On Some Entertaining Applications of the Concept of Set in Computer Science Course

Abstract

Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an example is the demonstrated algorithm for solving the widespread nowadays "Sudoku" puzzle. This is made, because of the connection with the term set and putting it into practice in the programming. Using the so built program there are solved some combinatorial problems, connected to the Sudoku matrices.

On an algorithm for receiving Sudoku matrices

“…Using a computer program based on described in section 3 algorithms, we calculated that when n = 2, there are θ 2 = 288 number of 4 × 4 Sudoku matrices. This number coincides with our results obtained using other methods described in [12]. In [3], it has been shown that there are exactly θ 3 = 9!…”

Random Permutations, Random Sudoku Matrices and Randomized Algorithms

“…When n = 2 σ 2 = 288 [12]. When n = 3, there are exactly σ 3 = 6 670 903 752 021 072 936 960 ≈ 6.671 × 10 21 in number Sudoku matrices [2].…”

“…. , n do begin 3) k := p st ; 4) l := p n+t s ; 5) We obtain n × n matrix A st = (a ij ) n×n such that a kl = 1 and a ij = 0 in all other occasions; end; 6) We obtain matrix A according to formula (12); Let s ∈ Z n = {1, 2, . .…”

“…A proof that a popular Sudoku puzzle is NP-complete is given in [10] and [11]. How to create computer program for Sudoku solving, using the concept set combined with the trial and error method is described in [12].…”

The Bitwise Operations in Relation to the Concept of Set

“…If 𝑘𝑘 bits are necessary for the integer type in the programming environment, then � 𝑚𝑚 𝑘𝑘 � + 1 variables of that certain type will be necessary, so as to put the above mentioned ideas into practice, where ⌊𝑥𝑥⌋ denotes the function "the whole part of 𝑥𝑥". For example, when 𝑛𝑛 ≤ 5, four bytes (thirty-two bits) are necessary to write a program that can solve a Sudoku puzzle in the size of 𝑛𝑛 2 × 𝑛𝑛 2 if we use the set theory method [15]. In this case, every set of the kind 𝐴𝐴 = {𝛼𝛼 1 , 𝛼𝛼 2 , .…”