Inlet -> front -> middle -> rear -> outlet
Those five properties have a value anything between 4 - 40. Now i want to calculate a specific match for each of those values that is either a full 10 or a 5 when a single property is summed from each pipe piece. There might be hundreds of different pipe pieces all with different properties.
So if i have all 5 pieces and when summed, their properties go like 54,51,23,71,37. That is not good and not what im looking.
Instead 55,50,25,70,40. That would be perfect.
My trouble is there are so many of the pieces that it would be insane to do the miss'matching manually, and new ones come up frequently.
I have manually inserted about 100 of these already into SQLite, but should be easy to convert into any excel or other database formats, so answer can be related to anything like mysql or googlesheets.
I need the calculation that takes every piece in account and results either in "no match" or tells me the id of each piece that is required for a match and if multiple matches are available, it separates them.
Edit: Even just the math needed to do this kind of calculation would be a lot of help here, not much of a math guy myself. I guess there should be a reference piece i need to use and then that gets checked against every possible scenario.
If the value you want to verify is in A1, use: =ROUND(A1/5,0)*5
If the pipes may not be shorter than the given values, use =CEILING(A1,5)
Mathematician here looking for a bit of help. (If you ever need math help I'll try to reciprocate on math.stackexchange!) Sorry if this is a dup. Couldn't find it myself.
Here's the thing. I write a lot of code (mostly in C) that is extremely slow and I know it could be sped up considerably but I'm not sure what data structure to use. I went to school 20 years ago and unfortunately never got to take a computer science course. I have watched a lot of open-course videos on data structures but I'm still a bit fuddled never taking an actual class.
Mostly my functions just take integers to integers. I almost always use 64-bit numbers and I have three use cases that I'm interested in. I use the word small to mean no more than a million or two in quantity.
Case 1: Small numbers as input. Outputs are arbitrary.
Case 2: Any 64-bit values as input, but only a small number of them. Outputs are arbitrary.
Case 3: Two parameter functions with one parameter that's small in value (say less than two million), and the other parameter is Large but with only a small number of possible inputs. Outputs are arbitrary.
For Case 1, I just make an array to cache the values. Easy and fast.
For Case 2, I think I should be using a hash. I haven't yet done this but I think I could figure it out if I took the time.
Case 3 is the one I'd like help with and I'm not even sure what I need.
For a specific example take a function F(n,p) that takes large inputs n for the first parameter and a prime p for the second. The prime is at most the square root of n. so even if n is about 10^12, the primes are only up to about a million. Suppose this function is recursive or otherwise difficult to calculate (expensive) and will be called over and over with the same inputs. What might be a good data structure to use to easily create and retrieve the possible values of F(n,p) so that I don't have to recalculate it every time? Total number of possible inputs should be 10 or 20 million at most.
Help please! and Thank you in advance!
You are talking about memoizing I presume. Trying to answer without a concrete exemple...
If you have to retrieve values from a small range (the 2nd parameter), say from 0 to 10^6, and that needs to be upper fast, and... you have enough memory, you could simply declare an array of int (long...), which basically stores the output values from all input.
To make things simple, let say the value 0 means there is no-value set
long *small = calloc(MAX, sizeof(*small)); // Calloc intializes to 0
then in a function that gives the value for a small range
if (small[ input ]) return small[ input ];
....calculate
small[ input ] = value;
+/-
+ Very fast
- Memory consumption takes the whole range, [ 0, MAX-1 ].
If you need to store arbitrary input, use the many libraries available (there are so many). Use a Set structure, that tells if the items exists or no.
if (set.exists( input )) return set.get( input );
....calculate
set.set( input, value );
+/-
+ less memory usage
+ still fast (said to be O(1))
- but, not as fast as a mere array
Add to this the hashed set (...), which are faster, as in terms of probabilities, values (hashes) are better distributed.
+/-
+ less memory usage than array
+ faster than a simple Set
- but, not as fast as a mere array
- use more memory than a simple Set
I'm trying to find a way to store my data with fast access (better than O(n)).
My database consists of data (4096 byte strings) that represents some information about some items.
