I'm learning Scala and have been trying some LeetCode problems with it, but I'm having trouble with the memory limit being exceeded. One problem I have tried goes like this:
A swap is defined as taking two distinct positions in an array and swapping the values in them.
A circular array is defined as an array where we consider the first element and the last element to be adjacent.
Given a binary circular array nums, return the minimum number of swaps required to group all 1's present in the array together at any location.
and my attempted solution looks like
object Solution {
def minSwaps(nums: Array[Int]): Int = {
val count = nums.count(_==1)
if (count == 0) return 0
val circular = nums.view ++ nums.view
circular.sliding(count).map(_.count(_==0)).min
}
}
however, when I submit it, I'm hit with Memory Limit Exceeded for one of the test case where nums is very large.
My understanding is that, because I'm using .view, I shouldn't be allocating over O(1) memory. Is that understanding incorrect? To be clear, I realise this is the most time efficient way of solving this, but I didn't expect it to be memory inefficient.
The version used is Scala 2.13.7, in case that makes a difference.
Update
I did some inspection of the types and it seems circular is only a View unless I replace ++ with concat which makes it IndexedSeqView, why is that, I thought ++ was just an alias for concat?
If I make the above change, and replace circular.sliding(count) with (0 to circular.size - count).view.map(i => circular.slice(i, i + count)) it "succeeds" in hitting the time limit instead, so I think sliding might not be optimised for IndexedSeqView.
Is there a native function that behaves like Haskell's range?
I found out that 2..1 returns a list [2, 1] in PureScript, unlike Haskell's [2..1] returning an empty list []. After Googling around, I found the behavior is written in the Differences from Haskell documentation, but it doesn't give a rationale behind.
In my opinion, this behavior is somewhat inconvenient/unintuitive since 0 .. (len - 1) doesn't give an empty list when len is zero, and this could possibly lead to cryptic bugs.
Is there a way to obtain the expected array (i.e. range of length len incrementing from 0) without handling the length == 0 case every time?
Also, why did PureScript decide to make range behave like that?
P.S. How I ran into this question: I wanted to write a getLocalStorageKeys function, which gets all keys from the local storage. My implementation gets the number of keys using the length function, creates a range from 0 to numKeys - 1, and then traverses it with the key function. However, the range didn't behave as I expected.
How about just make it yourself?
indicies :: Int -> Array Int
indicies n = if n <= 0 then [] else 0..(n-1)
As far as "why", I can only speculate, and my speculation is that the idea was to avoid this kind of iffy logic for creating "reverse" ranges - which is something that does come up for me in Haskell once in a while.
I am looping over the following lines from a csv file to parse them. I want to identify the first line since its the header. Whats the best way of doing this instead of making a var counter holder.
var counter = 0
for (line <- lines) {
println(CsvParser.parse(line, counter))
counter++
}
I know there is got to be a better way to do this, newbie to Scala.
Try zipWithIndex:
for (line <- lines.zipWithIndex) {
println(CsvParser.parse(line._1, line._2))
}
#tenshi suggested the following improvement with pattern matching:
for ((line, count) <- lines.zipWithIndex) {
println(CsvParser.parse(line, count))
}
I totally agree with the given answer, still that I've to point something important out and initially I planned to put in a simple comment.
But it would be quite long, so that, leave me set it as a variant answer.
It's prefectly true that zip* methods are helpful in order to create tables with lists, but they have the counterpart that they loop the lists in order to create it.
So that, a common recommendation is to sequence the actions required on the lists in a view, so that you combine all of them to be applied only producing a result will be required. Producing a result is considered when the returnable isn't an Iterable. So is foreach for instance.
Now, talking about the first answer, if you have lines to be the list of lines in a very big file (or even an enumeratee on it), zipWithIndex will go through all of 'em and produce a table (Iterable of tuples). Then the for-comprehension will go back again through the same amount of items.
Finally, you've impacted the running lenght by n, where n is the length of lines and added a memory footprint of m + n*16 (roughtly) where m is the lines' footprint.
Proposition
lines.view.zipWithIndex map Function.tupled(CsvParser.parse) foreach println
Some few words left (I promise), lines.view will create something like scala.collection.SeqView that will hold all further "mapping" function producing new Iterable, as are zipWithIndex and map.
