Local Extremas and Nesterov Accelerated Gradient

Python. To find a global minimum for a selected function, I compared brute force sweeping with Nesterov Accelerated Gradient (NAG)optimisation technique. By applying a small deltaX increments, I obtained local extremas in the range of […]

Arc Length by Simpson’s Rule

C++. I applied Simpson’s rule to the integral in the Arc length formula to get an approximate length of a quadratic equation curve. To do that, I applied Simpson rule by  sweeping small increments on […]

Curve Point Distribution

Python.  This implementation’s purpose is to distribute a desired number of points on the curve by equal path distance to each other. To do that, I applied an adaptable unit length strategy while trying to […]

Latitude Point Distribution

C++. This is for symmetrical distribution of points in each latitude on a sphere. As an input, different number of points for each latitude can be assigned. Top and bottom coordinates, of course, are the […]

Top Cut of Convex Hull

C++. I developed an algorithm based on “three penny algorithm” to find the top cut of a convex hull for dense circle shaped data. It takes the most left point as an entry point like Jarvis’s […]

Deepest Pit

C++. This is a question from Codility. Question: A non-empty zero-indexed array A consisting of N integers is given. A pit in this array is any triplet of integers (P, Q, R) such that: 0 ≤ P < […]

Totient Function

C++. This is the problem 69 from Project Euler. Question: Euler’s Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to […]

Pell Equation

C++. This is the problem 66 from Project Euler. Question: Consider quadratic Diophantine equations of the form:  x2 – Dy2 = 1 For example, when D=13, the minimal solution in x is 6492 – 13×1802 = 1. It can be assumed that there […]

Pentagonal Numbers

C++. This is the problem 44 from Project Euler. Question: Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are: 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, … It […]