diff --git a/Arrays/Anagram_Check_manual_Sol.py b/Arrays/AnagramCheckManualSol.py
similarity index 100%
rename from Arrays/Anagram_Check_manual_Sol.py
rename to Arrays/AnagramCheckManualSol.py
diff --git a/Arrays/Anagram_Check_Sorted_Sol.py b/Arrays/AnagramCheckSortedSol.py
similarity index 100%
rename from Arrays/Anagram_Check_Sorted_Sol.py
rename to Arrays/AnagramCheckSortedSol.py
diff --git a/Arrays/ArrayFindTheMissingElement_brute_force_sol.py b/Arrays/ArrayFindTheMissingElementBruteForceSol.py
similarity index 100%
rename from Arrays/ArrayFindTheMissingElement_brute_force_sol.py
rename to Arrays/ArrayFindTheMissingElementBruteForceSol.py
diff --git a/Arrays/ArrayFindTheMissingElement_hash_table_sol.py b/Arrays/ArrayFindTheMissingElementHashTableSol.py
similarity index 100%
rename from Arrays/ArrayFindTheMissingElement_hash_table_sol.py
rename to Arrays/ArrayFindTheMissingElementHashTableSol.py
diff --git a/Arrays/ArrayFindTheMissingElement_takingSumandSubtract_sol.py b/Arrays/ArrayFindTheMissingElementSumSol.py
similarity index 100%
rename from Arrays/ArrayFindTheMissingElement_takingSumandSubtract_sol.py
rename to Arrays/ArrayFindTheMissingElementSumSol.py
diff --git a/Arrays/ArrayFindTheMissingElement_XOR_sol.py b/Arrays/ArrayFindTheMissingElementXORSol.py
similarity index 100%
rename from Arrays/ArrayFindTheMissingElement_XOR_sol.py
rename to Arrays/ArrayFindTheMissingElementXORSol.py
diff --git a/Arrays/README.md b/Arrays/README.md
index 707a82e..8f42a20 100644
--- 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.
-- [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)](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. Time Complexity: $O(n)$
diff --git a/deque/DequeImple.py b/Deque/DequeImple.py
similarity index 100%
rename from deque/DequeImple.py
rename to Deque/DequeImple.py
diff --git a/deque/README.md b/Deque/README.md
similarity index 76%
rename from deque/README.md
rename to Deque/README.md
index 046a17f..fc93fe9 100644
--- a/deque/README.md
+++ b/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`. Time Complexity: $O(1)$ for front operations, $O(n)$ for rear operations due to list shifting.
diff --git a/Error-debug/ErrorExceptions.py b/ErrorHandling/ErrorExceptions.py
similarity index 100%
rename from Error-debug/ErrorExceptions.py
rename to ErrorHandling/ErrorExceptions.py
diff --git a/Error-debug/README.md b/ErrorHandling/README.md
similarity index 73%
rename from Error-debug/README.md
rename to ErrorHandling/README.md
index c8bc4d4..2a9cf5c 100644
--- a/Error-debug/README.md
+++ b/ErrorHandling/README.md
@@ -1,7 +1,7 @@
-# Error and Debugging
+# Error Handling
 
 This directory contains examples of error handling and debugging techniques 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.
diff --git a/GraphAlgorithms/README.md b/GraphAlgorithms/README.md
index f0330f8..1d5f8cc 100644
--- a/GraphAlgorithms/README.md
+++ b/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. Time Complexity: $O(V+E)$
+- [Breadth First Search (BFS)](BFS.py): Implements BFS to solve the Word Ladder problem. Time Complexity: $O(V+E)$
+- [General Depth First Search (DFS)](DFSGeneral.py): Provides a general implementation of DFS. Time Complexity: $O(V+E)$
+- [DFS - Knight's Tour Problem](DFSImpleTheKnightsTourProblem.py): 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. Time Complexity: $O(k^N)$
+- [Word Ladder Problem](WordLadderProblem.py): Specifically focuses on building the word ladder graph.
diff --git a/LinkedLists/README.md b/LinkedLists/README.md
index bead21d..f8b1fcb 100644
--- a/LinkedLists/README.md
+++ b/LinkedLists/README.md
@@ -1,11 +1,11 @@
 # Linked Lists
 
-This directory contains Python implementations of various types of linked lists and related algorithms.
+This directory contains Python implementations of linked list data structures and related problems.
 
