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Xavier Geerinck

Sorting Algorithm - Merge Sort

Sorting Algorithm - Merge Sort

Merge Sort is a comparison algorithm that tries to sort the dataset by a Divide And Conquer method. The performance of this algorithm is $O(n*log(n))$. How We start by splitting the array up into separate elements, then we start by merging pairs together and we make sure

Sorting Algorithm - Insertion Sort

Sorting Algorithm - Insertion Sort

Insertion sort is the core algorithm to know, it is also the easiest to understand and implement. The disadvantages however are that it is horribly slow. The recommendation is to use this algorithm when you are sorting really small tables (< 10). Insertion Sort is also used as the base

Sorting Algorithm - Heap Sort

Sorting Algorithm - Heap Sort

Heap Sort Heap sort works by using the heap datastructure. This sorting algorithm has a performance of $O(n*log(n))$ which makes it fast. How Heapsort works by first creating the heap datastructure, so let's say we have an array, it will then convert this array into

Solving a Sudoku with Discrete Math

Solving a Sudoku with Discrete Math

Solving a Sudoku is not an easy task, not for humans and even a computer can struggle with it if it has to go through each combination and try brute forcing the puzzle without any clue. Lucky for us we are able to tackle this problem by using Discrete Math

Fields - Prime Fields

Fields - Prime Fields

This post is about the discrete math that is being taught at the University Ghent for people attending the Bridge program to Master Of Science in Industrial Engineering (IT). In this program we learned about 3 specific sub-groups of Discrete Mathematics: * Fields * Graphs * Groups In this post I will summarise

Fields - Galois Fields

Fields - Galois Fields

1 Galois Fields 1.1 Construction of Galois Fields A Galois field has a finite amount of numbers and is written as GF(q) or Fq. Where q = pn. When knowing all this we can now construct a Galois Field with n dimensions and p elements. Example: When we want

Fields - Elliptical Curves Over Finite Fields

Fields - Elliptical Curves Over Finite Fields

1.1 Weierstrass Equations 1.1.1 Introduction A weierstrass equation is an elliptical curve with a collection of points (x, y) (xεF and yεF) and is of the third grade with the form: $$ y^2 + a1xy + a3y = x^3 + a2x^2 + a4x + a6, ai\epsilon F $$ and ∞ always added