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Hey I've been working on something from time to time and it has become relatively large now (and slow). However I managed to pinpoint the bottleneck after close up measuring of performance in function of time.
Say I want to "permute" the string "ABC". What I mean by "permute" is not quite a permutation but rather a continuous substring set following this pattern:
A
AB
ABC
B
BC
C
I have to check for every substring if it is contained within another string S2 so I've done some quick'n dirty literal implementation as follows:
for (int i = 0; i <= strlen1; i++)
{
for (int j = 0; j <= strlen2- i; j++)
{
sub = str1.Substring(i, j);
if (str2.Contains(sub)) {do stuff}
else break;
This was very slow initially but once I realised that if the first part doesnt exist, there is no need to check for the subsequent ones meaning that if sub isn't contained within str2, i can call break on the inner loop.
Ok this gave blazing fast results but calculating my algorithm complexity I realised that in worst case this will be N^4 ? I forgot that str.contains() and str.substr() both have their own complexities (N or N^2 I forgot which).
The fact that I have a huge amount of calls on those inside a 2nd for loop makes it perform rather.. well N^4 ~ said enough.
However I calculated the average run-time of this both mathematically using probability theory to evaluate the probability of growth of the substring in a pool of randomly generated strings (this was my base line) measuring when the probability became > 0.5 (50%)
This showed an exponential relationship between the number of different characters and the string length (roughly) which means that in the scenarios I use my algorithm the length of string1 wont (most probably) never exceed 7
Thus the average complexity would be ~O(N * M) where N is string length1 and M is string length 2. Due to the fact that I've tested N in function of constant M, I've gotten linear growth ~O(N) (not bad opposing to the N^4 eh?)
I did time testing and plotted a graph which showed nearly perfect linear growth so I got my actual results matching my mathematical predictions (yay!)
However, this was NOT taking into account the cost of string.contains() and string.substring() which made me wonder if this could be optimized even further?
I've been also thinking of making this in C++ because I need rather low-level stuff? What do you guys think? I have put a great time into analysing this hope I've elaborated everything clear enough :)!
Your question is tagged both C++ and C#.
In C++ the optimal solution will be to use iterators, and std::search. The original strings remains unmodified, and no intermediate objects get created. There won't be an equivalent of your Substring() taking place at all, so this eliminates that part of the overhead.
This should achieve the theoretically-best performance: brute force search, testing all permutations, with no intermediate object construction or destruction, other than the iterators themselves, which simply replace your two int index variables. I can't think of any faster way of implementing this basic algorithm.
Are You testing one string against one string? If You test bunch of strings against another bunch of strings, it is a whole different story. Even if You have the best algorithm for comparing one string against another O(X), it does not mean repeating it M*N times You would get the best algorithm for processing M strings against N.
When I made something simmiliar, I built dictionary of all substrings of all N strings
Dictionary<string, List<int>>
The string is a substring and int is index of string that contains that substring. Then I tested all substrings of all M strings against it. The speed was suddenly not O(M*N*X), but O(max(M,N)*S), where S is number of substrings of one string. Depending on M, N, X, S that may be faster. I do not say the dictionary of substrings is the best approach, I just want to point out that You should always try to see the whole picture.
I would like to know the following:
How to effectively make initial generation of chromosomes with high diversity using value encoding ?
One way is grid initialization, but it is too slow.
Till now I have been using Random class from .NET for choosing random values in value encoding but, although values are uniformly distributed, fitness function values calculated from such chromosomes are not. Here is a code for Chromosome initialization:
public Chromosome(Random rand)
{
Alele = new List<double>();
for (int i = 0; i < ChromosomeLength; i++)
{
Alele.Add(rand.NextDouble() * 2000 - 1000);
}
}
So, I developed a function that calculates fitness from new, randomly made chromosome (upper code) and if fitness is similar to any other already in the list of chromosomes, a new chromosome is made randomly and his fitness is calculated and this process is repeated until his fitness is not different enough from those already in the list.