The problem is, that the query is never exact. I get one Item, and then need to find the closest match using a function F(a,b).
just an example:
1234
3456
6466
F(a,b) = return % of similar digits
GetClosest(1233,F) = 1234
The problem is that F(a,b) is a complicated algorithm, (not a proper metric).
What I have now is just go over the whole database to search for the best match.
Is there a kind of tree or other cluster database type that can give me faster finding complexity ?
More information:
F gives back a similarity value in %percentage. where 100% is a perfect match.
Sorry, the answer is "probably not" unless there is some more structure to your problem that you haven't described. With 4096 byte strings you're suffering from the curse of dimensionality.
If you had shorter strings and enough data that there was a high likelihood of the nearest match being identical over a large chunk of the string, then you could store your data with multiple tree-like structures indexed over different chunks of the string. With high likelihood the nearest would be close enough that you could prove it was nearest based only on close elements in those trees. However with the size of your strings and the limited data that can be stored in a computer, there is no way this is possibly going to work.
That said, do you need the exact closest, or only a somewhat close one? If only a likely close one, then you could index it by several random sparse samples of bits. In your search you can only check elements that match exactly in one of the elements. This will greatly reduce the search space, while rejecting fewer of the close neighbors, and may produce reasonable (even though frequently wrong) answers.
Is there some way you could assign a 'score' to each datum.
You could index/sequence the data by your score.
When you search you assign a score to your search criteria, and look for the item with the closest score.
Depends very much on your data and your definition of "difference" whether this will work.
Say, i have 10 billions of numbers stored in a file. How would i find the number that has already appeared once previously?
Well i can't just populate billions of number at a stretch in array and then keep a simple nested loop to check if the number has appeared previously.
How would you approach this problem?
Thanks in advance :)
I had this as an interview question once.
Here is an algorithm that is O(N)
Use a hash table. Sequentially store pointers to the numbers, where the hash key is computed from the number value. Once you have a collision, you have found your duplicate.
Author Edit:
Below, #Phimuemue makes the excellent point that 4-byte integers have a fixed bound before a collision is guaranteed; that is 2^32, or approx. 4 GB. When considered in the conversation accompanying this answer, worst-case memory consumption by this algorithm is dramatically reduced.
Furthermore, using the bit array as described below can reduce memory consumption to 1/8th, 512mb. On many machines, this computation is now possible without considering either a persistent hash, or the less-performant sort-first strategy.
Now, longer numbers or double-precision numbers are less-effective scenarios for the bit array strategy.
Phimuemue Edit:
Of course one needs to take a bit "special" hash table:
Take a hashtable consisting of 2^32 bits. Since the question asks about 4-byte-integers, there are at most 2^32 different of them, i.e. one bit for each number. 2^32 bit = 512mb.
So now one has just to determine the location of the corresponding bit in the hashmap and set it. If one encounters a bit which already is set, the number occured in the sequence already.
The important question is whether you want to solve this problem efficiently, or whether you want accurately.
If you truly have 10 billion numbers and just one single duplicate, then you are in a "needle in the haystack" type of situation. Intuitively, short of very grimy and unstable solution, there is no hope of solving this without storing a significant amount of the numbers.
Instead, turn to probabilistic solutions, which have been used in most any practical application of this problem (in network analysis, what you are trying to do is look for mice, i.e., elements which appear very infrequently in a large data set).
A possible solution, which can be made to find exact results: use a sufficiently high-resolution Bloom filter. Either use the filter to determine if an element has already been seen, or, if you want perfect accuracy, use (as kbrimington suggested you use a standard hash table) the filter to, eh, filter out elements which you can't possibly have seen and, on a second pass, determine the elements you actually see twice.
And if your problem is slightly different---for instance, you know that you have at least 0.001% elements which repeat themselves twice, and you would like to find out how many there are approximately, or you would like to get a random sample of such elements---then a whole score of probabilistic streaming algorithms, in the vein of Flajolet & Martin, Alon et al., exist and are very interesting (not to mention highly efficient).
Read the file once, create a hashtable storing the number of times you encounter each item. But wait! Instead of using the item itself as a key, you use a hash of the item iself, for example the least significant digits, let's say 20 digits (1M items).
