple.py): Complete BST implementation
-- [BST Validation](Trees/): [Solution 1 (In-order)](Trees/BinarySearchTreeCheckImpleSol1.py) & [Solution 2 (Range check)](Trees/BinarySearchTreeCheckImpleSol2.py)
-- [Binary Search](Trees/): [Iterative](Trees/BinarySearchImple.py) & [Recursive](Trees/BinarySearchRecursiveImple.py)
-- [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)
+- [Binary Search Tree](Trees/BinarySearchTreesImple.py): Complete BST implementation ($O(\log n)$ average)
+- [BST Validation](Trees/): [Solution 1 (In-order)](Trees/BinarySearchTreeCheckImpleSol1.py) & [Solution 2 (Range check)](Trees/BinarySearchTreeCheckImpleSol2.py) (Both $O(n)$)
+- [Binary Search](Trees/): [Iterative](Trees/BinarySearchImple.py) & [Recursive](Trees/BinarySearchRecursiveImple.py) (Both $O(\log n)$)
+- [Binary Heap](Trees/BinaryHeapImple.py): Min-heap implementation ($O(\log n)$ for insert/delete)
+- [Tree Traversals](Trees/TreeLevelOrderPrintImple.py): Level order (BFS) printing ($O(n)$)
+- [Trim BST](Trees/TrimBinarySearchTreeImple.py): Keep nodes within a range ($O(n)$)
+- [Tree Representations](Trees/): [Nodes & References](Trees/TreeRepresentationWithNodesReferences.py) & [List of Lists](Trees/BuildTreeTest.py)
 
 ---
 
@@ -144,31 +144,31 @@ Algorithms for arranging elements in order.
 - [Bubble Sort](Sorting/BubbleSortImple.py) - $O(n^2)$
 - [Selection Sort](Sorting/SelectionSortImple.py) - $O(n^2)$
 - [Insertion Sort](Sorting/InsertionSortImple.py) - $O(n^2)$
-- [Shell Sort](Sorting/ShellSortImple.py) - $O(n \log n)$
+- [Shell Sort](Sorting/ShellSortImple.py) - $O(n^2)$ worst case
 - [Merge Sort](Sorting/MergeSortImple.py) - $O(n \log n)$
 - [Quick Sort](Sorting/QuickSortImple.py) - $O(n \log n)$ average
 
 ### Recursion & Dynamic Programming 🔀
 Solving problems by breaking them into smaller sub-problems.
-- [Fibonacci Sequence](Recursion/): [Iterative](Recursion/FibonacciSeqIterative.py), [Recursive](Recursion/FibonacciSeqRecursion.py), & [Dynamic Programming](Recursion/FibonacciSeqDynamic.py)
-- [Coin Change Problem](Recursion/): [Recursive](Recursion/CoinChangeProblemRecursion.py) & [Dynamic Programming](Recursion/CoinChangeProblemDynamic.py)
-- [String Operations](Recursion/): [Reverse](Recursion/RecursionReverseStr.py) & [Permutations](Recursion/RecursionStrPermutation.py)
-- [Math Operations](Recursion/): [Cumulative Sum](Recursion/RecursionCumulativeSum.py) & [Sum of Digits](Recursion/RecursionSumOfDigits.py)
+- [Fibonacci Sequence](Recursion/): [Iterative](Recursion/FibonacciSeqIterative.py) ($O(n)$), [Recursive](Recursion/FibonacciSeqRecursion.py) ($O(2^n)$), & [Dynamic Programming](Recursion/FibonacciSeqDynamic.py) ($O(n)$)
+- [Coin Change Problem](Recursion/): [Recursive](Recursion/CoinChangeProblemRecursion.py) (Exponential) & [Dynamic Programming](Recursion/CoinChangeProblemDynamic.py) ($O(n \cdot m)$)
+- [String Operations](Recursion/): [Reverse](Recursion/RecursionReverseStr.py) ($O(n)$) & [Permutations](Recursion/RecursionStrPermutation.py) ($O(n!)$)
+- [Math Operations](Recursion/): [Cumulative Sum](Recursion/RecursionCumulativeSum.py) ($O(n)$) & [Sum of Digits](Recursion/RecursionSumOfDigits.py) ($O(\log_{10} n)$)
 - [Word Split](Recursion/RecursionWordSplit.py): Dynamic Programming solution
 
 ### Graph Algorithms 🗺️
 Algorithms for graph traversal and pathfinding.
 - [Adjacency List](GraphAlgorithms/AdjacencyListGraphImple.py): Graph ADT implementation
-- [Breadth First Search (BFS)](GraphAlgorithms/BFS.py): Word Ladder problem
-- [Depth First Search (DFS)](GraphAlgorithms/DFSGeneral.py): General DFS implementation
-- [Knight's Tour Problem](GraphAlgorithms/): [Graph Generation](GraphAlgorithms/TheKnightsTourProblem.py) & [DFS Solution](GraphAlgorithms/DFSImpleTheKnightsTourProblem.py)
-- [Word Ladder Problem](GraphAlgorithms/WordLadderProblem.py): Building the word ladder graph
+- [Breadth First Search (BFS)](GraphAlgorithms/BFS.py): Word Ladder problem ($O(V+E)$)
+- [Depth First Search (DFS)](GraphAlgorithms/DFSGeneral.py): General DFS implementation ($O(V+E)$)
+- [Knight's Tour Problem](GraphAlgorithms/): [Graph Generation](GraphAlgorithms/TheKnightsTourProblem.py) & [DFS Solution](GraphAlgorithms/DFSImpleTheKnightsTourProblem.py) ($O(k^N)$)
+- [Word Ladder Problem](GraphAlgorithms/WordLadderProblem.py): Building the word ladder graph ($O(n^2 \cdot m)$)
 
 ---
 
 ## ⚠️ 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.
 
 ---