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‎algorithms/BFS.md

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title: Breadth First Search Algorithm Implementation and Analysis
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category: algorithms
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category: Algorithms
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tags: graph-traversal, shortest-paths, graph-theory, complexity-analysis
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description: A comprehensive explanation of the Breadth First Search (BFS) algorithm, including implementation, complexity analysis, and mathematical proofs. The document covers the algorithm's properties for finding shortest paths in graphs and includes Python implementations with detailed theoretical foundations and lemmas about level ordering.
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‎algorithms/DAGs.md

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title: Topological Ordering and Properties of Directed Acyclic Graphs
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category: algorithms
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category: Algorithms
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tags: graph theory, topological sorting, directed acyclic graphs, proofs
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description: A technical exploration of Directed Acyclic Graphs (DAGs) focusing on their topological ordering properties and fundamental lemmas. The document includes mathematical proofs of key DAG properties and presents a Python implementation of the topological sorting algorithm.
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‎algorithms/DFS.md

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title: Depth First Search Algorithm and Tree Properties
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category: algorithms
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category: Algorithms
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tags: graph theory, depth first search, spanning trees, graph traversal
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description: A technical explanation of Depth First Search (DFS) algorithm and its tree properties, including both recursive and iterative implementations. The document covers key properties of DFS trees, including the ancestor-descendant relationship of non-tree edges, and includes a formal lemma and proof about DFS tree characteristics.
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‎algorithms/approximation-algorithms.md

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title: Approximation Algorithms
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category: algorithms
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category: Algorithms
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tags: approximation, algorithms, vertex cover, set cover
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description: A survey of approximation algorithms, including the 2-approximation for vertex cover and the log(n) approximation for set cover.
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‎algorithms/connected-components.md

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title: Finding Connected Components in Undirected Graphs Using BFS/DFS
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category: algorithms
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category: Algorithms
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tags: graph theory, connected components, breadth-first search, depth-first search
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description: Explains how to partition an undirected graph into connected components using BFS or DFS algorithms in O(|V| + |E|) time complexity. Includes Python implementation using adjacency lists and demonstrates how to create a data structure that enables O(1) time queries for path existence between vertices.
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q.append(v)
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curr_label = 0
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for v in range(len(graph)):
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bfs(curr_label, graph, v)
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curr_label += 1

‎algorithms/divide-and-conquer.md

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title: Divide and Conquer Algorithm Analysis with Implementation Examples
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category: algorithms
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category: Algorithms
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tags: divide-and-conquer, algorithmic-complexity, recursive-algorithms, computational-geometry
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description: A comprehensive examination of divide and conquer algorithmic strategies, focusing on their implementation and analysis. The document covers theoretical foundations with mathematical proofs, practical examples including bisection method and closest pair problem, and includes Python implementations demonstrating these concepts.
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‎algorithms/dynamic-programming.md

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title: Dynamic Programming Algorithms and Problem Solutions Guide
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category: algorithms
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category: Algorithms
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tags: dynamic-programming, optimization, algorithm-analysis, problem-solving
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description: A comprehensive guide covering various dynamic programming algorithms and their implementations, including knapsack, sequence alignment, and tree-based problems. Includes detailed explanations of problem-solving approaches, correctness proofs, and runtime analysis for each algorithm, with practical Python implementations.
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‎algorithms/patterns/BFS.md

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title: Spring Boot Quickstart Guide
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category: software-engineering
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category: Software Engineering
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tags: spring boot, quick start, spring web, rest repositories
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description: A step-by-step guide to creating a Spring Boot application with Rest Repositories
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---
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---
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title: Breadth First Search Pattern
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category: algorithms
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category: Algorithms
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tags: breadth-first search, graph algorithms, graph traversal, shortest path
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description: A technical exploration of the Breadth First Search algorithm, focusing on its key properties and applications in graph problems.
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‎algorithms/patterns/sliding-window.md

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title: Sliding Window Pattern
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category: algorithms
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category: Algorithms
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tags: sliding window, fixed size window, dynamic size window, streaming algorithms, array problems, contiguous subarray, linear data structure
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description: A technical exploration of the sliding window pattern in algorithms, focusing on its applications and variations.
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Dynamic size windows often involve more complicated logic within each iteration, since at any given step you need to decide whether to expand or contract the window, on top of how to update the window state for each case.
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A typical algorithm might look like this:
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## Practice Problems

