Data Structures Overview

Study Notes

A data structure is a way to organize and store data in a computer so that it can be efficiently accessed, modified, and manipulated.
Data structures provide a means to manage and utilize data in a program.

Arrays: A collection of elements of the same data type stored in contiguous memory locations.
Linked Lists: A dynamic collection of elements, where each element (node) points to the next node.
Stacks: A Last-In-First-Out (LIFO) data structure, where elements are added and removed from the top.
Queues: A First-In-First-Out (FIFO) data structure, where elements are added to the end and removed from the front.
Trees: A hierarchical data structure, where each node has a value and zero or more child nodes.
Graphs: A non-linear data structure, where nodes are connected by edges.

Computational complexity is the study of the resources required to solve a computational problem.
It is concerned with the amount of time and space (memory) required to execute an algorithm.

Big O notation: A mathematical notation that describes the upper bound of an algorithm's complexity.
Time complexity: The amount of time an algorithm takes to complete, usually measured in terms of the number of operations.
Space complexity: The amount of memory an algorithm requires, usually measured in terms of the number of bytes.

Constant time complexity (O(1)): The algorithm takes the same amount of time regardless of the input size.
Linear time complexity (O(n)): The algorithm takes time proportional to the input size.
Quadratic time complexity (O(n^2)): The algorithm takes time proportional to the square of the input size.
Exponential time complexity (O(2^n)): The algorithm takes time proportional to 2 raised to the power of the input size.
Polynomial time complexity (O(n^k), k>0): The algorithm takes time proportional to the input size raised to a power.
Non-polynomial time complexity (O(a^n), a>1): The algorithm takes time proportional to a raised to the power of the input size.

Time-space tradeoff: An algorithm can be optimized for either time or space complexity, but not both.
Accuracy-efficiency tradeoff: An algorithm can be optimized for either accuracy or efficiency, but not both.

A data structure is a way to organize and store data in a computer, for efficient access, modification, and manipulation.
Data structures provide means to manage and utilize data in a program.

Arrays: Store elements of the same data type in contiguous memory locations.
Linked Lists: Dynamic collections of elements, where each element (node) points to the next node.
Stacks: Last-In-First-Out (LIFO) data structure, where elements are added and removed from the top.
Queues: First-In-First-Out (FIFO) data structure, where elements are added to the end and removed from the front.
Trees: Hierarchical data structure, where each node has a value and zero or more child nodes.
Graphs: Non-linear data structure, where nodes are connected by edges.

Computational complexity studies the resources required to solve a computational problem.
It is concerned with the amount of time and space (memory) required to execute an algorithm.

Big O notation: Mathematical notation that describes the upper bound of an algorithm's complexity.
Time complexity: Amount of time an algorithm takes to complete, usually measured in terms of the number of operations.
Space complexity: Amount of memory an algorithm requires, usually measured in terms of the number of bytes.

Constant time complexity (O(1)): Algorithm takes the same amount of time regardless of the input size.
Linear time complexity (O(n)): Algorithm takes time proportional to the input size.
Quadratic time complexity (O(n^2)): Algorithm takes time proportional to the square of the input size.
Exponential time complexity (O(2^n)): Algorithm takes time proportional to 2 raised to the power of the input size.
Polynomial time complexity (O(n^k), k>0): Algorithm takes time proportional to the input size raised to a power.
Non-polynomial time complexity (O(a^n), a>1): Algorithm takes time proportional to a raised to the power of the input size.

Time-space tradeoff: Algorithm can be optimized for either time or space complexity, but not both.
Accuracy-efficiency tradeoff: Algorithm can be optimized for either accuracy or efficiency, but not both.