Here is the code for this part:
private bool CheckSimilarFitnes(List<Chromosome> chromosome, Chromosome newCandidate)
{
Boolean flag=false;
double fitFromList, fitFromCandidate;
double fitBigger,fitSmaller;
foreach (var listElement in chromosome)
{
fitFromList = listElement.CalculateChromosomeFitness(listElement.Alele);
fitFromCandidate = newCandidate.CalculateChromosomeFitness(newCandidate.Alele);
fitBigger = fitFromList >= fitFromCandidate ? fitFromList : fitFromCandidate;
fitSmaller = fitFromList < fitFromCandidate ? fitFromList : fitFromCandidate;
if ((fitFromList / fitFromCandidate) < 1.5)
return false
}
else return true;
}
But, the more chromosomes I have in the list it takes longer to add a new one, with fitness that is enough different from others already in there.
So, is there a way to make this grid initialization more faster, it takes days to make 80 chromosomes like this?
here's some code that might help (which I just wrote): GA for ordering 10 values spaced by 1.0. It starts with a population of 100 completely random alleles, which is exactly how your code starts.
The goal I gave the GA to solve was to order the values in increasing order with a separation of 1.0. It does this in the fitness function Eval_OrderedDistance by by computing the standard deviation of each pair of samples from 1.0. As the fitness tends toward 0.0, the alleles should start to appear in sequential order.
Generation 0's fittest Chromosome was completely random, as were the rest of the Chromosomes. You can see the fitness value is very high (i.e., bad):
GEN: fitness (allele, ...)
0: 375.47460 (583.640, -4.215, -78.418, 164.228, -243.982, -250.237, 354.559, 374.306, 709.859, 115.323)
As the generations continue, the fitness (standard deviation from 1.0) decreases until it's nearly perfect in generation 100,000:
100: 68.11683 (-154.818, -173.378, -170.846, -193.750, -198.722, -396.502, -464.710, -450.014, -422.194, -407.162)
...
10000: 6.01724 (-269.681, -267.947, -273.282, -281.582, -287.407, -293.622, -302.050, -307.582, -308.198, -308.648)
...
99999: 0.67262 (-294.746, -293.906, -293.114, -292.632, -292.596, -292.911, -292.808, -292.039, -291.112, -290.928)
The interesting parts of the code are the fitness function:
// try to pack the aleles together spaced apart by 1.0
// returns the standard deviation of the samples from 1.0
static float Eval_OrderedDistance(Chromosome c) {
float sum = 0;
int n = c.alele.Length;
for(int i=1; i<n; i++) {
float diff = (c.alele[i] - c.alele[i-1]) - 1.0f;
sum += diff*diff; // variance from 1.0
}
return (float)Math.Sqrt(sum/n);
}
And the mutations. I used a simple crossover and a "completely mutate one allele":
Chromosome ChangeOne(Chromosome c) {
Chromosome d = c.Clone();
int i = rand.Next() % d.alele.Length;
d.alele[i] = (float)(rand.NextDouble()*2000-1000);
return d;
}
I used elitism to always keep one exact copy of the best Chromosome. Then generated 100 new Chromosomes using mutation and crossover.
It really sounds like you're calculating the variance of the fitness, which does of course tell you that the fitnesses in your population are all about the same. I've found that it's very important how you define your fitness function. The more granular the fitness function, the more you can discriminate between your Chromosomes. Obviously, your fitness function is returning similar values for completely different chromosomes, since your gen 0 returns a fitness variance of 68e-19.
Can you share your fitness calculation? Or what problem you're asking the GA to solve? I think that might help us help you.
