I'm attempting to estimate the total amount of results for app engine queries that will return large amounts of results.
In order to do this, I assigned a random floating point number between 0 and 1 to every entity. Then I executed the query for which I wanted to estimate the total results with the following 3 settings:
* I ordered by the random numbers that I had assigned in ascending order
* I set the offset to 1000
* I fetched only one entity
I then plugged the entities's random value that I had assigned for this purpose into the following equation to estimate the total results (since I used 1000 as the offset above, the value of OFFSET would be 1000 in this case):
1 / RANDOM * OFFSET
The idea is that since each entity has a random number assigned to it, and I am sorting by that random number, the entity's random number assignment should be proportionate to the beginning and end of the results with respect to its offset (in this case, 1000).
The problem I am having is that the results I am getting are giving me low estimates. And the estimates are lower, the lower the offset. I had anticipated that the lower the offset that I used, the less accurate the estimate should be, but I thought that the margin of error would be both above and below the actual number of results.
Below is a chart demonstrating what I am talking about. As you can see, the predictions get more consistent (accurate) as the offset increases from 1000 to 5000. But then the predictions predictably follow a 4 part polynomial. (y = -5E-15x4 + 7E-10x3 - 3E-05x2 + 0.3781x + 51608).
Am I making a mistake here, or does the standard python random number generator not distribute numbers evenly enough for this purpose?
Thanks!
Edit:
It turns out that this problem is due to my mistake. In another part of the program, I was grabbing entities from the beginning of the series, doing an operation, then re-assigning the random number. This resulted in a denser distribution of random numbers towards the end.
I did a little more digging into this concept, fixed the problem, and tried it again on a different query (so the number of results are different from above). I found that this idea can be used to estimate the total results for a query. One thing of note is that the "error" is very similar for offsets that are close by. When I did a scatter chart in excel, I expected the accuracy of the predictions at each offset to "cloud". Meaning that offsets at the very begging would produce a larger, less dense cloud that would converge to a very tiny, dense could around the actual value as the offsets got larger. This is not what happened as you can see below in the cart of how far off the predictions were at each offset. Where I thought there would be a cloud of dots, there is a line instead.
This is a chart of the maximum after each offset. For example the maximum error for any offset after 10000 was less than 1%:
When using GAE it makes a lot more sense not to try to do large amounts work on reads - it's built and optimized for very fast requests turnarounds. In this case it's actually more efficent to maintain a count of your results as and when you create the entities.
If you have a standard query, this is fairly easy - just use a sharded counter when creating the entities. You can seed this using a map reduce job to get the initial count.
If you have queries that might be dynamic, this is more difficult. If you know the range of possible queries that you might perform, you'd want to create a counter for each query that might run.
If the range of possible queries is infinite, you might want to think of aggregating counters or using them in more creative ways.
If you tell us the query you're trying to run, there might be someone who has a better idea.
Some quick thought:
Have you tried Datastore Statistics API? It may provide a fast and accurate results if you won't update your entities set very frequently.
http://code.google.com/appengine/docs/python/datastore/stats.html
[EDIT1.]
I did some math things, I think the estimate method you purposed here, could be rephrased as an "Order statistic" problem.
http://en.wikipedia.org/wiki/Order_statistic#The_order_statistics_of_the_uniform_distribution
For example:
If the actual entities number is 60000, the question equals to "what's the probability that your 1000th [2000th, 3000th, .... ] sample falling in the interval [l,u]; therefore, the estimated total entities number based on this sample, will have an acceptable error to 60000."
If the acceptable error is 5%, the interval [l, u] will be [0.015873015873015872, 0.017543859649122806]
I think the probability won't be very large.
This doesn't directly deal with the calculations aspect of your question, but would using the count attribute of a query object work for you? Or have you tried that out and it's not suitable? As per the docs, it's only slightly faster than retrieving all of the data, but on the plus side it would give you the actual number of results.
http://code.google.com/appengine/docs/python/datastore/queryclass.html#Query_count
Currently I am loooking for a way to develop an algorithm which is supposed to analyse a large dataset (about 600M records). The records have parameters "calling party", "called party", "call duration" and I would like to create a graph of weighted connections among phone users.