‎algorithms/practice/4.md

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title: Interval Sum Counting Algorithm
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category: algorithms
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category: Algorithms
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tags: interval sums, binary search, prefix sum, suffix sum
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description: An algorithm for counting the number of interval sums between a given range in an array of intervals.
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‎algorithms/problems/graphs-and-trees.md

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title: Graphs and Trees
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category: algorithms
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category: Algorithms
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tags: graphs, trees, induction, proof by contradiction, cycle detection
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description: A technical exploration of graphs and trees focusing on the properties and proofs of these fundamental data structures.
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---

‎cheatsheets/algorithms/divide-and-conquer.md

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title: Divide and Conquer Algorithms
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category: algorithms
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category: Algorithms
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tags: divide and conquer, master theorem, root finding, bisector algorithm, kth smallest element
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description: A technical exploration of Divide and Conquer algorithms focusing on the Master Theorem, Root Finding, and kth Smallest Element problems.
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‎cheatsheets/algorithms/graphs.md

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title: Graph Theory
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category: algorithms
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category: Algorithms
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tags: Graphs, Trees, DFS, BFS, Topological Sort, Minimum Spanning Tree, Disjoint Sets
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description: A comprehensive overview of graph theory, including concepts such as nodes, edges, trees, and minimum spanning trees, as well as algorithms like depth-first search and breadth-first search.
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‎cheatsheets/algorithms/intervals.md

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title: Interval Scheduling/Partitioning
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category: algorithms
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category: Algorithms
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tags: greedy algorithms, interval partitioning, scheduling, time complexity
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description: A technical exploration of Interval Scheduling and Partitioning focusing on their greedy algorithm properties and structural analysis.
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‎cheatsheets/circuits/components.md

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title: Electronic Components
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category: hardware
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category: Hardware
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tags: Transistors, Op-Amps, Filters, Amplifiers, Comparators
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description: A comprehensive overview of electronic components used in electronics devices, including Transistors, Op-Amps, Filters, Amplifiers, and Comparators.
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## DC Sources
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Direct current sources are sources that provide a constant voltage or current. Batteries are a common example of a DC voltage source. If you graph the voltage over time, it's a flat line.
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Direct current sources are sources that provide a constant voltage or current. Batteries are a common example of a DC voltage source. If you graph the voltage over time, it's a flat line.
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Voltage sources supply the required current to maintain a constant voltage, and current sources supply the required voltage to maintain a constant current.
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‎cheatsheets/circuits/electricity.md

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title: Electric Circuit Analysis
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category: electrical-engineering
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category: Electrical Engineering
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tags: Electrical Engineering,Circuits,Ohms Law,Kirchoffs Laws,Impedance,AC Circuits,DC Circuits,Power,Energy
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description: In-depth analysis of electric circuits, including short and open circuits, Ohm's law, Kirchoff's laws, impedance, power, and energy. A comprehensive guide for electrical engineers and students.
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Electricity, being the flow of electrons, is similar to many other types of flow. For prosperity, engineers use **conventional current**, a bad theory made long ago that positive charges flow from high potential to low potential. In reality, electrons are negatively charged and flow from low potentials to high potentials.
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**Potential**? What's that? It's the energy per unit charge at a point in space. It's measured in volts, and is the driving force behind the flow of electricity. From this point on I'll refer to potential as voltage, like a true engineer.
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**Potential**? What's that? It's the energy per unit charge at a point in space. It's measured in volts, and is the driving force behind the flow of electricity. From this point on I'll refer to potential as voltage, like a true engineer.
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If you're smooth brained like me, it helps to think of it as similar to potential energy of balls on a track, but for electrons. A higher voltage means the electron has a long way to fall. This model only takes you so far, but it helps as a mental model for characterizing the behavior of electricity.
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If potential is the driving factor behind the flow of electricity (like gravity), then **current** is the magnitude of the flow itself (like throughput). It's measured in amperes (A, Amp), which is a compound unit of charge per unit time.
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If potential is the driving factor behind the flow of electricity (like gravity), then **current** is the magnitude of the flow itself (like throughput). It's measured in amperes (A, Amp), which is a compound unit of charge per unit time.
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Finally, **resistance** is the opposition to the flow of electricity. It's measured in ohms ($\Omega$), and can be thought of as anything that drops the voltage (like a hill or friction for potential energy) when current flows through it.
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$$ = V_m \angle \phi = V_m e^{j\phi}$$
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## Series vs. Parallel
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## Series vs. Parallel
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### Series
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‎cheatsheets/java-spring-boot/reference.md