[Edit: Adding Explicit Fitness Sharing / Niching]
I rethought this a bit and updated my code. If you're trying to maintain unique chromosomes, you have to compare their content (as others have mentioned). One way to do this would be to compute the standard deviation between them. If it's less than some threshold, you can consider them the same. From class Chromosome:
// compute the population standard deviation
public float StdDev(Chromosome other) {
float sum = 0.0f;
for(int i=0; i<alele.Length; i++) {
float diff = other.alele[i] - alele[i];
sum += diff*diff;
}
return (float)Math.Sqrt(sum);
}
I think Niching will give you what you'd like. It compares all the Chromosomes in the population to determine their similarity and assigns a "niche" value to each. The chromosomes are then "penalized" for belonging to a niche using a technique called Explicit Fitness Sharing. The fitness values are divided by the number of Chromosomes in each niche. So if you have three in niche group A (A,A,A) instead of that niche being 3 times as likely to be chosen, it's treated as a single entity.
I compared my sample with Explicit Fitness Sharing on and off. With a max STDDEV of 500 and Niching turned OFF, there were about 18-20 niches (so basically 5 duplicates of each item in a 100 population). With Niching turned ON, there were about 85 niches. Thats 85% unique Chromosomes in the population. In the output of my test, you can see the diversity after 17000 generations.
Here's the niching code:
// returns: total number of niches in this population
// max_stddev -- any two chromosomes with population stddev less than this max
// will be grouped together
int ComputeNiches(float max_stddev) {
List<int> niches = new List<int>();
// clear niches
foreach(var c in population) {
c.niche = -1;
}
// calculate niches
for(int i=0; i<population.Count; i++) {
var c = population[i];
if( c.niche != -1) continue; // niche already set
// compute the niche by finding the stddev between the two chromosomes
c.niche = niches.Count;
int count_in_niche = 1; // includes the curent Chromosome
for(int j=i+1; j<population.Count; j++) {
var d = population[j];
float stddev = c.StdDev(d);
if(stddev < max_stddev) {
d.niche = c.niche; // same niche
++count_in_niche;
}
}
niches.Add(count_in_niche);
}
// penalize Chromosomes by their niche size
foreach(var c in population) {
c.niche_scaled_fitness = c.scaled_fitness / niches[c.niche];
}
return niches.Count;
}
[Edit: post-analysis and update of Anton's code]
I know this probably isn't the right forum to address homework problems, but since I did the effort before knowing this, and I had a lot of fun doing it, I figure it can only be helpful to Anton.
Genotip.cs, Kromosom.cs, KromoMain.cs
This code maintains good diversity, and I was able in one run to get the "raw fitness" down to 47, which is in your case the average squared error. That was pretty close!
As noted in my comment, I'd like to try to help you in your programming, not just help you with your homework. Please read these analysis of your work.
As we expected, there was no need to make a "more diverse" population from the start. Just generate some completely random Kromosomes.
Your mutations and crossovers were highly destructive, and you only had a few of them. I added several new operators that seem to work better for this problem.
You were throwing away the best solution. When I got your code running with only Tournament Selection, there would be one Kromo that was 99% better than all the rest. With tournament selection, that best value was very likely to be forgotten. I added a bit of "elitism" which keeps a copy of that value for the next generation.
Consider object oriented techniques. Compare the re-write I sent you with my original code.
Don't duplicate code. You had the sampling parameters in two different classes.
Keep your code clean. There were several unused parts of code. Especially when submitting questions to SO, try to narrow it down, remove unused code, and do some cleaning up.
Comment your code! I've commented the re-work significantly. I know it's Serbian, but even a few comments will help someone else understand what you are doing and what you intended to do.
Overall, nice job implementing some of the more sophisticated things like Tournament Selection
Prefer double[] arrays instead of List. There's less overhead. Also, several of your List temp variables weren't even needed. Your structure
List temp = new List();
for(...) {
temp.add(value);
}
for(each value in temp) {
sum += value
}
average = sum / temp.Count
can easily be written as:
sum = 0
for(...) {
sum += value;
}
average = sum / count;
In several places you forgot to initialize a loop variable, which could have easily added to your problem. Something like this will cause serious problems, and it was in your fitness code along with one or two other places
double fit = 0;
for(each chromosome) {
// YOU SHOULD INITIALIZE fit HERE inside the LOOP
for(each allele) {
fit += ...;
}
fit /= count;
}
Good luck programming!