Moreover, I think the expression is more elegant because it follows the reader and logical.
"For lines, create a view that will zip each item with its index, the result as to be mapped on the result of the parser which must be printed".
HTH.
Consider a lookup function with the following signature, which needs to return an integer for a given string key:
int GetValue(string key) { ... }
Consider furthermore that the key-value mappings, numbering N, are known in advance when the source code for function is being written, e.g.:
// N=3
{ "foo", 1 },
{ "bar", 42 },
{ "bazz", 314159 }
So a valid (but not perfect!) implementation for the function for the input above would be:
int GetValue(string key)
{
switch (key)
{
case "foo": return 1;
case "bar": return 42;
case "bazz": return 314159;
}
// Doesn't matter what we do here, control will never come to this point
throw new Exception();
}
It is also known in advance exactly how many times (C>=1) the function will be called at run-time for every given key. For example:
C["foo"] = 1;
C["bar"] = 1;
C["bazz"] = 2;
The order of such calls is not known, however. E.g. the above could describe the following sequence of calls at run-time:
GetValue("foo");
GetValue("bazz");
GetValue("bar");
GetValue("bazz");
or any other sequence, provided the call counts match.
There is also a restriction M, specified in whatever units is most convenient, defining the upper memory bound of any lookup tables and other helper structures that can be used by the GetValue (the structures are initialized in advance; that initialization is not counted against the complexity of the function). For example, M=100 chars, or M=256 sizeof(object reference).
The question is, how to write the body of GetValue such that it is as fast as possible - in other words, the aggregate time of all GetValue calls (note that we know the total count, per everything above) is minimal, for given N, C and M?
The algorithm may require a reasonable minimal value for M, e.g. M >= char.MaxValue. It may also require that M be aligned to some reasonable boundary - for example, that it may only be a power of two. It may also require that M must be a function of N of a certain kind (for example, it may allow valid M=N, or M=2N, ...; or valid M=N, or M=N^2, ...; etc).
The algorithm can be expressed in any suitable language or other form. For runtime performance constrains for generated code, assume that the generated code for GetValue will be in C#, VB or Java (really, any language will do, so long as strings are treated as immutable arrays of characters - i.e. O(1) length and O(1) indexing, and no other data computed for them in advance). Also, to simplify this a bit, answers which assume that C=1 for all keys are considered valid, though those answers which cover the more general case are preferred.
Some musings on possible approaches
The obvious first answer to the above is using a perfect hash, but generic approaches to finding one seem to be imperfect. For example, one can easily generate a table for a minimal perfect hash using Pearson hashing for the sample data above, but then the input key would have to be hashed for every call to GetValue, and Pearson hash necessarily scans the entire input string. But all sample keys actually differ in their third character, so only that can be used as the input for the hash instead of the entire string. Furthermore, if M is required to be at least char.MaxValue, then the third character itself becomes a perfect hash.
For a different set of keys this may no longer be true, but it may still be possible to reduce the amount of characters considered before the precise answer can be given. Furthermore, in some cases where a minimal perfect hash would require inspecting the entire string, it may be possible to reduce the lookup to a subset, or otherwise make it faster (e.g. a less complex hashing function?) by making the hash non-minimal (i.e. M > N) - effectively sacrificing space for the sake of speed.
It may also be that traditional hashing is not such a good idea to begin with, and it's easier to structure the body of GetValue as a series of conditionals, arranged such that the first checks for the "most variable" character (the one that varies across most keys), with further nested checks as needed to determine the correct answer. Note that "variance" here can be influenced by the number of times each key is going to be looked up (C). Furthermore, it is not always readily obvious what the best structure of branches should be - it may be, for example, that the "most variable" character only lets you distinguish 10 keys out of 100, but for the remaining 90 that one extra check is unnecessary to distinguish between them, and on average (considering C) there are more checks per key than in a different solution which does not start with the "most variable" character. The goal then is to determine the perfect sequence of checks.
You could use the Boyer search, but I think that the Trie would be a much more effiecent method. You can modify the Trie to collapse the words as you make the hit count for a key zero, thus reducing the number of searches you would have to do the farther down the line you get. The biggest benefit you would get is that you are doing array lookups for the indexes, which is much faster than a comparison.
You've talked about a memory limitation when it comes to precomputation - is there also a time limitation?