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title: Spring Boot Annotations
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category: software-engineering
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category: Software Engineering
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tags: spring-boot, annotations, java, configuration
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description: A documentation on the Spring Boot annotations used for configuration, auto-configuration, component scanning, and more.
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‎cheatsheets/java-spring-boot/running.md

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title: Spring Boot Quickstart Guide
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category: software-engineering
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category: Software Engineering
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tags: spring boot, quick start, spring web, rest repositories
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description: A step-by-step guide to creating a Spring Boot application with Rest Repositories
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---

‎digital-design/combinational-logic.md

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title: Combinational Logic
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category: hardware
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category: Hardware
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tags: combinational logic, sequential logic, boolean algebra, logic gates, minimization
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description: Explains the concept of combinatorial logic, its differences with sequential logic, and various techniques for minimizing boolean expressions.
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‎digital-design/karnaugh-maps.md

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title: Karnaugh Maps
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category: hardware
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category: Hardware
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tags: karnaugh maps, truth tables, graph theory, computer science
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description: Method for simplifying Boolean expressions
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‎digital-design/quartus-workflow.md

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title: Developing FPGA Designs with Quartus and ModelSim
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category: hardware
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category: Hardware
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tags: Quartus, ModelSim, Verilog, testing process, modular design
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description: Describes a structured approach to testing and verifying digital circuits using Quartus and ModelSim.
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‎digital-design/sequential-logic.md

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title: Sequential Logic (SL)
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category: hardware
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category: Hardware
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tags: sequential logic, digital systems, finite state machines, flip-flops, clock signals
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description: Explains the concept of sequential logic in digital systems and its applications.
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‎digital-design/system-verilog.md

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title: SystemVerilog
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category: hardware
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category: Hardware
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tags: system-verilog, hardware, digital electronics, programming languages for hardware
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description: Programming language for describing hardware behavior, including modules, primitives, execution, and structural representation
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module AOI (F, A, B, C, D);
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output logic F; // each variable
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input logic A, B, C, D; // is 1-bit (logic)
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assign F = ~((A & B) | (C & D)); // continuous assignment
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output logic F;
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logic AB, CD, O; // now necessary
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and a1(AB, A, B);

‎digital-design/waveform-diagram.md

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title: Waveform Diagrams
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category: hardware
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category: Hardware
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tags: waveform diagrams, bit vectors, bus, circuit timing behavior
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description: Explains the concept of waveform diagrams in digital design, and how to use them to visualize the state of a system.
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// instance of module we want to test ("device under test")
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MUX2 dut (.V(V), .SEL(SEL), .I(I), .J(J));
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initial // build stimulus (test vectors)
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begin // start of "block" of code
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{SEL, I, J} = 3'b100; #10; // t=0: S=1, I=0, J=0 -> V=0

‎distributed-systems/RPC.md

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title: Remote Procedure Call (RPC)
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category: distributed-systems
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category: Distributed Systems
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tags: Distributed Systems, Communication, Concurrency
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description: A discussion on the challenges of message passing in a distributed system, including the two generals problem.
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‎distributed-systems/bigtable.md

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title: Bigtable, A Distributed Storage System for Structured Data
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category: distributed-systems
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category: Distributed Systems
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tags: Bigtable, Distributed Storage, Google
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description: A highly scalable, reliable, and fault-tolerant distributed storage system designed for structured data. Built by Google, it uses a combination of commodity hardware and software to provide low-latency, high-throughput access to large amounts of data.
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‎distributed-systems/clocks.md

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title: Clocks
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category: Distributed Systems
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tags: clocks, distributed systems, logical clocks, vector clocks, causality, consistency
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description: Explains the concepts of physical and virtual clocks in distributed systems, including their limitations and potential solutions.
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‎distributed-systems/consistency.md