The basic problem here is that most randomly generated chromosomes have similar fitness, right? That's fine; the idea isn't for your initial chromosomes to have wildly different fitnesses; it's for the chromosomes themselves to be different, and presumably they are. In fact, you should expect the initial fitness of most of your first generation to be close to zero, since you haven't run the algorithm yet.
Here's why your code is so slow. Let's say the first candidate is terrible, basically zero fitness. If the second one has to be 1.5x different, that really just means it has to be 1.5x better, since it can't really get worse. Then the next one has to 1.5x better than that, and so on up to 80. So what you're really doing is searching for increasingly better chromosomes by generating completely random ones and comparing them to what you have. I bet if you logged the progress, you'd find it takes more and more time to find the subsequent candidates, because really good chromosomes are hard to find. But finding better chromosomes is what the GA is for! Basically what you've done is optimize some of the chromosomes by hand before, um, actually optimizing them.
If you want to ensure that your chromosomes are diverse, compare their content, don't compare their fitness. Comparing the fitness is the algo's job.
I'm going to take a quick swing at this, but Isaac's pretty much right. You need to let the GA do its job. You have a generation of individuals (chromosomes, whatever), and they're all over the scale on fitness (or maybe they're all identical).
You pick some good ones to mutate (by themselves) and crossover (with each other). You maybe use the top 10% to generate another full population and throw out the bottom 90%. Maybe you always keep the top guy around (Elitism).
You iterate at this for a while until your GA stops improving because the individuals are all very much alike. You've ended up with very little diversity in your population.
What might help you is to 1) make your mutations more effective, 2) find a better way to select individuals to mutate. In my comment I recommended AI Techniques for Game Programmers. It's a great book. Very easy to read.
To list a few headings from the book, the things you're looking for are:
Selection techniques like Roulette Selection (on stackoveflow) (on wikipedia) and Stochastic Universal Sampling, which control how you select your individuals. I've always liked Roulette Selection. You set the probabilities that an individual will be selected. It's not just simple white-noise random sampling.
I used this outside of GA for selecting 4 letters from the Roman alphabet randomly. I assigned a value from 0.0 to 1.0 to each letter. Every time the user (child) would pick the letter correctly, I would lower that value by, say 0.1. This would increase the likelihood that the other letters would be selected. If after 10 times, the user picked the correct letter, the value would be 0.0, and there would be (almost) no chance that letter would be presented again.
Fitness Scaling techniques like Rank Scaling, Sigma Scaling, and Boltzmann Scaling (pdf on ftp!!!) that let you modify your raw fitness values to come up with adjusted fitness values. Some of these are dynamic, like Boltzmann Scaling, which allows you to set a "pressure" or "temperature" that changes over time. Increased "pressure" means that fitter individuals are selected. Decreased pressure means that any individual in the population can be selected.
I think of it this way: you're searching through multi-dimensional space for a solution. You hit a "peak" and work your way up into it. The pressure to be fit is very high. You snug right into that local maxima. Now your fitness can't change. Your mutations aren't getting you out of the peak. So you start to reduce the pressure and just, oh, select items randomly. Your fitness levels start to drop, which is okay for a while. Then you start to increase the pressure again, and surprise! You've skipped out of the local maxima and found a lovely new local maxima to climb into. Increase the pressure again!
Niching (which I've never used, but appears to be a way to group similar individuals together). Say you have two pretty good individuals, but they're wildly different. They keep getting selected. They keep mutating slightly, and not getting much better. Now you have half your population as minor variants of A, and half your population minor variants of B. This seems like a way to say, hey, what's the average fitness of that entire group A? and what for B? And what for every other niche you have. Then do your selection based on the average fitness for each niche. Pick your niche, then select a random individual from that niche. Maybe I'll start using this after all. I like it!