The whole dataset consists of similar records - people mostly talk to their friends and don't dial random numbers but occasionaly a person calls "random" numbers as well. For analysing the records I was thinking about the following logic:
create an array of numbers to indicate the which records (row number) have already been scanned.
start scanning from the first line and for the first line combination "calling party", "called party" check for the same combinations in the database
sum the call durations and divide the result by the sum of all call durations
add the numbers of summed lines into the array created at the beginning
check the array if the next record number has already been summed
if it has already been summed then skip the record, else perform step 2
I would appreciate if anyone of you suggested any improvement of the logic described above.
p.s. the edges are directed therefore the (calling party, called party) is not equal to (called party, calling party)
Although the fact is not programming related I would like to emphasize that due to law and respect for user privacy all the informations that could possibly reveal the user identity have been hashed before the analysis.
As always with large datasets the more information you have about the distribution of values in them the better you can tailor an algorithm. For example, if you knew that there were only, say, 1000 different telephone numbers to consider you could create a 1000x1000 array into which to write your statistics.
Your first step should be to analyse the distribution(s) of data in your dataset.
In the absence of any further information about your data I'm inclined to suggest that you create a hash table. Read each record in your 600M dataset and calculate a hash address from the concatenation of calling and called numbers. Into the table at that address write the calling and called numbers (you'll need them later, and bear in mind that the hash is probably irreversible), add 1 to the number of calls and add the duration to the total duration. Repeat 600M times.
Now you have a hash table which contains the data you want.
Since there are 600 M records, it seems to be large enough to leverage a database (and not too large to require a distributed Database). So, you could simply load this into a DB (MySQL, SQLServer, Oracle, etc) and run the following queries:
select calling_party, called_party, sum(call_duration), avg(call_duration), min(call_duration), max (call_duration), count(*) from call_log group by calling_party, called_party order by 7 desc
That would be a start.
Next, you would want to run some Association analysis (possibly using Weka), or perhaps you would want to analyze this information as cubes (possibly using Mondrian/OLAP). If you tell us more, we can help you more.
Algorithmically, what the DB is doing internally is similar to what you would do yourself programmatically:
Scan each record
Find the record for each (calling_party, called_party) combination, and update its stats.
A good way to store and find records for (calling_party, called_party) would be to use a hashfunction and to find the matching record from the bucket.
Althought it may be tempting to create a two dimensional array for (calling_party, called_party), that will he a very sparse array (very wasteful).
How often will you need to perform this analysis? If this is a large, unique dataset and thus only once or twice - don't worry too much about the performance, just get it done, e.g. as Amrinder Arora says by using simple, existing tooling you happen to know.
You really want more information about the distribution as High Performance Mark says. For starters, it's be nice to know the count of unique phone numbers, the count of unique phone number pairs, and, the mean, variance and maximum of the count of calling/called phone numbers per unique phone number.
You really want more information about the analysis you want to perform on the result. For instance, are you more interested in holistic statistics or identifying individual clusters? Do you care more about following the links forward (determining who X frequently called) or following the links backward (determining who X was frequently called by)? Do you want to project overviews of this graph into low-dimensional spaces, i.e. 2d? Should be easy to indentify indirect links - e.g. X is near {A, B, C} all of whom are near Y so X is sorta near Y?
If you want fast and frequently adapted results, then be aware that a dense representation with good memory & temporal locality can easily make a huge difference in performance. In particular, that can easily outweigh a factor ln N in big-O notation; you may benefit from a dense, sorted representation over a hashtable. And databases? Those are really slow. Don't touch those if you can avoid it at all; they are likely to be a factor 10000 slower - or more, the more complex the queries are you want to perform on the result.
Just sort records by "calling party" and then by "called party". That way each unique pair will have all its occurrences in consecutive positions. Hence, you can calculate the weight of each pair (calling party, called party) in one pass with little extra memory.
For sorting, you can sort small chunks separately, and then do a N-way merge sort. That's memory efficient and can be easily parallelized.
