I'm working on an iOS Objective C app where you accumulate a large amount of wealth. By the end of the app, the amount of money users can accumulate is more than a long long can handle. What data type should I use instead? I know I could use an unsigned long, but that only adds a little bit more. I need users to have like 6 more digits to be safe, so instead of the max being 18,446,744,073,709,551,615 (about 1.8x10^19), it would be ideal to have something like 1.8x10^25 as my maximum value.
Precision isn't actually all that important in the end, but it would defiantly save me time to not have to do more than just changing data types throughout my application. Any ideas?
Short Answer
Go for a 3rd party library.
Long Answer
When dealing with large numbers, probably one of the most fundamental design decisions is how am I going to represent the large number?
Will it be a string, an array, a list, or custom (homegrown) storage class.
After that decision is made, the actual math operations can be broken down in smaller parts and then executed with native language types such as int or integer.
Even with strings there is a limit in the number of characters or "numbers" in the number, as indicated here:
What is the maximum possible length of a .NET string?
You might also want to check: Arbitrary description Arithmetic
Related
I am trying to build a Sieve of Eratosthenes in Lua and i tried several things but i see myself confronted with the following problem:
The tables of Lua are to small for this scenario. If I just want to create a table with all numbers (see example below), the table is too "small" even with only 1/8 (...) of the number (the number is pretty big I admit)...
max = 600851475143
numbers = {}
for i=1, max do
table.insert(numbers, i)
end
If I execute this script on my Windows machine there is an error message saying: C:\Program Files (x86)\Lua\5.1\lua.exe: not enough memory. With Lua 5.3 running on my Linux machine I tried that too, error was just killed. So it is pretty obvious that lua can´t handle the amount of entries.
I don´t really know whether it is just impossible to store that amount of entries in a lua table or there is a simple solution for this (tried it by using a long string aswell...)? And what exactly is the largest amount of entries in a Lua table?
Update: And would it be possible to manually allocate somehow more memory for the table?
Update 2 (Solution for second question): The second question is an easy one, I just tested it by running every number until the program breaks: 33.554.432 (2^25) entries fit in one one-dimensional table on my 12 GB RAM system. Why 2^25? Because 64 Bit per number * 2^25 = 2147483648 Bits which are exactly 2 GB. This seems to be the standard memory allocation size for the Lua for Windows 32 Bit compiler.
P.S. You may have noticed that this number is from the Euler Project Problem 3. Yes I am trying to accomplish that. Please don´t give specific hints (..). Thank you :)
The Sieve of Eratosthenes only requires one bit per number, representing whether the number has been marked non-prime or not.
One way to reduce memory usage would be to use bitwise math to represent multiple bits in each table entry. Current Lua implementations have intrinsic support for bitwise-or, -and etc. Depending on the underlying implementation, you should be able to represent 32 or 64 bits (number flags) per table entry.
Another option would be to use one or more very long strings instead of a table. You only need a linear array, which is really what a string is. Just have a long string with "t" or "f", or "0" or "1", at every position.
Caveat: String manipulation in Lua always involves duplication, which rapidly turns into n² or worse complexity in terms of performance. You wouldn't want one continuous string for the whole massive sequence, but you could probably break it up into blocks of a thousand, or of some power of 2. That would reduce your memory usage to 1 byte per number while minimizing the overhead.
Edit: After noticing a point made elsewhere, I realized your maximum number is so large that, even with a bit per number, your memory requirements would optimally be about 73 gigabytes, which is extremely impractical. I would recommend following the advice Piglet gave in their answer, to look at Jon Sorenson's version of the sieve, which works on segments of the space instead of the whole thing.
I'll leave my suggestion, as it still might be useful for Sorenson's sieve, but yeah, you have a bigger problem than you realize.
Lua uses double precision floats to represent numbers. That's 64bits per number.
600851475143 numbers result in almost 4.5 Terabytes of memory.
So it's not Lua's or its tables' fault. The error message even says
not enough memory
You just don't have enough RAM to allocate that much.
