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I am currently working on a procedurally generated game, and vaguely remember having read a book/paper/article in which it was said that there exists a published algorithm which can generate high quality game board games with a random set of rules, which are as good as human designed game board games. The algorithm was NOT limited to a single game such as Sudoku or Crossword puzzles, it rather would generate a set of rules for the players to play by, so it could potentially generate tic tac toe, checkers or 4 in-a-row wins and variations of all 3 games.
I think the article was published between 1980's and 2006ish
and that it was published in a journal.
Sadly I cannot remember where I read the article, only that it must've been in the last 8 months. If you know about this algorithm or something similar to it, please post.
Hi i have this Algorithm, could anyone help me figure out the answer to it, and how?
Create a recurrence function to represent the following algorithm's time complexity and use the master method to analyse the following algorithm:
/* The function f(x) is unimodal over the range [min, max] and can be evaluated in Θ(1) time
* ε > 0 is the precision of the algorithm, typically ε is very small
* max > min
* n = (max - min)/ε, n > 0, where n is the problem size */
if ((max - min) < ε)
return (max - min)/2 // return the answer
leftThird = (2 * min + max) / 3 // represents the point which is 1/3 of the way from min to max
rightThird = (min + 2 * max) / 3 // represents the point which is 2/3 of the way from min to max
if (f(leftThird) < f(rightThird))
return Algorithm(leftThird, max) // look for the answer in the interval between leftThird and max
return Algorithm(min, rightThird) // look for the answer in the interval between min and rightThird
If you are familiar with idle game or incremental games like Adventure Capitalist or Clicker Heroes you know that after a while you are dealing with very large numbers. If you are not aware basically you earn points in these games which you invest so that you can earn more points even quicker, rinse and repeat.
I wrote a small game of this style myself but didn't leave the range that a double couldn't handle but it did get me thinking on how to deal with extraordinarily large numbers.
Just to play around I figured a quick and easy way was to just keep a list with ints, each index represents a higher power and you can easily go higher if needed. index zero keeps numbers between 0-999 and index 1 then starts at 10^3. So index 5 would be ^7 etc.
Except for numbers 0-999 if you want to increase the number I have a function where you specify what number 1-9 you want to add and to which power. If you add say 9^5 to 3^5 it sorts this out by becoming 2^5 and 1^6.
So far I haven't accounted for subtraction yet in my little project but that should be fairly easy in a similar manner.
I think this shouldn't be too computationally heavy unless if used to run addition between several large lists.
Should I want to use this in a game I think it could also be easily adapted to use some approximation to reduce unnecessary work. For example if you have an entity in the game which adds 10^15 points per second and one that adds 10^3 and you show 5 decimals instead of doing all the background computations of adding those smaller numbers every second you just approximate how many seconds before they add as much so that it shows and then go from there if I made myself clear.
publicvoid AddNumber(intvalue, int power) // 10^3 = power1, 10^4 = power 2, 10^5 = power 3 etc.
if (power == 0)
NumberContainer += value;
while (NumberContainer >= 1000)
NumberContainer -= 1000;
} elseif(power < mPower)
NumberContainer[power] += value;
while( NumberContainer[power] >= 10)
NumberContainer[power] -= 10;
AddNumber(1, power + 1);
//power too large
publicstatic NumberControl operator +(NumberControl c1, NumberControl c2)
//set new maxpower to largest of the two
int mMaxp = c1.mPower;
if (c2.mPower > mMaxp) mMaxp = c2.mPower;
NumberControl nc = new NumberControl(mMaxp);
for(int i = 0;i < c1.NumberContainer.Count;i++)
for (int i = 0; i < c2.NumberContainer.Count; i++)
Here is how I add numbers. Thinking about this really got me wondering about how others would choose to solve it instead.
Number container is just a list.
I'm planning on profile how well it handles a few different scenarios, for example if you have a list that goes to the power of 100 and have say 80 "generators" which adds a number at different power levels each second how will it will hold out compared to if I approximate those that are smaller than a certain range from the biggest number.
Reading the numbers is done by specifying how many decimals I want shown and then just walk backwards in the list and adding to a string so unless I want full precision it also works fairly well.
Maybe but then it would need a bit more polish and I'm not sure it would fit, maybe a small blog post and carry with it some test results and discussion around it.
When I started thinking about how to solve this I had a nagging suspicion that there already was something readily available but I couldn't figure out what search terms to use to find it so I turned it in to code instead. That blog post was interesting I admire how some people can go so in-depth in a subject.
It may be a good idea to create a struct or class I'll call it LN which has a private vector with intergers VEC in the range of 0 to 9. The class has functions for Algebraic operations (+,-,*,/) to add two LN together. These functions must:
- determine the sizes of both VEC and resize accordingly.
- iterate though both VEC and execute the operation digit by digit.
Since vectors are dynamically allocated, you have virtually no cap on how many digits the number has (accept for RAM).