I'm currently preparing for an interview, and it reminded me of a question I was once asked in a previous interview that went something like this:
"You have been asked to design some software to continuously display the top 10 search terms on Google. You are given access to a feed that provides an endless real-time stream of search terms currently being searched on Google. Describe what algorithm and data structures you would use to implement this. You are to design two variations:
(i) Display the top 10 search terms of all time (i.e. since you started reading the feed).
(ii) Display only the top 10 search terms for the past month, updated hourly.
You can use an approximation to obtain the top 10 list, but you must justify your choices."
I bombed in this interview and still have really no idea how to implement this.
The first part asks for the 10 most frequent items in a continuously growing sub-sequence of an infinite list. I looked into selection algorithms, but couldn't find any online versions to solve this problem.
The second part uses a finite list, but due to the large amount of data being processed, you can't really store the whole month of search terms in memory and calculate a histogram every hour.
The problem is made more difficult by the fact that the top 10 list is being continuously updated, so somehow you need to be calculating your top 10 over a sliding window.
Any ideas?
Frequency Estimation Overview
There are some well-known algorithms that can provide frequency estimates for such a stream using a fixed amount of storage. One is Frequent, by Misra and Gries (1982). From a list of n items, it find all items that occur more than n / k times, using k - 1 counters. This is a generalization of Boyer and Moore's Majority algorithm (Fischer-Salzberg, 1982), where k is 2. Manku and Motwani's LossyCounting (2002) and Metwally's SpaceSaving (2005) algorithms have similar space requirements, but can provide more accurate estimates under certain conditions.
The important thing to remember is that these algorithms can only provide frequency estimates. Specifically, the Misra-Gries estimate can under-count the actual frequency by (n / k) items.
Suppose that you had an algorithm that could positively identify an item only if it occurs more than 50% of the time. Feed this algorithm a stream of N distinct items, and then add another N - 1 copies of one item, x, for a total of 2N - 1 items. If the algorithm tells you that x exceeds 50% of the total, it must have been in the first stream; if it doesn't, x wasn't in the initial stream. In order for the algorithm to make this determination, it must store the initial stream (or some summary proportional to its length)! So, we can prove to ourselves that the space required by such an "exact" algorithm would be Ω(N).
Instead, these frequency algorithms described here provide an estimate, identifying any item that exceeds the threshold, along with some items that fall below it by a certain margin. For example the Majority algorithm, using a single counter, will always give a result; if any item exceeds 50% of the stream, it will be found. But it might also give you an item that occurs only once. You wouldn't know without making a second pass over the data (using, again, a single counter, but looking only for that item).
The Frequent Algorithm
Here's a simple description of Misra-Gries' Frequent algorithm. Demaine (2002) and others have optimized the algorithm, but this gives you the gist.
Specify the threshold fraction, 1 / k; any item that occurs more than n / k times will be found. Create an an empty map (like a red-black tree); the keys will be search terms, and the values will be a counter for that term.
Look at each item in the stream.
If the term exists in the map, increment the associated counter.
Otherwise, if the map less than k - 1 entries, add the term to the map with a counter of one.
However, if the map has k - 1 entries already, decrement the counter in every entry. If any counter reaches zero during this process, remove it from the map.
Note that you can process an infinite amount of data with a fixed amount of storage (just the fixed-size map). The amount of storage required depends only on the threshold of interest, and the size of the stream does not matter.
Counting Searches
In this context, perhaps you buffer one hour of searches, and perform this process on that hour's data. If you can take a second pass over this hour's search log, you can get an exact count of occurrences of the top "candidates" identified in the first pass. Or, maybe its okay to to make a single pass, and report all the candidates, knowing that any item that should be there is included, and any extras are just noise that will disappear in the next hour.
Any candidates that really do exceed the threshold of interest get stored as a summary. Keep a month's worth of these summaries, throwing away the oldest each hour, and you would have a good approximation of the most common search terms.
Well, looks like an awful lot of data, with a perhaps prohibitive cost to store all frequencies. When the amount of data is so large that we cannot hope to store it all, we enter the domain of data stream algorithms.