If you would have read the linked Wikipedia article carefully you would have found the following section:
As Sorenson notes, the problem with the sieve of Eratosthenes is not
the number of operations it performs but rather its memory
requirements.[8] For large n, the range of primes may not fit in
memory; worse, even for moderate n, its cache use is highly
suboptimal. The algorithm walks through the entire array A, exhibiting
almost no locality of reference.
A solution to these problems is offered by segmented sieves, where
only portions of the range are sieved at a time.[9] These have been
known since the 1970s, and work as follows
...
I hope this is the right forum to ask this sort of question. I'm trying to minimize the amount of data performing a sync with iCloud, while ensuring ideal app speed as well... I am trying to use an efficient model... My application (which is a basic checklist application) will have around 8 variables that can be marked as "owned" for each item.
Would it be better to create 8 attributes as Boolean attributes or a single String attribute? With the string attribute, I would simply include 8 numbers like "00000000" or "10000000" or "10001000" with each character of the string linked to a particular item and retrieved by looking for a particular index of the string.
My initial thought is that the 8 booleans would allow for faster reading and writing, and would have a minimal footprint, but I would appreciate some more intelligent feedback from the experts.
I would not recommend nothing of this to minimize memory usage. Reason is that bool costs 1 byte - 8 bit (but wee need only one and other 7 wont be used), string same but with characters. If you want to minimize memory usage - than use 1 byte. Because 1 byte - 8 bit you can set each bit with 1 or 0 using memory mask(bit mask). And than all your values will be allocated in 1 byte what will use eight time less memory than bool. How to use memory mask(bit mask) you can read this topic
Declaring and checking/comparing (bitmask-)enums in Objective-C
I would think any difference in speed or memory is likely to be marginal. Design and code it in the most logical way, which at first sight seems to be using 8 booleans. For example, if you need to fetch a subset of the data based on the boolean values, it will be far easier to construct the required predicate.
There is a problem in a competitive programming site(hackerrank) in which the input number is of the range 10^18.So,is it possible to store (10^18) in java?If yes then which data type should be used?
For some easy HackerRank problems, BigInteger or BigDecimal do work for extremely large inputs,but they usually don't work in moderate/difficult problems as they tend to reduce performance & a high number of test-cases of extremely large inputs can cause a timeout.
In such cases,you will need go for different storage techniques e.g. an array of int,each element of the array representing a digit of the large input. You will then need to do digit-based arithmetic on the array for your computations.
BigInteger.valueOf(10).pow(10000)
No real need not be careful, as the BigInteger.valueOf(long) method will give you a compilation error if you try to write a literal that exceeds Long.MAX_VALUE. Furthermore, it's easy to construct a BigInteger much greater, say BigInteger.valueOf(10).pow(10000)
This question was asked in one of the big software company. I have come up with a simple solution and I want to know what others feel about the solution.
You are supposed to design an API and a backend for a system that can
allot phone numbers to people living in a city. The phone numbers will
start from 111-111-1111 and end at 999-999-9999. The API should enable
the clients (people in the city) to do the following:
When a client requests for a phone number, it allots one of the available numbers to them.
Some clients may want fancy numbers, so they can specifically ask for a number to be alloted to them. If the requested number is
available then the system allots it to them, otherwise the system
allots any available number.
The system need not have to know which number is alloted to which
client. The same client may make successive requests and get multiple
phone numbers for himself, but the system is not bothered. At any
point of time, the system only knows which phone numbers are alloted
and which phone numbers are free.
The numbers from 111-111-1111 to 999-999-9999 roughly corresponds to 8 billion numbers. Assuming that memory is not a constraint, I can think of the following two approaches (which are almost similar).
Maintain a huge boolean array of length 8 billion and have a next pointer that points to an array index (next is initialized to zero). If the value pointed by next is not free, then forward next until a free number is found. When fancy numbers are requested, just check whether the corresponding index position is free and return the number. The downside of this approach is, when allocating numbers in a regular way, if there is a huge chunk (say 1 billion) numbers in the middle that was allocated by fancy allocation, then the next pointer has to be moved 1 billion times.