Hope you find some of that helpful!
If you need true random numbers for your application, I recommend you check out Random.org. They have a free HTTP API, and clients for just about every language.
The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs.
(I am unaffiliated with Random.org, although I did contribute the PHP client).
I think your problem is in how your fitness function and how you select candidates, not in how random values are. Your filtering feels too strict that may not even allow enough elements to be accepted.
Sample
values: random float 0-10000.
fitness function square root(n)
desired distribution of fitness - linear with distance at least 1.
With this fitness function you will quickly get most of the 1-wide "spots" taken (as you have at most 100 places), so every next one will take longer. At some point there will be several tiny ranges left and most of the results will simply rejected, even worse after you get about 50 numbers places there is a good chance that next one simply will not be able to fit.
OK so I need to know if anyone can see a way to reduce the number of iterations of these loops because I can't. The first while loop is for going through a file, reading one line at a time. The first foreach loop is then comparing each of the compareSet with what was read in the first while loop. Then the next while loop is to do with bit counting.
As requested, an explaination of my algorithm:
There is a file that is too large to fit in memory. It contains a word followed by the pages in a very large document that this word is on. EG:
sky 1 7 9 32....... (it is not in this format, but you get the idea).
so parseLine reads in the line and converts it into a list of ints that are like a bit array where 1 means the word is on the page, and 0 means it isn't.
CompareSet is a bunch of other words. I can't fit my entire list of words into memory so I can only fit a subset of them. This is a bunch of words just like the "sky" example. I then compare each word in compareSet with Sky by seeing if they are on the same page.
So if sky and some other word both have 1 set at a certain index in the bit array (simulated as an int array for performance), they are on the same page. The algorithm therefore counts the occurances of any two words on a particular page. So in the end I will have a list like:
(for all words in list) is on the same page as (for all words in list) x number of times.
eg sky and land is on the same page x number of times.
while ((line = parseLine(s)) != null) {
getPageList(line.Item2, compareWord);
foreach (Tuple<int, uint[], List<Tuple<int, int>>> word in compareSet) {
unchecked {
for (int i = 0; i < 327395; i++) {
if (word.Item2[i] == 0 || compareWord[i] == 0)
continue;
uint combinedNumber = word.Item2[i] & compareWord[i];
while (combinedNumber != 0) {
actual++;
combinedNumber = combinedNumber & (combinedNumber - 1);
}
}
}
As my old professor Bud used to say: "When you see nested loops like this, your spidey senses should be goin' CRAZY!"
You have a while with a nested for with another while. This nesting of loops is an exponential increase on the order of operations. Your one for loop has 327395 iterations. Assuming they have the same or similar number of iterations, that means you have an order of operations of
327,395 * 327,395 * 327,395 = 35,092,646,987,154,875 (insane)
It's no wonder that things would be slowing down. You need to redefine your algorithm to remove these nested loops or combine work somewhere. Even if the numbers are smaller than my assumptions, the nesting of the loops is creating a LOT of operations that are probably unnecessary.
As Joal already mentioned nobody is able to optimize this looping algorithm. But what you can do is trying to better explain what you are trying to accomplish and what your hard requirements are. Maybe you can take a different approach by using some like HashSet<T>.IntersectWith() or BloomFilter or something like this.
So if you really want help from here you should not only post the code that doesn't work, but also what the overall task is you like to accomplish. Maybe someone has a completely other idea to solve your problem, making your whole algorithm obsolete.
