Data Structures Overview

Data Structures

• Data structures are different ways to organize data on a computer for efficient use.
• A data structure is a way to store and organize data to facilitate access and modifications.

Data Structure Types

• Linear Data Structure: Elements are arranged sequentially, with each element linked to its previous and next adjacent elements.

  • Static Data Structure: Fixed memory size; easy to access elements. Example: Arrays
  • Dynamic Data Structure: Size is not fixed; can be updated during runtime. More efficient regarding memory (space) complexity. Example: Linked Lists, Queues, Stacks

• Non-Linear Data Structure: Elements are not arranged sequentially.

  • Tree: Non-linear and hierarchical; elements are arranged in a tree-like structure with a root node. Elements are connected by nodes. Example: Binary Tree, AVL Tree
  • Graph: Non-linear; consists of vertices (or nodes) and edges that connect a pair of nodes/vertices. Used to solve complex programming problems.

Data Structures - Arrays

• Arrays are a collection of items stored in contiguous memory locations.
• They allow relatively fast processing of large amounts of data.
• The first element of the array is indexed by 0.

Data Structures - Stacks

• A stack is a linear data structure that follows the LIFO (Last-In, First-Out) principle.
• Operations like pushing (entering data) and popping (retrieving data) are performed at the top of the stack.

Data Structures - Queues

• A queue is a linear data structure that follows the FIFO (First-In, First-Out) principle.
• Data is added to the rear (Enqueue) and removed from the front (Dequeue).

Data Structures - Linked Lists

• A linked list is a linear data structure where elements are not stored in contiguous memory.
• Elements are linked using pointers.

Data Structure Operations

• Navigating: Accessing each data element exactly once.
• Searching: Finding the location of a specific data element.
• Insertion: Adding a new data element to the structure.
• Deletion: Removing a data element.
• Sorting: Arranging data in a specific logical order (ascending/descending).
• Merging: Combining data elements from two or more data structures into one.

What is an Algorithm?

• An algorithm is a step-by-step procedure for solving a problem in a finite amount of time.
• It takes input, follows a sequence of steps, and produces output.

What is a Good Algorithm?

• A good algorithm must be correct, finite (in terms of time and size), terminate, unambiguous, and efficient (space and time).

What is Complexity?

• Complexity measures how difficult a problem or a solution is.
• Time Complexity: How long an operation takes to execute on a data structure (e.g., insertion, deletion, searching, sorting).
• Space Complexity: How much memory or storage is required to store a data structure.
• Both time and space complexity are dependent on the input size (n).

Measurement of Complexity of an Algorithm

• Best-Case Analysis (Ω-notation): Lower bound on the running time of an algorithm (minimum number of operations).
• Worst-Case Analysis (O-notation): Upper bound on the running time (maximum number of operations).
• Average-Case Analysis (Θ-notation): Average time considering all possible inputs.

Big O Notation

• Big O notation is a standardized way to describe the efficiency of algorithms in terms of their worst-case performance.
• It expresses the growth rate of the running time or space complexity as the input size (n) increases.
• Common complexities (from most to least efficient): O(1), O(log n), O(n), O(n log n), O(n^2), O(2^n), O(n!).

Time Complexity Examples

• O(1): Constant time (e.g., accessing an array element by index).
• O(log n): Logarithm time (e.g., binary search).
• O(n): Linear time (e.g., traversing an array).
• O(n log n): Log-linear time (e.g., merge sort).
• O(n^2): Quadratic time (e.g., nested loops).
• O(2^n): Exponential time (e.g., some recursive algorithms).
• O(n!): Factorial time (e.g., some very complex combinatorial problems).

Explore the fundamental concepts of data structures, including linear and non-linear types. Learn about key examples like arrays, linked lists, trees, and graphs. This quiz will enhance your understanding of how data is organized for efficient access and modification.