Useful book in this area:
Muthukrishnan - "Data Streams: Algorithms and Applications"
Closely related reference to the problem at hand which I picked from the above:
Manku, Motwani - "Approximate Frequency Counts over Data Streams" [pdf]
By the way, Motwani, of Stanford, (edit) was an author of the very important "Randomized Algorithms" book. The 11th chapter of this book deals with this problem. Edit: Sorry, bad reference, that particular chapter is on a different problem. After checking, I instead recommend section 5.1.2 of Muthukrishnan's book, available online.
Heh, nice interview question.
This is one of the research project that I am current going through. The requirement is almost exactly as yours, and we have developed nice algorithms to solve the problem.
The Input
The input is an endless stream of English words or phrases (we refer them as tokens).
The Output
Output top N tokens we have seen so
far (from all the tokens we have
seen!)
Output top N tokens in a
historical window, say, last day or
last week.
An application of this research is to find the hot topic or trends of topic in Twitter or Facebook. We have a crawler that crawls on the website, which generates a stream of words, which will feed into the system. The system then will output the words or phrases of top frequency either at overall or historically. Imagine in last couple of weeks the phrase "World Cup" would appears many times in Twitter. So does "Paul the octopus". :)
String into Integers
The system has an integer ID for each word. Though there is almost infinite possible words on the Internet, but after accumulating a large set of words, the possibility of finding new words becomes lower and lower. We have already found 4 million different words, and assigned a unique ID for each. This whole set of data can be loaded into memory as a hash table, consuming roughly 300MB memory. (We have implemented our own hash table. The Java's implementation takes huge memory overhead)
Each phrase then can be identified as an array of integers.
This is important, because sorting and comparisons on integers is much much faster than on strings.
Archive Data
The system keeps archive data for every token. Basically it's pairs of (Token, Frequency). However, the table that stores the data would be so huge such that we have to partition the table physically. Once partition scheme is based on ngrams of the token. If the token is a single word, it is 1gram. If the token is two-word phrase, it is 2gram. And this goes on. Roughly at 4gram we have 1 billion records, with table sized at around 60GB.
Processing Incoming Streams
The system will absorbs incoming sentences until memory becomes fully utilized (Ya, we need a MemoryManager). After taking N sentences and storing in memory, the system pauses, and starts tokenize each sentence into words and phrases. Each token (word or phrase) is counted.
For highly frequent tokens, they are always kept in memory. For less frequent tokens, they are sorted based on IDs (remember we translate the String into an array of integers), and serialized into a disk file.
(However, for your problem, since you are counting only words, then you can put all word-frequency map in memory only. A carefully designed data structure would consume only 300MB memory for 4 million different words. Some hint: use ASCII char to represent Strings), and this is much acceptable.
Meanwhile, there will be another process that is activated once it finds any disk file generated by the system, then start merging it. Since the disk file is sorted, merging would take a similar process like merge sort. Some design need to be taken care at here as well, since we want to avoid too many random disk seeks. The idea is to avoid read (merge process)/write (system output) at the same time, and let the merge process read form one disk while writing into a different disk. This is similar like to implementing a locking.
End of Day
At end of day, the system will have many frequent tokens with frequency stored in memory, and many other less frequent tokens stored in several disk files (and each file is sorted).
The system flush the in-memory map into a disk file (sort it). Now, the problem becomes merging a set of sorted disk file. Using similar process, we would get one sorted disk file at the end.
Then, the final task is to merge the sorted disk file into archive database.
Depends on the size of archive database, the algorithm works like below if it is big enough:
for each record in sorted disk file
update archive database by increasing frequency
if rowcount == 0 then put the record into a list
end for
for each record in the list of having rowcount == 0
insert into archive database
end for
The intuition is that after sometime, the number of inserting will become smaller and smaller. More and more operation will be on updating only. And this updating will not be penalized by index.
Hope this entire explanation would help. :)
You could use a hash table combined with a binary search tree. Implement a <search term, count> dictionary which tells you how many times each search term has been searched for.
Obviously iterating the entire hash table every hour to get the top 10 is very bad. But this is google we're talking about, so you can assume that the top ten will all get, say over 10 000 hits (it's probably a much larger number though). So every time a search term's count exceeds 10 000, insert it in the BST. Then every hour, you only have to get the first 10 from the BST, which should contain relatively few entries.