I have built an application that is used to simulate the number of products that a company can produce in different "modes" per month. This simulation is used to aid in finding the optimal series of modes to run in for a month to best meet the projected sales forecast for the month. This application has been working well, until recently when the plant was modified to run in additional modes. It is now possible to run in 16 modes. For a month with 22 work days this yields 9,364,199,760 possible combinations. This is up from 8 modes in the past that would have yielded a mere 1,560,780 possible combinations. The PC that runs this application is on the old side and cannot handle the number of calculations before an out of memory exception is thrown. In fact the entire application cannot support more than 15 modes because it uses integers to track the number of modes and it exceeds the upper limit for an integer. Baring that issue, I need to do what I can to reduce the memory utilization of the application and optimize this to run as efficiently as possible even if it cannot achieve the stated goal of 16 modes. I was considering writing the data to disk rather than storing the list in memory, but before I take on that overhead, I would like to get people’s opinion on the method to see if there is any room for optimization there.
EDIT
Based on a suggestion by few to consider something more academic then merely calculating every possible answer, listed below is a brief explanation of how the optimal run (combination of modes) is chosen.
Currently the computer determines every possible way that the plant can run for the number of work days that month. For example 3 Modes for a max of 2 work days would result in the combinations (where the number represents the mode chosen) of (1,1), (1,2), (1,3), (2,2), (2,3), (3,3) For each mode a product produces at a different rate of production, for example in mode 1, product x may produce at 50 units per hour where product y produces at 30 units per hour and product z produces at 0 units per hour. Each combination is then multiplied by work hours and production rates. The run that produces numbers that most closely match the forecasted value for each product for the month is chosen. However, because some months the plant does not meet the forecasted value for a product, the algorithm increases the priority of a product for the next month to ensure that at the end of the year the product has met the forecasted value. Since warehouse space is tight, it is important that products not overproduce too much either.
Thank you
private List<List<int>> _modeIterations = new List<List<int>>();
private void CalculateCombinations(int modes, int workDays, string combinationValues)
{
List<int> _tempList = new List<int>();
if (modes == 1)
{
combinationValues += Convert.ToString(workDays);
string[] _combinations = combinationValues.Split(',');
foreach (string _number in _combinations)
{
_tempList.Add(Convert.ToInt32(_number));
}
_modeIterations.Add(_tempList);
}
else
{
for (int i = workDays + 1; --i >= 0; )
{
CalculateCombinations(modes - 1, workDays - i, combinationValues + i + ",");
}
}
}
This kind of optimization problem is difficult but extremely well-studied. You should probably read up in the literature on it rather than trying to re-invent the wheel. The keywords you want to look for are "operations research" and "combinatorial optimization problem".
It is well-known in the study of optimization problems that finding the optimal solution to a problem is almost always computationally infeasible as the problem grows large, as you have discovered for yourself. However, it is frequently the case that finding a solution guaranteed to be within a certain percentage of the optimal solution is feasible. You should probably concentrate on finding approximate solutions. After all, your sales targets are already just educated guesses, therefore finding the optimal solution is already going to be impossible; you haven't got complete information.)
What I would do is start by reading the wikipedia page on the Knapsack Problem:
http://en.wikipedia.org/wiki/Knapsack_problem
This is the problem of "I've got a whole bunch of items of different values and different weights, I can carry 50 pounds in my knapsack, what is the largest possible value I can carry while meeting my weight goal?"
This isn't exactly your problem, but clearly it is related -- you've got a certain amount of "value" to maximize, and a limited number of slots to pack that value into. If you can start to understand how people find near-optimal solutions to the knapsack problem, you can apply that to your specific problem.
You could process the permutation as soon as you have generated it, instead of collecting them all in a list first:
public delegate void Processor(List<int> args);
private void CalculateCombinations(int modes, int workDays, string combinationValues, Processor processor)
{
if (modes == 1)
{
List<int> _tempList = new List<int>();
combinationValues += Convert.ToString(workDays);
string[] _combinations = combinationValues.Split(',');
foreach (string _number in _combinations)
{
_tempList.Add(Convert.ToInt32(_number));
}
processor.Invoke(_tempList);
}
else
{
for (int i = workDays + 1; --i >= 0; )
{
CalculateCombinations(modes - 1, workDays - i, combinationValues + i + ",", processor);
}
}
}
I am assuming here, that your current pattern of work is something along the lines
CalculateCombinations(initial_value_1, initial_value_2, initial_value_3);
foreach( List<int> list in _modeIterations ) {
... process the list ...
