In this particular team of excercises, I've had to implement 2 introductory type of problems, and one problem of constraints.
In the first directory of this team, I've implemented a program who takes as input a matrix (which is a list of lists), and it gives us back the Upper and Lower Diagonals of this very Matrix.
Example:
Given a matrix L:
| a | b | c | d |
|---|---|---|---|
| e | f | g | h |
| i | j | k | l |
- DiagsDown = [[i],[e,j],[a,f,k],[b,g,l],[c,h],[d]]
- DiagsUp = [[a],[b,e],[c,f,i],[d,g,j],[h,k],[l]]
?- diags([[a,b,c,d],[e,f,g,h],[i,j,k,l]],DiagsDown,DiagsUp).
In the second directory if this team , the task was to implement the Hopfield's Formula.
So here, our program takes as input the training vectors, and returns back the "weight" of the network. This task was most about matrix addition, substraction, inversion and multiplication.
?- hopfield([[+1,-1,-1,+1],[-1,-1,+1,-1],[+1,+1,+1,+1]],W).
Answer: W = [[0,1,-1,3],[1,0,1,1],[-1,1,0,-1],[3,1,-1,0]].
In the third and the most demanding excercise in this team of homeworks, we had to implement a constraint problem.
Consider that in an entertainment space there are specific electronics games, in which you can play in a given order. You start with first, continue to the second, and so on, until the last. Every game you can play it more than once, but all will be consecutive.
To play a game once, you have to pay a chip. Your chips are in a box, which has a capacity of T chips, which initially it is full. After completing all the times a game has been played, and before you start the next, you are given a gift of K chips, or less, and however, no more than can fit in your box.
Every time you play game i, your pleasure is P_i.
The pleasure of a game it can also be negative, which means that you did not like the game, or zero, which means that your game is indifferent.
The question is, considering of T, K and P_i, how many times you have to play each game in order to finally have the maximum overall pleasure.
You have to play every game at least once so you can find out how much you like it.
So, given {Ps, T, K}, you must find the list(s) Gs, which contains the number of times for each game (inside of Ps), and the P which is equal to the final pleasure of this combination of games.
?- games([4,1,2,3],5,2,Gs,P)
Answer: Gs = [5,1,1,4] and P = 35.
?- games([2,-3,4,1,-2,2,1],8,3,Gs,P).
Answer: Gs = [5,1,8,1,1,7,3] and P = 55.
In this group of exercises, we dealt exclusively with the problems of satisfying constraints and minimizing/maximizing objective functions. To do this, we've utilized the power of the ic and ic_global's library.
A two-dimensional black and white image is scanned horizontally, vertically, and diagonally (in its descending and ascending diagonals) and is coded based on the numbers of black pixels in each row, each column, each descending diagonal and any ascending diagonal.
We defined a decode/4 predicate, which accepts as arguments the number of black pixels for:
- Rows
- Columns
- Desceding and Asceding diagonals
In order to decode the image.
?- decode([1,1,10,11,10,1,1],[3,3,3,3,3,3,3,5,5,3,1], [0,0,1,2,3,3,3,4,3,4,3,3,2,4,0,0,0], [0,0,1,2,3,3,3,4,3,4,3,3,2,4,0,0,0]).
It's the same exercise as the third in ../A_Team/games.pl.
We just changed the approach of this exercise (we utilized the ic library).
In this exercise, we had to find the best possible combination (this with the minimum cost) of flights.
?- member(I,[1]), write('I = '), writeln(I), flights(I,Pairings,Cost), write('Pairings = '), writeln(Pairings), nl, fail.
Answer: I = 1 Pairings = [[1, 2, 3, 7] / 10, [5, 8] / 12, [4, 9, 10] / 34, [6] / 34] Cost = 90
In this exercise, we solved a heterogeneous capacitated vehicle routing problem.
?- hcvrp(3, 2, 0, Solution, Cost, Time). Found a solution with cost 485874 Found a solution with cost 476394 Found no solution with cost 0.0 .. 476393.0
Answer: Solution = [[3], [2, 1]] Cost = 476394 Time = 0.0
This project is part of the course: Logic Programming , Spring of 2021. University of Athens, DiT.