This solves the problem of top-10-of-all-time.
The really tricky part is dealing with one term taking another's place in the monthly report (for example, "stack overflow" might have 50 000 hits for the past two months, but only 10 000 the past month, while "amazon" might have 40 000 for the past two months but 30 000 for the past month. You want "amazon" to come before "stack overflow" in your monthly report). To do this, I would store, for all major (above 10 000 all-time searches) search terms, a 30-day list that tells you how many times that term was searched for on each day. The list would work like a FIFO queue: you remove the first day and insert a new one each day (or each hour, but then you might need to store more information, which means more memory / space. If memory is not a problem do it, otherwise go for that "approximation" they're talking about).
This looks like a good start. You can then worry about pruning the terms that have > 10 000 hits but haven't had many in a long while and stuff like that.
case i)
Maintain a hashtable for all the searchterms, as well as a sorted top-ten list separate from the hashtable. Whenever a search occurs, increment the appropriate item in the hashtable and check to see if that item should now be switched with the 10th item in the top-ten list.
O(1) lookup for the top-ten list, and max O(log(n)) insertion into the hashtable (assuming collisions managed by a self-balancing binary tree).
case ii)
Instead of maintaining a huge hashtable and a small list, we maintain a hashtable and a sorted list of all items. Whenever a search is made, that term is incremented in the hashtable, and in the sorted list the term can be checked to see if it should switch with the term after it. A self-balancing binary tree could work well for this, as we also need to be able to query it quickly (more on this later).
In addition we also maintain a list of 'hours' in the form of a FIFO list (queue). Each 'hour' element would contain a list of all searches done within that particular hour. So for example, our list of hours might look like this:
Time: 0 hours
-Search Terms:
-free stuff: 56
-funny pics: 321
-stackoverflow: 1234
Time: 1 hour
-Search Terms:
-ebay: 12
-funny pics: 1
-stackoverflow: 522
-BP sucks: 92
Then, every hour: If the list has at least 720 hours long (that's the number of hours in 30 days), look at the first element in the list, and for each search term, decrement that element in the hashtable by the appropriate amount. Afterwards, delete that first hour element from the list.
So let's say we're at hour 721, and we're ready to look at the first hour in our list (above). We'd decrement free stuff by 56 in the hashtable, funny pics by 321, etc., and would then remove hour 0 from the list completely since we will never need to look at it again.
The reason we maintain a sorted list of all terms that allows for fast queries is because every hour after as we go through the search terms from 720 hours ago, we need to ensure the top-ten list remains sorted. So as we decrement 'free stuff' by 56 in the hashtable for example, we'd check to see where it now belongs in the list. Because it's a self-balancing binary tree, all of that can be accomplished nicely in O(log(n)) time.
Edit: Sacrificing accuracy for space...
It might be useful to also implement a big list in the first one, as in the second one. Then we could apply the following space optimization on both cases: Run a cron job to remove all but the top x items in the list. This would keep the space requirement down (and as a result make queries on the list faster). Of course, it would result in an approximate result, but this is allowed. x could be calculated before deploying the application based on available memory, and adjusted dynamically if more memory becomes available.
Rough thinking...
For top 10 all time
Using a hash collection where a count for each term is stored (sanitize terms, etc.)
An sorted array which contains the ongoing top 10, a term/count in added to this array whenever the count of a term becomes equal or greater than the smallest count in the array
For monthly top 10 updated hourly:
Using an array indexed on number of hours elapsed since start modulo 744 (the number of hours during a month), which array entries consist of hash collection where a count for each term encountered during this hour-slot is stored. An entry is reset whenever the hour-slot counter changes
the stats in the array indexed on hour-slot needs to be collected whenever the current hour-slot counter changes (once an hour at most), by copying and flattening the content of this array indexed on hour-slots
Errr... make sense? I didn't think this through as I would in real life
Ah yes, forgot to mention, the hourly "copying/flattening" required for the monthly stats can actually reuse the same code used for the top 10 of all time, a nice side effect.