To overcome the difficulty mentioned in the previos design, we can use some sort of a linked hashmap. We maintain a doubly linked list (this replaces the array in the previous design) and another array of the same length as the list where each element of the array points to a corresponding element in the list. So when allocating numbers in regular method, we advance a pointer in the linked list and mark nodes as and when we allocate (same as the previous method). When allocating fancy numbers, we can directly find the node in the list that corresponds to the special number requested by first indexing into the array and the following the pointer. Once the node is identified, short circuit the previous node and the next node so that we do not have to skip the used numbers one by one (which was the problem with the previous approach) when doing a regular allocation.
Let me know whether I am on the right track. Please enlighten me with any important details that I am missing.
You can do significantly better in the anser to this question.
First you should design you API. The one recommended by Icarus3 is perfectly good:
string acquireNextAvailableNumber();
boolean acquireRequestedNumber(string special);
The second one returns true (and reserves the number) if it is available, otherwise returns false.
The question doesn't specify how you allocate phone numbers, so allocate them to suit yourself. Make the first 'next available' request return "111-111-1111", the next "111-111-1112" etc. This means you can record all the numbers allocated through 'next' by just remembering the last one allocated. (You'll need to ask whether '111-111-1119" is followed by "111-111-1120" or 111-111-1121", but that's the sort of thing you should be asking anyway. In any case, the important thing is you can work out what is the next number knowing the last allocated one.)
Special requests you will need to store individually. A hash table work, but so does a BST or simply an ordered list. It depends on what tradeoffs you want between space and speed, and how often special numbers are likely to be requested. I'll use a BST (ordered by the number) in the rest of this, for reasons I'll come to.
So, how do you code this? For the next allocated number:
Look at the last allocated number, and find the next in sequence.
Check that number hasn't been allocated as a special number. You can do this very quickly with a BST because if it's there, it will be the lowest entry in the BST.
If the number was in the 'special numbers' database, increment the 'allocated numbers' value (to include that number) and remove the entry from the special numbers. Then repeat this process until you get a number that isn't in the special numbers.
Note that this process ensures that all 'special numbers' lower than the last one allocated by 'next' do not appear in the special numbers database. As the 'last normal number allocated' increases, it absorbs any special numbers allocated that were less than that, removing them from the table. This is what ensures that when we ask whether the next number in sequence is in the special numbers database, we only have to look at the lowest entry.
Checking for a special number is easy. If it is lower than the last 'normal' number allocated it isn't available. Otherwise you check to see if it exists in the BST. If it doesn't, you add it to the BST.
You can optimize this process by storing not just single numbers in the BST, but storing ranges of numbers. If the allocated special numbers are dense, then it reduces the amount of space in the tree and the number of accesses to find if one is in there. During the test to find if the 'next' number discovers a rnage of size n, then you can immediately increment the highest normal number by n, instead of having to go round the loop n times.
First, you did not prototype your APIs. For example, if I have to design these APIs I will publish 2 APIs.
string acquireNextAvailableNumber();
string acquireRequestedNumber(string special);
Second, you need to decide how you are going to implement it. code driven or data driven ?
You can maintain hash for all these numbers ( it will consume memory ) and quickly query the availability of the number. Or
you could maintain single list to store only distributed numbers ( less memory ). So, whenever request comes, you start searching 1 to n numbers in that list ( increased time-complexity ). if any first (or requested) number isn't there then you allocate it to client and add that entry in the list.
As, there are billion numbers, you will need to consider the trade-off between space and time.
You could also take the advantage of the database.
To enhance previous answers, any BST may not be good enough as insertions or deletions can make it unbalanced. A balanced BST, e.g. Red-Black Tree, should be a good choice.
So, a Red-Black Tree can be created and filled in the beginning to represent available numbers, and each allocation should remove an element from it.
init(from, to) - can be done in O(n) time, a straightforward implementation would be O(n log n). But that is a one-time initialization on your server's start
acquireNextAvailableNumber() - should remove smallest element, time cost O(1)
acquireRequestedNumber(special) - should make a search and remove element if found, guaranteed time cost O(log n)
In Java, a TreeSet<String> or TreeSet<Integer> could be used since it is implemented with Red-Black Tree.
