Data Structures and Algorithm Design

Abstract class

A class that cannot be instantiated on its own and is meant to be subclassed. It can contain abstract methods that must be implemented by its subclasses.

Algorithm

a set of step-by-step instructions designed to perform a specific task or solve a particular problem, often used in programming and computational processes.

Array

a collection of elements identified by index or key, typically of the same data type, allowing for efficient access and manipulation of data.

Linked list

a linear collection of data elements, where each element points to the next, allowing for dynamic memory allocation and efficient insertions and deletions.

Stack

a data structure that follows the Last In First Out (LIFO) principle, where elements are added and removed from the same end, often referred to as the top.

Wrapper class

a class that encapsulates a primitive data type into an object, allowing methods to be used on it and enabling the use of the type in collection frameworks.

Comparable

A marker interface in Java used to define the natural ordering of objects, allowing them to be compared to each other.

Inheritance

A fundamental concept in object-oriented programming that allows a class to inherit properties and methods from another class, promoting code reusability and hierarchical relationships.

Interface

A reference type in Java that defines a contract of methods that implementing classes must provide, supporting multiple inheritance.

Generic

A programming construct that allows developers to write a class, interface, or method with a placeholder for types, enabling type-safe code and code reuse.

Static

A keyword in programming that indicates a member variable or method belongs to the class rather than any instance of the class, allowing access without creating an object.

Set

A collection of distinct elements or objects, written using braces {}.

Element

Single member of a set

Subset

A set whose elements are all contained within another set.

Union (A ∪ B)

A set containing all elements in either A or B.

Intersection (A ∩ B)

A set containing elements that appear in both A and B.

Difference (A − B)

Elements that are in A but not B.

Complement (Ā)

All elements not in A (with respect to a universal set).

Relation

A set of ordered pairs showing how elements of one set relate to another.

Function

A special relation where each input has exactly one output.

Reflexive Relation

Every element is related to itself.

Symmetric Relation

If a is related to b, then b is related to a.

Transitive Relation

If a is related to b and b to c, then a is related to c.

Equivalence Relation

A relation that is reflexive, symmetric, and transitive.

Summation (Σ)

Symbol for adding a sequence of numbers.

Product (Π)

Symbol for multiplying a sequence of numbers.

Floor (⌊x⌋)

The greatest integer ≤ x.

Ceiling (⌈x⌉)

The smallest integer ≥ x.

Mod (modulus)

The remainder after integer division.

Index

The position of an element within a sequence or array.

Recursion

A programming technique in which a function calls itself to solve smaller instances of a problem. It is often used to break down complex problems into simpler ones.

Recursive Call

The function invocation inside itself.

Stack Frame

Memory block created for each function call containing local variables and return address.

Big O Notation

Describes the upper bound of an algorithm's time or space complexity in the worst-case scenario, helping to analyze performance.