After the first pass, all items that have counter > 1 may point to a duplicated item, or be a false positive. Rescan the file, consider only items that may lead to a duplicate (looking up each item in table one), build a new hashtable using real values as keys now and storing the count again.
After the second pass, items with count > 1 in the second table are your duplicates.
This is still O(n), just twice as slow as a single pass.
How about:
Sort input by using some algorith which allows only portion of input to be in RAM. Examples are there
Seek duplicates in output of 1st step -- you'll need space for just 2 elements of input in RAM at a time to detect repetitions.
Finding duplicates
Noting that its a 32bit integer means that you're going to have a large number of duplicates, since a 32 bit int can only represent 4.3ish billion different numbers and you have "10 billions".
If you were to use a tightly packed set you could represent whether all the possibilities are in 512 MB, which can easily fit into current RAM values. This as a start pretty easily allows you to recognise the fact if a number is duplicated or not.
Counting Duplicates
If you need to know how many times a number is duplicated you're getting into having a hashmap that contains only duplicates (using the first 500MB of the ram to tell efficiently IF it should be in the map or not). At a worst case scenario with a large spread you're not going to be able fit that into ram.
Another approach if the numbers will have an even amount of duplicates is to use a tightly packed array with 2-8 bits per value, taking about 1-4GB of RAM allowing you to count up to 255 occurrances of each number.
Its going to be a hack, but its doable.
You need to implement some sort of looping construct to read the numbers one at a time since you can't have them in memory all at once.
How? Oh, what language are you using?
You have to read each number and store it into a hashmap, so that if a number occurs again, it will automatically get discarded.
If possible range of numbers in file is not too large then you can use some bit array to indicate if some of the number in range appeared.
If the range of the numbers is small enough, you can use a bit field to store if it is in there - initialize that with a single scan through the file. Takes one bit per possible number.
With large range (like int) you need to read through the file every time. File layout may allow for more efficient lookups (i.e. binary search in case of sorted array).
If time is not an issue and RAM is, you could read each number and then compare it to each subsequent number by reading from the file without storing it in RAM. It will take an incredible amount of time but you will not run out of memory.
I have to agree with kbrimington and his idea of a hash table, but first of all, I would like to know the range of the numbers that you're looking for. Basically, if you're looking for 32-bit numbers, you would need a single array of 4.294.967.296 bits. You start by setting all bits to 0 and every number in the file will set a specific bit. If the bit is already set then you've found a number that has occurred before. Do you also need to know how often they occur?Still, it would need 536.870.912 bytes at least. (512 MB.) It's a lot and would require some crafty programming skills. Depending on your programming language and personal experience, there would be hundreds of solutions to solve it this way.
Had to do this a long time ago.
What i did... i sorted the numbers as much as i could (had a time-constraint limit) and arranged them like this while sorting:
1 to 10, 12, 16, 20 to 50, 52 would become..
[1,10], 12, 16, [20,50], 52, ...
Since in my case i had hundreds of numbers that were very "close" ($a-$b=1), from a few million sets i had a very low memory useage
p.s. another way to store them
1, -9, 12, 16, 20, -30, 52,
when i had no numbers lower than zero
After that i applied various algorithms (described by other posters) here on the reduced data set
#include <stdio.h>
#include <stdlib.h>
/* Macro is overly general but I left it 'cos it's convenient */
#define BITOP(a,b,op) \
((a)[(size_t)(b)/(8*sizeof *(a))] op (size_t)1<<((size_t)(b)%(8*sizeof *(a))))
int main(void)
{
unsigned x=0;
size_t *seen = malloc(1<<8*sizeof(unsigned)-3);
while (scanf("%u", &x)>0 && !BITOP(seen,x,&)) BITOP(seen,x,|=);
if (BITOP(seen,x,&)) printf("duplicate is %u\n", x);
else printf("no duplicate\n");
return 0;
}
This is a simple problem that can be solved very easily (several lines of code) and very fast (several minutes of execution) with the right tools
my personal approach would be in using MapReduce
MapReduce: Simplified Data Processing on Large Clusters
i'm sorry for not going into more details but once getting familiar with the concept of MapReduce it is going to be very clear on how to target the solution
basicly we are going to implement two simple functions
Map(key, value)
Reduce(key, values[])
so all in all:
open file and iterate through the data
for each number -> Map(number, line_index)
in the reduce we will get the number as the key and the total occurrences as the number of values (including their positions in the file)
so in Reduce(key, values[]) if number of values > 1 than its a duplicate number
print the duplicates : number, line_index1, line_index2,...