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title: Distributed Systems Consistency Models
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category: other
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category: Distributed Systems
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tags: Consistency Models,Paxos,Linearizability,Sequential Consistency,Snapshot Reads,Causal Consistency,Processor Consistency,Memory Barrier/Fence
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description: This document discusses various consistency models used in distributed systems, including Paxos, linearizability, sequential consistency, snapshot reads, causal consistency, processor consistency, and memory barriers. It explains the differences between these models and when to use them.
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## Types of Consistency
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| Type | Description |
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| Strong Consistency | The system behaves as if there is a single server. Systems that maintain a single consistent log of operations are often strongly consistent. |
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| Weak Consistency | Definitions vary, but basically just *not* strong consistency. |

‎distributed-systems/consistent-global-state.md

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title: Consistent Global State in Distributed Systems
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category: Distributed Systems
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tags: consistent global state, distributed systems, global predicate evaluation, asynchronous distributed systems
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description: Explains the concept of maintaining a consistent global state in distributed systems and its implications.
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‎distributed-systems/disconnected-operation.md

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title: Disconnected Operation
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category: distributed-systems
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category: Distributed Systems
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tags: disconnected operation, distributed systems, conflict resolution, eventual consistency
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description: Explains the concept of disconnected operation in distributed systems and its implications.
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‎distributed-systems/distributed-cache-coherence.md

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title: Linearizable Caches
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category: Distributed Systems
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tags: Cache Coherence, Consistency Models, Distributed Systems
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description: A linearizable cache is a cache that provides strong consistency guarantees for reads and writes. It is a type of cache coherence protocol that ensures all copies of data are consistent with each other, even in the presence of failures or network partitions.
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‎distributed-systems/dynamo-db.md

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title: Dynamo: Amazon's Highly Available Key-value Store
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category: database-systems
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category: Distributed Systems
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tags: key-value store, database-design, high-availability, consistency, object-versioning, conflict-resolution
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description: A highly available key-value storage system sacrificing consistency under failure conditions, using object versioning and application assisted conflict resolution.
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‎distributed-systems/google-file-system.md

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title: Google File System (GFS) Overview
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category: distributed-systems
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category: Distributed Systems
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tags: Cloud Storage, Distributed Systems, Google Cloud
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description: An overview of the Google File System (GFS), a highly scalable and fault-tolerant distributed storage system designed to handle large amounts of data across many commodity hardware nodes.
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‎distributed-systems/load-balancing.md

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title: Load Balancing
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category: distributed-systems
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category: Distributed Systems
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tags: load balancing, distributed systems, paxos, sharding, edge caching, queueing, zipf distribution
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description: Explains load balancing strategies and their implications on distributed systems.
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‎distributed-systems/managing-critical-state.md

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title: Distributed Systems Consistency Models
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category: distributed-systems
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category: Distributed Systems
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tags: Consistency Models,Paxos,Linearizability,Sequential Consistency,Snapshot Reads,Causal Consistency,Processor Consistency,Memory Barrier/Fence
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description: This document discusses various consistency models used in distributed systems, including Paxos, linearizability, sequential consistency, snapshot reads, causal consistency, processor consistency, and memory barriers. It explains the differences between these models and when to use them.
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title: Distributed Consensus Fundamentals
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category: distributed-systems
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category: Distributed Systems
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tags: Distributed Systems, Consensus Algorithms
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description: This document covers the fundamentals of distributed consensus algorithms, including leader election, replicated state machines, reliable datastores, and coordination services.
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‎distributed-systems/mutual-exclusion.md

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title: Distributed Mutual Exclusion
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category: distributed-systems
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category: Distributed Systems
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tags: distributed systems, mutual exclusion, locking, ordering, consistency
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description: Explains a distributed mutual exclusion algorithm using timestamps and sequence numbers.
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‎distributed-systems/non-blocking-two-phase-commit.md

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title: Non-Blocking Two Phase Commit
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category: distributed-systems
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category: Distributed Systems
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tags: paxos, two-phase commit, distributed transactions, consistency models
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description: Explains the concept of non-blocking two phase commit using Paxos
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