Exact solution
First, a solution that guarantees correct results, but requires a lot of memory (a big map).
"All-time" variant
Maintain a hash map with queries as keys and their counts as values. Additionally, keep a list f 10 most frequent queries so far and the count of the 10th most frequent count (a threshold).
Constantly update the map as the stream of queries is read. Every time a count exceeds the current threshold, do the following: remove the 10th query from the "Top 10" list, replace it with the query you've just updated, and update the threshold as well.
"Past month" variant
Keep the same "Top 10" list and update it the same way as above. Also, keep a similar map, but this time store vectors of 30*24 = 720 count (one for each hour) as values. Every hour do the following for every key: remove the oldest counter from the vector add a new one (initialized to 0) at the end. Remove the key from the map if the vector is all-zero. Also, every hour you have to calculate the "Top 10" list from scratch.
Note: Yes, this time we're storing 720 integers instead of one, but there are much less keys (the all-time variant has a really long tail).
Approximations
These approximations do not guarantee the correct solution, but are less memory-consuming.
Process every N-th query, skipping the rest.
(For all-time variant only) Keep at most M key-value pairs in the map (M should be as big as you can afford). It's a kind of an LRU cache: every time you read a query that is not in the map, remove the least recently used query with count 1 and replace it with the currently processed query.
Top 10 search terms for the past month
Using memory efficient indexing/data structure, such as tightly packed tries (from wikipedia entries on tries) approximately defines some relation between memory requirements and n - number of terms.
In case that required memory is available (assumption 1), you can keep exact monthly statistic and aggregate it every month into all time statistic.
There is, also, an assumption here that interprets the 'last month' as fixed window.
But even if the monthly window is sliding the above procedure shows the principle (sliding can be approximated with fixed windows of given size).
This reminds me of round-robin database with the exception that some stats are calculated on 'all time' (in a sense that not all data is retained; rrd consolidates time periods disregarding details by averaging, summing up or choosing max/min values, in given task the detail that is lost is information on low frequency items, which can introduce errors).
Assumption 1
If we can not hold perfect stats for the whole month, then we should be able to find a certain period P for which we should be able to hold perfect stats.
For example, assuming we have perfect statistics on some time period P, which goes into month n times.
Perfect stats define function f(search_term) -> search_term_occurance.
If we can keep all n perfect stat tables in memory then sliding monthly stats can be calculated like this:
add stats for the newest period
remove stats for the oldest period (so we have to keep n perfect stat tables)
However, if we keep only top 10 on the aggregated level (monthly) then we will be able to discard a lot of data from the full stats of the fixed period. This gives already a working procedure which has fixed (assuming upper bound on perfect stat table for period P) memory requirements.
The problem with the above procedure is that if we keep info on only top 10 terms for a sliding window (similarly for all time), then the stats are going to be correct for search terms that peak in a period, but might not see the stats for search terms that trickle in constantly over time.
This can be offset by keeping info on more than top 10 terms, for example top 100 terms, hoping that top 10 will be correct.
I think that further analysis could relate the minimum number of occurrences required for an entry to become a part of the stats (which is related to maximum error).
(In deciding which entries should become part of the stats one could also monitor and track the trends; for example if a linear extrapolation of the occurrences in each period P for each term tells you that the term will become significant in a month or two you might already start tracking it. Similar principle applies for removing the search term from the tracked pool.)
Worst case for the above is when you have a lot of almost equally frequent terms and they change all the time (for example if tracking only 100 terms, then if top 150 terms occur equally frequently, but top 50 are more often in first month and lest often some time later then the statistics would not be kept correctly).
Also there could be another approach which is not fixed in memory size (well strictly speaking neither is the above), which would define minimum significance in terms of occurrences/period (day, month, year, all-time) for which to keep the stats. This could guarantee max error in each of the stats during aggregation (see round robin again).
What about an adaption of the "clock page replacement algorithm" (also known as "second-chance")? I can imagine it to work very well if the search requests are distributed evenly (that means most searched terms appear regularly rather than 5mio times in a row and then never again).