}
With the direct-process-approach, this would be
private void ProcessPermutation(List<int> args)
{
... process ...
}
... somewhere else ...
CalculateCombinations(initial_value_1, initial_value_2, initial_value_3, ProcessPermutation);
I would also suggest, that you try to prune the search tree as early as possible; if you can already tell, that certain combinations of the arguments will never yield something, which can be processed, you should catch those already during generation, and avoid the recursion alltogether, if this is possible.
In new versions of C#, generation of the combinations using an iterator (?) function might be usable to retain the original structure of your code. I haven't really used this feature (yield) as of yet, so I cannot comment on it.
The problem lies more in the Brute Force approach that in the code itself. It's possible that brute force might be the only way to approach the problem but I doubt it. Chess, for example, is unresolvable by Brute Force but computers play at it quite well using heuristics to discard the less promising approaches and focusing on good ones. Maybe you should take a similar approach.
On the other hand we need to know how each "mode" is evaluated in order to suggest any heuristics. In your code you're only computing all possible combinations which, anyway, will not scale if the modes go up to 32... even if you store it on disk.
if (modes == 1)
{
List<int> _tempList = new List<int>();
combinationValues += Convert.ToString(workDays);
string[] _combinations = combinationValues.Split(',');
foreach (string _number in _combinations)
{
_tempList.Add(Convert.ToInt32(_number));
}
processor.Invoke(_tempList);
}
Everything in this block of code is executed over and over again, so no line in that code should make use of memory without freeing it. The most obvious place to avoid memory craziness is to write out combinationValues to disk as it is processed (i.e. use a FileStream, not a string). I think that in general, doing string concatenation the way you are doing here is bad, since every concatenation results in memory sadness. At least use a stringbuilder (See back to basics , which discusses the same issue in terms of C). There may be other places with issues, though. The simplest way to figure out why you are getting an out of memory error may be to use a memory profiler (Download Link from download.microsoft.com).
By the way, my tendency with code like this is to have a global List object that is Clear()ed rather than having a temporary one that is created over and over again.
I would replace the List objects with my own class that uses preallocated arrays to hold the ints. I'm not really sure about this right now, but I believe that each integer in a List is boxed, which means much more memory is used than with a simple array of ints.
Edit: On the other hand it seems I am mistaken: Which one is more efficient : List<int> or int[]
I'm trying to work through the problems on projecteuler.net but I keep running into a couple of problems.
The first is a question of storing large quanities of elements in a List<t>. I keep getting OutOfMemoryException's when storing large quantities in the list.
Now I admit I might not be doing these things in the best way but, is there some way of defining how much memory the app can consume?
It usually crashes when I get abour 100,000,000 elements :S
Secondly, some of the questions require the addition of massive numbers. I use ulong data type where I think the number is going to get super big, but I still manage to wrap past the largest supported int and get into negative numbers.
Do you have any tips for working with incredibly large numbers?
Consider System.Numerics.BigInteger.
You need to use a large number class that uses some basic math principals to split these operations up. This implementation of a C# BigInteger library on CodePoject seems to be the most promising. The article has some good explanations of how operations with massive numbers work, as well.
Also see:
Big integers in C#
As far as Project Euler goes, you might be barking up the wrong tree if you are hitting OutOfMemory exceptions. From their website:
Each problem has been designed according to a "one-minute rule", which means that although it may take several hours to design a successful algorithm with more difficult problems, an efficient implementation will allow a solution to be obtained on a modestly powered computer in less than one minute.