again this approach can result in a very fast execution depending on how your MapReduce framework is set, highly scalable and very reliable, there are many diffrent implementations for MapReduce in many languages
there are several top companies presenting already built up cloud computing environments like Google, Microsoft azure, Amazon AWS, ...
or you can build your own and set a cluster with any providers offering virtual computing environments paying very low costs by the hour
good luck :)
Another more simple approach could be in using bloom filters
AdamT
Implement a BitArray such that ith index of this array will correspond to the numbers 8*i +1 to 8*(i+1) -1. ie first bit of ith number is 1 if we already had seen 8*i+1. Second bit of ith number is 1 if we already have seen 8*i + 2 and so on.
Initialize this bit array with size Integer.Max/8 and whenever you saw a number k, Set the k%8 bit of k/8 index as 1 if this bit is already 1 means you have seen this number already.
I have a system that stores vectors and allows a user to find the n most similar vectors to the user's query vector. That is, a user submits a vector (I call it a query vector) and my system spits out "here are the n most similar vectors." I generate the similar vectors using a KD-Tree and everything works well, but I want to do more. I want to present a list of the n most similar vectors even if the user doesn't submit a complete vector (a vector with missing values). That is, if a user submits a vector with three dimensions, I still want to find the n nearest vectors (stored vectors are of 11 dimensions) I have stored.
I have a couple of obvious solutions, but I'm not sure either one seem very good:
Create multiple KD-Trees each built using the most popular subset of dimensions a user will search for. That is, if a user submits a query vector of thee dimensions, x, y, z, I match that query to my already built KD-Tree which only contains vectors of three dimensions, x, y, z.
Ignore KD-Trees when a user submits a query vector with missing values and compare the query vector to the vectors (stored in a table in a DB) one by one using something like a dot product.
This has to be a common problem, any suggestions? Thanks for the help.
Your first solution might be fastest for queries (since the tree-building doesn't consider splits in directions that you don't care about), but it would definitely use a lot of memory. And if you have to rebuild the trees repeatedly, it could get slow.
The second option looks very slow unless you only have a few points. And if that's the case, you probably didn't need a kd-tree in the first place :)
I think the best solution involves getting your hands dirty in the code that you're working with. Presumably the nearest-neighbor search computes the distance between the point in the tree leaf and the query vector; you should be able to modify this to handle the case where the point and the query vector are different sizes. E.g. if the points in the tree are given in 3D, but your query vector is only length 2, then the "distance" between the point (p0, p1, p2) and the query vector (x0, x1) would be
sqrt( (p0-x0)^2 + (p1-x1)^2 )
I didn't dig into the java code that you linked to, but I can try to find exactly where the change would need to go if you need help.
-Chris
PS - you might not need the sqrt in the equation above, since distance squared is usually equivalent.
EDIT
Sorry, didn't realize it would be so obvious in the source code. You should use this version of the neighbor function:
nearest(double [] key, int n, Checker<T> checker)
And implement your own Checker class; see their EuclideanDistance.java to see the Euclidean version. You may also need to comment out any KeySizeException that the query code throws, since you know that you can handle differently sized keys.
Your second option looks like a reasonable solution for what you want.
You could also populate the missing dimensions with the most important( or average or whatever you think it should be) values if there are any.
You could try using the existing KD tree -- by taking both branches when the split is for a dimension that is not supplied by the source vector. This should take less time than doing a brute force search, and might be less trouble than trying to maintain a bunch of specialized trees for dimension subsets.
You would need to adapt your N-closest algorithm (without more info I can't advise you on that...), and for distance you would use the sum of the squares of only those elements supplied by the source vector.
Here's what I ended up doing: When a user didn't specify a value (when their query vector lacked a dimension), I I simply adjusted my matching range (in the API) to something huge so that I match any value.