The next question would probably have been that several request-processing threads would access your API, so since Java's TreeSet is not thread-safe, you should have wrapped it at initialization like so:
TreeSet numbers = init(...);
SortedSet availableNumbers = Collections.synchronizedSortedSet(numbers);
I have an application in which I have to store a couple of millions of integers, I have to store them in a Look up table, obviously I cannot store such amount of data in memory and in my requirements I am very limited I have to store the data in an embebedded system so I am very limited in the space, so I would like to ask you about recommended methods that I can use for the reduction of the look up table. I cannot use function approximation such as neural networks, the values needs to be in a table. The range of the integers is not known at the moment. When I say integers I mean a 32 bit value.
Basically the idea is use some copmpression method to reduce the amount of memory but without losing many precision. This thing needs to run in hardware so the computation overhead cannot be very high.
In my algorithm I have to access to one value of the table do some operations with it and after update the value. In the end what I should have is a function which I pass an index to it and then I get a value, and after I have to use another function to write a value in the table.
I found one called tile coding , this one is based on several look up tables, does anyone know any other method?.
Thanks.
I'd look at the types of numbers you need to store and pull out the information that's common for many of them. For example, if they're tightly clustered, you can take the mean, store it, and store the offsets. The offsets will have fewer bits than the original numbers. Or, if they're more or less uniformly distributed, you can store the first number and then store the offset to the next number.
It would help to know what your key is to look up the numbers.
I need more detail on the problem. If you cannot store the real value of the integers but instead an approximation, that means you are going to reduce (throw away) some of the data (detail), correct? I think you are looking for a hash, which can be an artform in itself. For example say you have 32 bit values, one hash would be to take the 4 bytes and xor them together, this would result in a single 8 bit value, reducing your storage by a factor of 4 but also reducing the real value of original data. Typically you could/would go further and perhaps and only use a few of those 8 bits , say the lower 4 and reduce the value further.
I think my real problem is either you need the data or you dont, if you need the data you need to compress it or find more memory to store it. If you dont, then use a hash of some sort to reduce the number of bits until you reach the amount of memory you have for storage.
Read http://www.cs.ualberta.ca/~sutton/RL-FAQ.html
"Function approximation" refers to the
use of a parameterized functional form
to represent the value function
(and/or the policy), as opposed to a
simple table."
Perhaps that applies. Also, update your question with additional facts -- don't merely answer in the comments.
Edit.
A bit array can easily store a bit for each of your millions of numbers. Let's say you have numbers in the range of 1 to 8 million. In a single megabyte of storage you can have a 1 bit for each number in your set and a 0 for each number not in your set.
If you have numbers in the range of 1 to 32 million, you'll require 4Mb of memory for a big table of all 32M distinct numbers.
See my answer to Modern, high performance bloom filter in Python? for a Python implementation of a bit array of unlimited size.
If you are merely looking for the presence of the number in question a bloom filter, might be what you are looking for. Honestly though your question is fairly vague and confusing. It would help to explain what Q values are, and what you do with them once you find them in the table.
If your set of integers is homongenous, then you could try a hash table, because there is a trick you can use to cut the size of the stored integers, in your case, in half.
Assume the integer, n, because its set is homogenous can be the hash. Assume you have 0x10000 (16k) buckets. Each bucket index, iBucket = n&FFFF. Each item in a bucket need only store 16 bits, since the first 16 bits are the bucket index. The other thing you have to do to keep the data small is to put the count of items in the bucket, and use an array to hold the items in the bucket. Using a linked list will be too large and slow. When you iterate the array looking for a match, remember you only need to compare the 16 bits that are stored.
So assuming a bucket is a pointer to the array and a count. On a 32 bit system, this is 64 bits max. If the number of ints was small enough we might be able to do some fancy things and use 32 bits for a bucket. 16k * 8 bytes = 524k, 2 million shorts = 4mb. So this gets you a method to lookup the ints and about 40% compression.