You'll have to replace all score related constant values in your code with LN's
I'm not sure how your game mechanics are designed, but if you have many hundreds of entities which add some constant value per second, it might be a good idea to have a single variable X which is added to the game score S every second, instead of iterating through all entities and adding the constant value to S. That is, when an entity is created, it adds it value per second constant E to X and when the entity is destroyed it subtracts E from X.
In every game step you then add X to S. This therefore only requires a single addition operation per game step and of course an addition operation when creating or destroying an entity.
i've got this homework problem which i tried to solve and didnt succeed so far. it goes like this:
Given k sets of integers A1,A2,..,Ak of total size O(n), you should determine whether exist a1A1, a2A2,...,akAk, such that a1+a2+..+ak-1 =ak. Your algorithm should run in Tk(n) time, where Tk(n) = O(n^(k/2)*log n) for even k, and O(n^((k+1)/2)) for odd values of k.
I have to implement 3 data compression algorithms. I was thinking about LZW, Deflate and Bzip2. I can't find any good documentation for these algorithms. Do you know any data compression algorithms with good documentation, samples etc.?
I find that extremely hard to believe. A TON of documentation and discussion comes up with a simple Google for "LZW compression algorithm" "Deflate compression algorithm" and "bzip2 compression algorithm".
If you were looking for copy'n'paste code, yeah, that's going to get you a failing grade in class.
Can anyone say which subjects and chapters in mathematics I need to know (thorough or basic) for learning algorithms? Also help me find a book on this mathematical subjects and a good book on algorithms for beginner?
The general definition of "algorithm", in simple terms, is: A sequence of instructions to solve a problem. I can write an algorithm for how to clean my house. Or for picking apples from a tree. Or for flying a plane. There are as many potential algorithms as there are ideas what to do in this world and the variety of required skills to handle all of them is vast. The same holds true when entering the domain of computer science: There are algorithms for all sorts of stuff. Obviously, logical thinking and some sense for numbers won't hurt. In fact, most algorithms I've come across should be understandable by non-computer scientists if only written down in normal language instead of a programming language. Of course there are algorithms for which you will need very specific mathematical knowledge but the intersection of required skills for understanding arbitrary algorithms remains as simple as: Logical thinking and some sense for numbers.
If the brain were so simple we could understand it, we would be so simple we couldn't. — Lyall Watson
I'm looking for an algorithm to find all the possible combinations of meetings (details in attached photo). I would like to introduce the teams algorithm calculates all threrefore combinations of matches, or better yet, I could enter the value to the team as the level of play by all the teams and I got all the options from the most probably
The problem at first seems to be simple but it is not, al least form me...
Have array/set/group of numbers,
I need to make groups of these numbers, so that each group has element(s) that sum is euqal or max close to certain value, for example 10. Of course I understand that there are lots of solutions, but I need only one.
So, for this set I should get:
A - 2,7,1 -> 10
B - 9,1 -> 10
C - 2,8 -> 10
D - 5,5 -> 10
E - 6,3 -> 9
F - 3 -> 3
of course this is one of possible solution, but I don't need super optimalization for this algorithm.
If anyone has some idea how to approach to this problem I would be very grateful for help.
You would have to extend that classical approach to allow sub-optimal group-solutions (where sum < 10 or maybe also where sum > 10 up to a certain maximum)*, temporarily store all potential overall-solutions and when the backtracking is done, pick the best based on some criteria that you have to define. E.g. where the sum of differences from 10 is smallest (would be 8 in your example). Or, as you don't need the best possible solution, you could cancel the process once a satisfactory overall-solution has been found.
* : Which means that the evaluation should continue even after finding a potential group-solution until exceeding the tolerable limit.
If the brain were so simple we could understand it, we would be so simple we couldn't. — Lyall Watson
I'd go for a rather simple implementation; sort the values, highest value first. In a loop, fetch a number from the array. Move right and keep adding numbers until you hit maximum. At maximum, fetch new number.
That's a rather blunt way of doing it though - backtracking would give a better result.
Bastard Programmer from Hell
If you can't read my code, try converting it here[^]
I'm a long time reader and lurker of codeproject articles in the Daily Build. I really enjoy that some articles are quite simple and as I've progressed through my career, I've been able to learn from more in-depth thoughtful articles. I'm wondering if anyone has a similar place for mathematics. It would be nice if the articles would come to my email, but I'd like for it to have a wide array of expertise. Also, I'm not looking for a question/answer site, but rather somewhere people can share their ideas and findings that are not quite at the level of novel academic research (i.e. I'd like to understand what I'm reading). Does anyone know of a place?
Rhode Island Hospital
Adam works in the in networking security cell. He wants to generate secret keys
following a pattern. The pattern consists of the characters X and Y.
where X means increasing and Y means decreasing. Help him devise an
algorithm to generate the secret key which is the minimum number encoded
following that pattern. Digits from 1-9 and digits can’t repeat.
Sample Input: Sample Output:
whenusing master theorem
i know that a = the number of subproblems
b = size of the subproblem
d = time takes to combine the solutions
when b, the size of the subproblem is given as n-1, a = 2, d=1
how do you work out T(n)??
What I have tried:
T(n) = aT(n/b) + O(n)
T(n) = 4T(n-1) + O(n)