Here's a visual representation of the algorithm:
The problem is not universally solvable when you have a fixed amount of memory and an 'infinite' (think very very large) stream of tokens.
A rough explanation...
To see why, consider a token stream that has a particular token (i.e., word) T every N tokens in the input stream.
Also, assume that the memory can hold references (word id and counts) to at most M tokens.
With these conditions, it is possible to construct an input stream where the token T will never be detected if the N is large enough so that the stream contains different M tokens between T's.
This is independent of the top-N algorithm details. It only depends on the limit M.
To see why this is true, consider the incoming stream made up of groups of two identical tokens:
T a1 a2 a3 ... a-M T b1 b2 b3 ... b-M ...
where the a's, and b's are all valid tokens not equal to T.
Notice that in this stream, the T appears twice for each a-i and b-i. Yet it appears rarely enough to be flushed from the system.
Starting with an empty memory, the first token (T) will take up a slot in the memory (bounded by M). Then a1 will consume a slot, all the way to a-(M-1) when the M is exhausted.
When a-M arrives the algorithm has to drop one symbol so let it be the T.
The next symbol will be b-1 which will cause a-1 to be flushed, etc.
So, the T will not stay memory-resident long enough to build up a real count. In short, any algorithm will miss a token of low enough local frequency but high global frequency (over the length of the stream).
Store the count of search terms in a giant hash table, where each new search causes a particular element to be incremented by one. Keep track of the top 20 or so search terms; when the element in 11th place is incremented, check if it needs to swap positions with #10* (it's not necessary to keep the top 10 sorted; all you care about is drawing the distinction between 10th and 11th).
*Similar checks need to be made to see if a new search term is in 11th place, so this algorithm bubbles down to other search terms too -- so I'm simplifying a bit.
sometimes the best answer is "I don't know".
Ill take a deeper stab. My first instinct would be to feed the results into a Q. A process would continually process items coming into the Q. The process would maintain a map of
term -> count
each time a Q item is processed, you simply look up the search term and increment the count.
At the same time, I would maintain a list of references to the top 10 entries in the map.
For the entry that was currently implemented, see if its count is greater than the count of the count of the smallest entry in the top 10.(if not in the list already). If it is, replace the smallest with the entry.
I think that would work. No operation is time intensive. You would have to find a way to manage the size of the count map. but that should good enough for an interview answer.
They are not expecting a solution, that want to see if you can think. You dont have to write the solution then and there....
One way is that for every search, you store that search term and its time stamp. That way, finding the top ten for any period of time is simply a matter of comparing all search terms within the given time period.
The algorithm is simple, but the drawback would be greater memory and time consumption.
What about using a Splay Tree with 10 nodes? Each time you try to access a value (search term) that is not contained in the tree, throw out any leaf, insert the value instead and access it.
The idea behind this is the same as in my other answer. Under the assumption that the search terms are accessed evenly/regularly this solution should perform very well.
edit
One could also store some more search terms in the tree (the same goes for the solution I suggest in my other answer) in order to not delete a node that might be accessed very soon again. The more values one stores in it, the better the results.
Dunno if I understand it right or not.
My solution is using heap.
Because of top 10 search items, I build a heap with size 10.
Then update this heap with new search. If a new search's frequency is greater than heap(Max Heap) top, update it. Abandon the one with smallest frequency.
But, how to calculate the frequency of the specific search will be counted on something else.
Maybe as everyone stated, the data stream algorithm....
Use cm-sketch to store count of all searches since beginning, keep a min-heap of size 10 with it for top 10.
For monthly result, keep 30 cm-sketch/hash-table and min-heap with it, each one start counting and updating from last 30, 29 .., 1 day. As a day pass, clear the last and use it as day 1.
Same for hourly result, keep 60 hash-table and min-heap and start counting for last 60, 59, ...1 minute. As a minute pass, clear the last and use it as minute 1.
Montly result is accurate in range of 1 day, hourly result is accurate in range of 1 min
How do I distribute a small amount of data in a random order in a much larger volume of data?
For example, I have several thousand lines of 'real' data, and I want to insert a dozen or two lines of control data in a random order throughout the 'real' data.
