Problems and Algorithms

Persisting state on a static site, for free.

Motivation Let’s explore how we can simulate physical phenomena in Python by building everything from scratch, step by step.

Background \[(x \lor \neg y) \land (\neg x \lor y) \land (\neg x \lor \neg y) \land (y \lor z)\] While (SAT) is generally NP-complete, meaning no efficient algorithm is known to solve it for all cases, 2-SAT, a special case of SAT where each clause contai…

Summary In Building Ads Optimization we explored the process of building ads optimization and highlighted common pitfalls from an intuitive perspective.

Summary I’ve observed many companies struggle to build a successful ads revenue business.

Motivation Let’s take a look at how we multiply two polynomials of degree \(N\): \[\begin{align*} f(x) &= 4x^{4}-2x^{3}-6x^{2}\ +4x\ +\ 3\\ g(x) &= -x^{4}+11x^{3}-9x^{2}+-1x\ +\ 6\\ \end{align*}\] We can use the distributive property to multiply two polyn…

The Chaos Game The Sierpiński triangle is a famous fractal with many interesting properties.

Puzzle You are a single point in a square room and all the walls are mirrors.

Introduction Fibonacci Numbers form a sequence in which each number is the sum of the two preceding ones, defined recursively as: \[\begin{equation*} \begin{aligned} &F(0) = 0\\ &F(1) = 1\\ &F(n) = F(n-1) + F(n-2) \end{aligned} \end{equation*}\] We would…

Problem Inversions Find the number of permutations of \({1,2,...,N}\) with exactly \(K\) inversions (modulus \(2\)).