 ## 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. Time Complexity: $O(1)$ for adding/removing at head.
+- [Doubly Linked List Implementation](DoublyLinkedListImple.py): Basic implementation of a doubly linked list. Time Complexity: $O(1)$ for linkage operations.
+- [Singly Linked List Cycle Check](SinglyLinkedListCycleCheckImple.py): Implementation of Floyd's cycle-finding algorithm. Time Complexity: $O(n)$
+- [Linked List Reversal](LinkedListReversal.py): In-place reversal of a linked list. Time Complexity: $O(n)$
+- [Nth to Last Node](LinkedListNthToLastNode.py): Finding the n-th to last node in a singly linked list. Time Complexity: $O(n)$
diff --git a/LinkedLists/SinglyLinkedListCycleCheckImple.py b/LinkedLists/SinglyLinkedListCycleCheckImple.py
index 71a1b5c..5a302e8 100644
--- a/LinkedLists/SinglyLinkedListCycleCheckImple.py
+++ b/LinkedLists/SinglyLinkedListCycleCheckImple.py
@@ -19,39 +19,46 @@ def __init__(self, value):
         self.value = value
         self.nextnode = None
         
-    def cycle_check(node):
-        # Set two pointers initialize to passed node
-        pt1 = node
-        pt2 = node
-        # loop through end of the list
-        while pt2 != None and pt2.nextnode != None:
-            pt1 = pt1.nextnode
-            pt2 = pt2.nextnode.nextnode
-            # If pt2 meet pt1 then there is a cycle
-            if pt2 == pt1:
+    def cycle_check(self):
+        """
+        Check if the linked list has a cycle using Floyd's cycle-finding algorithm.
+        Returns True if a cycle exists, False otherwise.
+        """
+        # Set two pointers initialize to current node (self)
+        slow = self
+        fast = self
+
+        # Loop through the list
+        while fast is not None and fast.nextnode is not None:
+            slow = slow.nextnode
+            fast = fast.nextnode.nextnode
+
+            # If fast meets slow then there is a cycle
+            if fast == slow:
                 return True
+
         return False
+
 # Test
-# Create a Linked List 
-a = LinkedListNode(1)
-b = LinkedListNode(2)
-c = LinkedListNode(3)
-# Create a cycle
-a.nextnode = b
-b.nextnode = c
-# This is a cycle -- to test non-cycle scnerio comment this line
-c.nextnode = a
-
-print (a.value)
-print (b.value)
-print (c.value)
-
-# Since cycle_check is a method but it doesn't use self and is defined inside class
-# it should be called on an instance or changed to static method.
-# In its current definition it behaves like a regular method but is missing 'self'.
-# Actually it is defined as def cycle_check(node): which means it takes one arg.
-# If called as LinkedListNode.cycle_check(a) it should work if it was just a function.
-
-print(a.cycle_check())
+if __name__ == "__main__":
+    # Create a Linked List
+    a = LinkedListNode(1)
+    b = LinkedListNode(2)
+    c = LinkedListNode(3)
+
+    # Create a cycle
+    a.nextnode = b
+    b.nextnode = c
+    c.nextnode = a
+
+    print(f"Node A value: {a.value}")
+    print(f"Node B value: {b.value}")
+    print(f"Node C value: {c.value}")
+
+    print(f"Cycle detected: {a.cycle_check()}")
+
+    # Break the cycle and test again
+    c.nextnode = None
+    print(f"Cycle detected after breaking: {a.cycle_check()}")
 
 
diff --git a/LinkedLists/SingleLinkedListImple.py b/LinkedLists/SinglyLinkedListImple.py
similarity index 100%
rename from LinkedLists/SingleLinkedListImple.py
rename to LinkedLists/SinglyLinkedListImple.py
diff --git a/Queues/README.md b/Queues/README.md
index a1c90d0..1c7c40a 100644
--- 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. Time Complexity: $O(n)$ for enqueue, $O(1)$ for dequeue.
+- [Queue with Two Stacks](QueueWith2StacksImple.py): Implements a queue using two stacks. Time Complexity: $O(1)$ amortized for both operations.
diff --git a/README.md b/README.md
index b8de7d5..768bc1c 100644
--- 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
@@ -80,7 +80,8 @@ 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)
@@ -88,7 +89,6 @@ python3 Sorting/BubbleSortImple.py
 ├── 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
@@ -98,42 +98,42 @@ python3 Sorting/BubbleSortImple.py
 
