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algorithm - Extracting values with multiple keys


I want to extract sorted data from a huge database based upon two (or more) keys in a very timely manner. Here is a reproducible toy example for two keys only:


n = 10^5;
keys = RandomInteger[{1, 100}, n];
vals = RandomReal[{0, 1}, n];

data = Transpose[{keys, vals}];


The fastest "traditional" way I' ve found:


result1 = Sort @ Cases[data, {25 | 73, r_} :> r];

Much much faster is a V10 solution:


assoc = Merge[Association /@ Rule @@@ data, Identity];

(I use Mergeto allow for duplicate keys, and the time cost of getting assoc is not important to me).


result2 = Sort[assoc[25] ~ Join ~ assoc[73]];


result1 == result2


True



Speed comparison:


Do[Sort @ Cases[data, {25 | 73, r_} :> r], {100}]; // AbsoluteTiming // First


2.017115




Do[Sort[assoc[25] ~ Join ~ assoc[73]], {100}]; // AbsoluteTiming // First


0.030002



Certainly one reason to upgrade, but two or more questions remain:


(a) Could this code be improved ?


(b) And, passing to n = 10^6, result1 still works, but result2 runs forever and has to be aborted.



Answer




In response to a), you can write Merge[Rule @@@ data, Identity], which is slightly simpler.


In response to b), there are two different ways to do this nicely. One of which works in 10.0.0, the other will have to wait for 10.0.1.


In 10.0.0 we can use GroupBy to associate each unique key with the set of corresponding values:


grouped = GroupBy[data, First -> Last];

Now do lookups by writing, e.g.:


grouped[25]

or


Catenate @ Lookup[grouped, {25, 73}]


You can also use PositionIndex. Unfortunately 10.0.0 has a slow implementation of PositionIndex as described here. But this is fixed in 10.0.1, takes a fraction of a second to complete on your example for n=6. It's actually faster than the GroupBy code above.


keyindex = PositionIndex[keys];

Now we can easily look up the positions for which the key was 25, and from that get the corresponding values:


Part[vals, keyindex[25]]

To look up both 25 and 73 we just do:


Part[vals, Catenate @ Lookup[keyindex, {25, 73}]]

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