As user Jakers said, if you're using Big Numbers, probably you're doing it wrong.
Of the ProjectEuler problems I've done, none have required big-number math so far.
Its more about finding the proper algorithm to avoid big-numbers.
Want hints? Post here, and we might have an interesting Euler-thread started.
I assume this is C#? F# has built in ways of handling both these problems (BigInt type and lazy sequences).
You can use both F# techniques from C#, if you like. The BigInt type is reasonably usable from other languages if you add a reference to the core F# assembly.
Lazy sequences are basically just syntax friendly enumerators. Putting 100,000,000 elements in a list isn't a great plan, so you should rethink your solutions to get around that. If you don't need to keep information around, throw it away! If it's cheaper to recompute it than store it, throw it away!
See the answers in this thread. You probably need to use one of the third-party big integer libraries/classes available or wait for C# 4.0 which will include a native BigInteger datatype.
As far as defining how much memory an app will use, you can check the available memory before performing an operation by using the MemoryFailPoint class.
This allows you to preallocate memory before doing the operation, so you can check if an operation will fail before running it.
string Add(string s1, string s2)
{
bool carry = false;
string result = string.Empty;
if (s1.Length < s2.Length)
s1 = s1.PadLeft(s2.Length, '0');
if(s2.Length < s1.Length)
s2 = s2.PadLeft(s1.Length, '0');
for(int i = s1.Length-1; i >= 0; i--)
{
var augend = Convert.ToInt64(s1.Substring(i,1));
var addend = Convert.ToInt64(s2.Substring(i,1));
var sum = augend + addend;
sum += (carry ? 1 : 0);
carry = false;
if(sum > 9)
{
carry = true;
sum -= 10;
}
result = sum.ToString() + result;
}
if(carry)
{
result = "1" + result;
}
return result;
}
I am not sure if it is a good way of handling it, but I use the following in my project.
I have a "double theRelevantNumber" variable and an "int PowerOfTen" for each item and in my relevant class I have a "int relevantDecimals" variable.
So... when large numbers is encountered they are handled like this:
First they are changed to x,yyy form. So if the number 123456,789 was inputed and the "powerOfTen" was 10, it would start like this:
theRelevantNumber = 123456,789
PowerOfTen = 10
The number was then: 123456,789*10^10
It is then changed to:
1,23456789*10^15
It is then rounded by the number of relevant decimals (for example 5) to 1,23456 and then saved along with "PowerOfTen = 15"
When adding or subracting numbers together, any number outside the relevant decimals are ignored. Meaning if you take:
1*10^15 + 1*10^10 it will change to 1,00001 if "relevantDecimals" is 5 but will not change at all if "relevantDecimals" are 4.
This method make you able to deal with numbers up doubleLimit*10^intLimit without any problem, and at least for OOP it is not that hard to keep track of.
You don't need to use BigInteger. You can do this even with string array of numbers.
class Solution
{
static void Main(String[] args)
{
int n = 5;
string[] unsorted = new string[6] { "3141592653589793238","1", "3", "5737362592653589793238", "3", "5" };
string[] result = SortStrings(n, unsorted);
foreach (string s in result)
Console.WriteLine(s);
Console.ReadLine();
}
static string[] SortStrings(int size, string[] arr)
{
Array.Sort(arr, (left, right) =>
{
if (left.Length != right.Length)
return left.Length - right.Length;
return left.CompareTo(right);
});
return arr;
}
}
If you want to work with incredibly large numbers look here...
MIKI Calculator
I am not a professional programmer i write for myself, sometimes, so sorry for unprofessional use of c# but the program works. I will be grateful for any advice and correction.
I use this calculator to generate 32-character passwords from numbers that are around 58 digits long.
Since the program adds numbers in the string format, you can perform calculations on numbers with the maximum length of the string variable. The program uses long lists for the calculation, so it is possible to calculate on larger numbers, possibly 18x the maximum capacity of the list.