 ## 📊 Data Structures
 
-### Arrays 🔤
+### 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) & [Manual](Arrays/AnagramCheckManualSol.py) solutions
+- [Array Pair Sum](Arrays/ArrayPairSumSol.py): Find pairs that sum to $k$ ($O(n)$)
+- [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.
-- [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)
+- [Cycle Detection](LinkedLists/SinglyLinkedListCycleCheckImple.py): Detect cycles using Floyd's algorithm ($O(n)$)
+- [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 ($O(1)$ push, pop)
+- [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 ($O(n)$ enqueue, $O(1)$ dequeue)
+- [Queue with Two Stacks](Queues/QueueWith2StacksImple.py): Implementing FIFO using LIFO structures ($O(1)$ amortized)
 
 ### Deque 🔄
 Double-ended queue operations.
-- [Deque Implementation](deque/DequeImple.py): Operations at both ends
+- [Deque Implementation](Deque/DequeImple.py): Operations at both ends ($O(1)$ front, $O(n)$ rear)
 
 ### Trees 🌳
 Hierarchical data structures.
-- [Binary Search Tree](Trees/BinarySearchTreesImple.py): Complete BST implementation
+- [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)
-- [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](Trees/): [Iterative](Trees/BinarySearchImple.py) & [Recursive](Trees/BinarySearchRecursiveImple.py) ($O(\log n)$)
+- [Binary Heap](Trees/BinaryHeapImple.py): Min-heap implementation ($O(\log n)$)
+- [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)
-- [Word Split](Recursion/RecursionWordSplit.py): Dynamic Programming solution
+- [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) & [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 ($O(n^2)$)
 
 ### 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)
+- [Adjacency List](GraphAlgorithms/AdjacencyListGraphImple.py): Graph ADT implementation ($O(V+E)$)
+- [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
 
 ---
 
 ## ⚠️ 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/FibonacciSeqDynamic.py b/Recursion/FibonacciSeqDynamic.py
index b16783e..6d81b6c 100644
--- a/Recursion/FibonacciSeqDynamic.py
+++ b/Recursion/FibonacciSeqDynamic.py
@@ -2,26 +2,36 @@
 # memoization + recursion = dynamic programming
 # Author: Pradeep K. Pant, ppant@cpan.org
 
-# Instantiate Cache information
-n = 10
-cache = [None] * (n + 1)
-
 # Implement fibonacci_dynamic
-def fibonacci_dynamic(n):
+def fibonacci_dynamic(n, cache=None):
+    """
+    Finds the n-th Fibonacci number using dynamic programming (memoization).
+    :param n: The position in the Fibonacci sequence.
+    :param cache: Optional cache dictionary for memoization.
+    :return: The n-th Fibonacci number.
+    """
+    if cache is None:
+        cache = {}
+
     # Base Case
     if n == 0 or n == 1:
         return n
 
-    # Check cache if already val of n present if yes pick from there this will save time
-    if cache[n] != None:
+    # Check cache if already val of n present
+    if n in cache:
         return cache[n]
 
     # Recursive call to and keep setting cache
-    cache[n] = fibonacci_dynamic(n - 1) + fibonacci_dynamic(n - 2)
+    cache[n] = fibonacci_dynamic(n - 1, cache) + fibonacci_dynamic(n - 2, cache)
     return cache[n]
 
 # Test
-# We'll try to find the 9th no in the fibnacci sequence which is 34
-print (fibonacci_dynamic(9))
-# 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
-# The recursive-memoization solution is exponential time Big-O , with O(n)
+if __name__ == "__main__":
+    # We'll try to find the 9th no in the fibonacci sequence which is 34
+    # 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
+    n_test = 9
+    print(f"The {n_test}th Fibonacci number is: {fibonacci_dynamic(n_test)}")
+
+    # Large value to test performance and avoidance of fixed-size global cache
+    n_large = 50
+    print(f"The {n_large}th Fibonacci number is: {fibonacci_dynamic(n_large)}")
diff --git a/Recursion/README.md b/Recursion/README.md
index 7265340..3fdfb9e 100644
--- a/Recursion/README.md
+++ b/Recursion/README.md
@@ -1,21 +1,21 @@
-# Recursion
+# Recursion and Dynamic Programming
 
 This directory contains Python implementations of problems solved using recursion and dynamic programming.
 