Now I am not trying to ask how to use random number generators, I am asking a statistical question, I know how to generate random numbers, but my question is how do I ensure that this the data is inserted in a random order while at the same time being fairly evenly scattered through the file.
If I just rely on generating random numbers there is a possibility (albeit a very small one) that all my control data, or at least clumps of it, will be inserted within a fairly narrow selection of 'real' data. What is the best way to stop this from happening?
To phrase it another way, I want to insert control data throughout my real data without there being a way for a third party to calculate which rows are control and which are real.
Update: I have made this a 'community wiki' so if anyone wants to edit my question so it makes more sense then go right ahead.
Update: Let me try an example (I do not want to make this language or platform dependent as it is not a coding question, it is a statistical question).
I have 3000 rows of 'real' data (this amount will change from run to run, depending on the amount of data the user has).
I have 20 rows of 'control' data (again, this will change depending on the number of control rows the user wants to use, anything from zero upwards).
I now want to insert these 20 'control' rows roughly after every 150 rows or 'real' data has been inserted (3000/20 = 150). However I do not want it to be as accurate as that as I do not want the control rows to be identifiable simply based on their location in the output data.
Therefore I do not mind some of the 'control' rows being clumped together or for there to be some sections with very few or no 'control' rows at all, but generally I want the 'control' rows fairly evenly distributed throughout the data.
There's always a possibility that they get close to each other if you do it really random :)
But What I would do is:
You have N rows of real data and x of control data
To get an index of a row you should insert i-th control row, I'd use: N/(x+1) * i + r, where r is some random number, diffrent for each of the control rows, small compared to N/x. Choose any way of determining r, it can be either gaussian or even flat distribution. i is an index of the control row, so it's 1<=i<x
This way you can be sure that you avoid condensation of your control rows in one single place. Also you can be sure that they won't be in regular distances from each other.
Here's my thought. Why don't you just loop through the existing rows and "flip a coin" for each row to decide whether you will insert random data there.
for (int i=0; i<numberOfExistingRows; i++)
{
int r = random();
if (r > 0.5)
{
InsertRandomData();
}
}
This should give you a nice random distribution throughout the data.
Going with the 3000 real data rows and 20 control rows for the following example (I'm better with example than with english)
If you were to spread the 20 control rows as evenly as possible between the 3000 real data rows you'd insert one at each 150th real data row.
So pick that number, 150, for the next insertion index.
a) Generate a random number between 0 and 150 and subtract it from the insertion index
b) Insert the control row there.
c) Increase insertion index by 150
d) Repeat at step a)
Of course this is a very crude algorithm and it needs a few improvements :)
If the real data is large or much larger than the control data, just generate interarrival intervals for your control data.
So pick a random interval, copy out that many lines of real data, insert control data, repeat until finished. How to pick that random interval?
I'd recommend using a gaussian deviate with mean set to the real data size divided by the control data size, the former of which could be estimated if necessary, rather than measured or assumed known. Set the standard deviation of this gaussian based on how much "spread" you're willing to tolerate. Smaller stddev means a more leptokurtic distribution means tighter adherence to uniform spacing. Larger stdev means a more platykurtic distribution and looser adherence to uniform spacing.
Now what about the first and last sections of the file? That is: what about an insertion of control data at the very beginning or very end? One thing you can do is to come up with special-case estimates for these... but a nice trick is as follows: start your "index" into the real data at minus half the gaussian mean and generate your first deviate. Don't output any real data until your "index" into the real data is legit.
A symmetric trick at the end of the data should also work quite well (simply: keep generating deviates until you reach an "index" at least half the gaussian mean beyond the end of the real data. If the index just before this was off the end, generate data at the end.
You want to look at more than just statistics: it's helpful in developing an algorithm for this sort of thing to look at rudimentary queueing theory. See wikipedia or the Turing Omnibus, which has a nice, short chapter on the subject whose title is "Simulation".
Also: in some circumstance non-gaussian distributions, particularly the Poisson distribution, give better, more natural results for this sort of thing. The algorithm outline above still applies using half the mean of whatever distribution seems right.