Data Structures and Algorithms Cheat Sheet
Big-O and Theta Notation
1 < log n < (log n)² < n < n log n < n² < n²log n < n³ < 2ⁿ
- Θ (Theta): Tight bound/actual growth.
- O (Big-O): Upper bound/worst-case.
- Ω (Omega): Lower bound.
Note: Ignore constants and smaller terms. Example: 3n²+5n+1 = Θ(n²)
Loop Complexity Rules
- i++ or i=i+2: O(n)
- i=i*2 or i=i/2: O(log n)
- Nested loops: Multiply complexities (e.g., O(n log n)).
- Sequential loops: Add complexities (e.g., O(n) + O(log n) = O(n)).
Universal Loop Analysis
“Outer loop
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1. Algebraic System
An algebraic system is a non-empty set together with one or more operations (like addition or multiplication) defined on it.
Example: A set AAA with an operation ∗*∗ is written as (A,∗)(A, *)(A,∗).
2. Semigroup
A semigroup is a set SSS with a binary operation ∗*∗ that is associative:
(a∗b)∗c=a∗(b∗c),∀a,b,c∈S(a * b) * c = a * (b * c), \quad \forall a,b,c \in S(a∗b)∗c=a∗(b∗c),∀a,b,c∈S
3. Monoid
A monoid is a semigroup that has an identity element eee,
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BASIC DEFINITIONS
Static Website
Fixed content, same for all users, no server processing
Dynamic Website
Content changes based on user/data, uses backend
Web Application
Interactive software running in browser (like Gmail)
Frontend vs Backend
Frontend → UI (HTML, CSS, JS)
Backend → Server, database, logic
Full Stack Development
Working on both frontend + backend
SPA (Single Page Application)
Loads one page, updates content dynamically
Advantages of SPA
Fast, smooth UX, less reload, better performance
🔹 NODE.
Read MoreNatural Language Processing: Meaning Representation and Parsing
1. Meaning Representation in NLP
Meaning representation in Natural Language Processing (NLP) refers to the process of converting natural language into a formal structure that a machine can understand and reason about. It involves representing the semantics of words, phrases, and sentences using logical forms, semantic networks, frames, or predicate logic. The goal is to capture the intended meaning of a sentence rather than just its syntactic structure.
The need for meaning representation arises because
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Regression and Segmentation are two important analytical approaches used in data science. Regression is used to predict continuous numerical values, such as sales, profit, or temperature. It establishes a relationship between dependent and independent variables. On the other hand, Segmentation (often linked with clustering) is used to group similar data points into distinct categories based on patterns, such as customer segmentation in marketing.Supervised and Unsupervised learning are the two main
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Data Architecture and Analytics Fundamentals
- Data Architecture: The structured design of data systems, defining collection, storage, integration, and management for efficient use.
- Sensor Data: Information collected automatically from devices measuring physical conditions like temperature, pressure, motion, or environmental changes.
- Outliers: Data points significantly different from other observations, often caused by errors, variability, or rare, unusual events.
- Duplicate Data: Repeated records within