Definition: A data structure is a way of organizing data for efficient use.
Importance: Essential for creating fast algorithms, managing data, and improving code readability.
Key Insight: Understanding and applying the appropriate data structure is crucial for programming excellence.
Abstract Data Types vs Data Structures
Abstract Data Type (ADT): Defines a data type purely by its behavior (methods) without implementation details.
Example: Different modes of transportation (walking, biking) represent ADTs, while specific implementations (like using arrays or linked lists) represent data structures.
Computational Complexity
Big O Notation: Used to describe time and space complexity in algorithms, focusing on worst-case scenarios.
Common Complexities:
Constant Time: O(1)
Logarithmic: O(log n)
Linear: O(n)
Quadratic: O(n^2)
Exponential: O(2^n)
Arrays
Definition: A collection of items stored at contiguous memory locations.
Operations:
Access Time: O(1)
Search Time: O(n)
Insertion/Deletion: O(n) (for static arrays)
Dynamic Arrays: Can grow and shrink in size, allowing for more efficient use of memory.
Linked Lists
Definition: A linear data structure where elements (nodes) are stored in non-contiguous locations.
Types:
Singly Linked List: Nodes have a pointer to the next node.
Doubly Linked List: Nodes have pointers to both next and previous nodes.
Operations:
Access/Search Time: O(n)
Insertion/Deletion: O(1) (if you have a reference to the node).
Stacks
Definition: A Last-In-First-Out (LIFO) data structure.
Operations:
Push: Add an item to the top.
Pop: Remove the top item.
Use Cases: Backtracking algorithms, undo functionality in applications.
Queues
Definition: A First-In-First-Out (FIFO) data structure.
Operations:
Enqueue: Add an item to the back.
Dequeue: Remove an item from the front.
Use Cases: Order processing, scheduling algorithms.
Priority Queues
Definition: A data structure where each element has a priority. Elements with higher priority are dequeued before those with lower priority.
Implementation: Often implemented with heaps.
Operations:
Insert (with priority): O(log n)
Remove (highest priority): O(log n)
Trees
Definition: A hierarchical data structure with nodes connected by edges.
Binary Trees: Each node has at most two children.
Binary Search Trees (BST): A binary tree where the left child contains nodes with values less than the parent, and the right child contains values greater than the parent.
Balancing: Keeping trees balanced (such as AVL trees) ensures efficient operations.
Hash Tables
Definition: A data structure that maps keys to values using a hash function.
Collision Resolution Techniques:
Separate Chaining: Uses linked lists for entries with the same hash index.
Open Addressing: Finds another slot within the table itself.
Operations:
Insert: O(1) average case, O(n) worst case
Search: O(1) average case, O(n) worst case
Suffix Arrays
Definition: An array of indices representing suffixes of a string sorted in lexicographical order.
Use: Efficiently solving problems around substrings, such as longest repeated substrings.
LCP Array: Longest Common Prefix array, which tracks how many characters two adjacent suffixes have in common.
Conclusion
Understanding various data structures is foundational for computer science.
The correct application of data structures leads to efficient algorithms and better program performance.