Computer Science

Algorithms, complexity, automata, number representation and digital logic.

• How to Interpret SVD in Text Mining and Topic Analysis
  SVD represents a term-document matrix using latent directions, allowing you to interpret reduced dimensions as broad textual themes.
• Fast 2D Line–Triangle Intersection Test
  Test whether an infinite 2D line intersects a triangle using three cross products, without calculating an intersection point or dividing.
• Which Discrete Mathematics Books Are Best for Computer Science Self-Study?
  For computer science self-study, compare Rosen, Epp, and MIT's free Mathematics for Computer Science, then choose one book and work its exercises.
• How to Compute the Modular Inverse in Elliptic-Curve Addition
  For elliptic-curve addition over a prime field, invert the coordinate difference modulo p with the extended Euclidean algorithm—not ordinary division.
• How to Build a Logic Circuit in Conway’s Game of Life
  Conway’s Game of Life can compute with moving patterns such as gliders; design a Boolean circuit first, then implement and test its signal interactions.
• Can an NFA Reach Two Final States at the Same Time?
  An NFA can have multiple accepting states reachable after the same input. Acceptance requires at least one successful path, not a unique final state.
• What Is the Boolean Expression for a 3-Input XOR Gate?
  A 3-input XOR outputs 1 for odd-parity inputs. Its expression is A XOR B XOR C, or A'B'C + A'BC' + AB'C' + ABC.
• How Do Brackets Work in Boolean Algebra’s Distributive Laws?
  Learn how parentheses group Boolean expressions, when to distribute AND or OR, and how to simplify bracketed expressions without changing their value.
• What Does a 3-Input XOR Gate Do?
  A 3-input XOR outputs 1 when an odd number of inputs are high. See its truth table, Boolean expression, and two-gate implementation.
• How to Write Pseudocode in Markdown and Export It to PDF
  Use a fenced code block for plain pseudocode, or embed a LaTeX algorithm environment in Pandoc Markdown for a numbered, structured PDF algorithm.
• How to Apply Alpha-Max-Beta-Min to Three Numbers
  The two-input alpha-max-beta-min formula does not directly extend to three values; sort their magnitudes and include the middle value.
• How to Convert a Number to Binary
  Use repeated division by 2 for the integer part and repeated multiplication by 2 for the fraction, then normalize and round for IEEE 754.
• Can Any NFA Be Converted to a DFA?
  Yes. Every finite NFA has an equivalent DFA; the subset construction tracks sets of possible NFA states, with up to 2^n DFA states.
• Why Is There a Conflict Between UTF-8 and ANSI Encoding?
  UTF-8 and “ANSI” are not competing text formats: encoding mismatches happen when software decodes bytes using the wrong code page. Learn how to diagnose and fix them.
• How to Create an Algorithm for Solving a Rubik’s Cube
  A Rubik’s Cube solver needs a cubie-state model, legal move tables, and a search strategy such as IDA* with pattern databases.
• How to Find the Mantissa in a Floating-Point Binary Number
  To find a floating-point mantissa, split the IEEE 754 fields, restore the implicit leading bit for normal values, and account for subnormals.
• How Does the Closest-Pair-of-Points Algorithm Work?
  The divide-and-conquer closest-pair algorithm finds the nearest two points in 2D in O(n log n) time by checking a narrow strip after each split.
• How to Get a Simplified Sum of Products from a Truth Table
  Write the canonical SOP from the rows where the output is 1, then simplify with Boolean algebra or a Karnaugh map. Fully worked 3-variable example.
• Insertion Sort Average Case – Comparisons, Shifts and Θ(n²)
  Derivation of insertion sort's average case on a random permutation, about n²/4 comparisons and shifts, with the exact formula (n² + 3n)/4 − Hₙ.