 ## 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. Time Complexity: $O(n)$
+- [Fibonacci (Recursive)](FibonacciSeqRecursion.py): Simple recursive implementation. Time Complexity: $O(2^n)$
+- [Fibonacci (Dynamic Programming)](FibonacciSeqDynamic.py): Optimized Fibonacci sequence using memoization. Time Complexity: $O(n)$
 
 ### 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. Time Complexity: Exponential.
+- [Coin Change (Dynamic Programming)](CoinChangeProblemDynamic.py): Optimized solution using dynamic programming. Time Complexity: $O(n \cdot m)$
 
 ### 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.
-- [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. Time Complexity: $O(n)$
+- [Reverse a String](RecursionReverseStr.py): Reverses a string using recursion. Time Complexity: $O(n)$
+- [String Permutations](RecursionStrPermutation.py): Generates all permutations of a string. Time Complexity: $O(n!)$
+- [Sum of Digits](RecursionSumOfDigits.py): Calculates the sum of digits in an integer recursively. Time Complexity: $O(\log_{10} n)$
+- [Word Split](RecursionWordSplit.py): Determines if a string can be split into words from a list. Time Complexity: $O(n^2)$
diff --git a/Sorting/README.md b/Sorting/README.md
index 0b76399..bcd136a 100644
--- a/Sorting/README.md
+++ b/Sorting/README.md
@@ -4,9 +4,9 @@ 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.
+- [Bubble Sort](BubbleSortImple.py): Implementation of Bubble Sort. Time Complexity: $O(n^2)$
+- [Selection Sort](SelectionSortImple.py): Implementation of Selection Sort. Time Complexity: $O(n^2)$
+- [Insertion Sort](InsertionSortImple.py): Implementation of Insertion Sort. Time Complexity: $O(n^2)$
+- [Shell Sort](ShellSortImple.py): Implementation of Shell Sort (diminishing increment sort). Time Complexity: $O(n^2)$ (worst case)
+- [Merge Sort](MergeSortImple.py): A recursive "divide and conquer" algorithm. Time Complexity: $O(n \log n)$
+- [Quick Sort](QuickSortImple.py): Implementation of Quick Sort (partition exchange sort). Time Complexity: $O(n \log n)$ average.
diff --git a/Stacks/BalanceParenthlessCheckImple.py b/Stacks/BalanceParenthesesCheckImple.py
similarity index 100%
rename from Stacks/BalanceParenthlessCheckImple.py
rename to Stacks/BalanceParenthesesCheckImple.py
diff --git a/Stacks/README.md b/Stacks/README.md
index e799a74..d9cbb5c 100644
--- 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. Time Complexity: $O(1)$ for push and pop.
+- [Balanced Parentheses Check](BalanceParenthesesCheckImple.py): Uses a stack to check if a string of parentheses is balanced. Time Complexity: $O(n)$
diff --git a/Trees/buildTreeTest.py b/Trees/BuildTreeTest.py
similarity index 100%
rename from Trees/buildTreeTest.py
rename to Trees/BuildTreeTest.py
diff --git a/Trees/README.md b/Trees/README.md
index 2047225..ed312b1 100644
--- a/Trees/README.md
+++ b/Trees/README.md
@@ -1,23 +1,16 @@
 # Trees
 
-This directory contains Python implementations of various tree-based data structures and algorithms.
+This directory contains Python implementations of tree-based data structures and algorithms.
 
 ## 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 $[min, max]$.
-
-### 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.
-
-### Heaps
-- [Binary Heap Implementation](BinaryHeapImple.py): Implements a min-heap using a recursive approach, including `insert`, `delMin`, and `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.
+- [Binary Search Tree Implementation](BinarySearchTreesImple.py): Complete BST implementation. Time Complexity: $O(\log n)$ average, $O(n)$ worst case.
+- [Binary Search Tree Check (Solution 1)](BinarySearchTreeCheckImpleSol1.py): Validates a BST using in-order traversal. Time Complexity: $O(n)$
+- [Binary Search Tree Check (Solution 2)](BinarySearchTreeCheckImpleSol2.py): Validates a BST using range checks. Time Complexity: $O(n)$
+- [Binary Search (Iterative)](BinarySearchImple.py): Iterative implementation of binary search. Time Complexity: $O(\log n)$
+- [Binary Search (Recursive)](BinarySearchRecursiveImple.py): Recursive implementation of binary search. Time Complexity: $O(\log n)$
+- [Binary Heap Implementation](BinaryHeapImple.py): Min-heap implementation. Time Complexity: $O(\log n)$ for insert and extract-min.
+- [Tree Level Order Print](TreeLevelOrderPrintImple.py): BFS-based level order traversal. Time Complexity: $O(n)$
+- [Trim a Binary Search Tree](TrimBinarySearchTreeImple.py): Trims a BST within a given range. Time Complexity: $O(n)$
+- [Tree Representation (Nodes and References)](TreeRepresentationWithNodesReferences.py): Basic tree structure using nodes.
+- [Build Tree Test](BuildTreeTest.py): Tree implementation using a list of lists.