I would consider a trie, but one where you didn't necessarily start with the first character. Instead, find the index which will cut down the search space most, and consider that first. So in your sample case ("foo", "bar", "bazz") you'd take the third character, which would immediately tell you which string it was. (If we know we'll always be given one of the input words, we can return as soon as we've found a unique potential match.)
Now assuming that there isn't a single index which will get you down to a unique string, you need to determine the character to look at after that. In theory you precompute the trie to work out for each branch what the optimal character to look at next is (e.g. "if the third character was 'a', we need to look at the second character next; if it was 'o' we need to look at the first character next) but that potentially takes a lot more time and space. On the other hand, it could save a lot of time - because having gone down one character, each of the branches may have an index to pick which will uniquely identify the final string, but be a different index each time. The amount of space required by this approach would depend on how similar the strings were, and might be hard to predict in advance. It would be nice to be able to dynamically do this for all the trie nodes you can, but then when you find you're running out of construction space, determine a single order for "everything under this node". (So you don't end up storing a "next character index" on each node underneath that node, just the single sequence.) Let me know if this isn't clear, and I can try to elaborate...
How you represent the trie will depend on the range of input characters. If they're all in the range 'a'-'z' then a simple array would be incredibly fast to navigate, and reasonably efficient for trie nodes where there are possibilities for most of the available options. Later on, when there are only two or three possible branches, that becomes wasteful in memory. I would suggest a polymorphic Trie node class, such that you can build the most appropriate type of node depending on how many sub-branches there are.
None of this performs any culling - it's not clear how much can be achieved by culling quickly. One situation where I can see it helping is when the number of branches from one trie node drops to 1 (because of the removal of a branch which is exhausted), that branch can be eliminated completely. Over time this could make a big difference, and shouldn't be too hard to compute. Basically as you build the trie you can predict how many times each branch will be taken, and as you navigate the trie you can subtract one from that count per branch when you navigate it.
That's all I've come up with so far, and it's not exactly a full implementation - but I hope it helps...
Is a binary search of the table really so awful? I would take the list of potential strings and "minimize" them, the sort them, and finally do a binary search upon the block of them.
By minimize I mean reducing them to the minimum they need to be, kind of a custom stemming.
For example if you had the strings: "alfred", "bob", "bill", "joe", I'd knock them down to "a", "bi", "bo", "j".
Then put those in to a contiguous block of memory, for example:
char *table = "a\0bi\0bo\0j\0"; // last 0 is really redundant..but
char *keys[4];
keys[0] = table;
keys[1] = table + 2;
keys[2] = table + 5;
keys[3] = table + 8;
Ideally the compiler would do all this for you if you simply go:
keys[0] = "a";
keys[1] = "bi";
keys[2] = "bo";
keys[3] = "j";
But I can't say if that's true or not.
Now you can bsearch that table, and the keys are as short as possible. If you hit the end of the key, you match. If not, then follow the standard bsearch algorithm.
The goal is to get all of the data close together and keep the code itty bitty so that it all fits in to the CPU cache. You can process the key from the program directly, no pre-processing or adding anything up.
For a reasonably large number of keys that are reasonably distributed, I think this would be quite fast. It really depends on the number of strings involved. For smaller numbers, the overhead of computing hash values etc is more than search something like this. For larger values, it's worth it. Just what those number are all depends on the algorithms etc.
This, however, is likely the smallest solution in terms of memory, if that's important.
This also has the benefit of simplicity.
Addenda:
You don't have any specifications on the inputs beyond 'strings'. There's also no discussion about how many strings you expect to use, their length, their commonality or their frequency of use. These can perhaps all be derived from the "source", but not planned upon by the algorithm designer. You're asking for an algorithm that creates something like this:
inline int GetValue(char *key) {
return 1234;
}
For a small program that happens to use only one key all the time, all the way up to something that creates a perfect hash algorithm for millions of strings. That's a pretty tall order.
Any design going after "squeezing every single bit of performance possible" needs to know more about the inputs than "any and all strings". That problem space is simply too large if you want it the fastest possible for any condition.
An algorithm that handles strings with extremely long identical prefixes might be quite different than one that works on completely random strings. The algorithm could say "if the key starts with "a", skip the next 100 chars, since they're all a's".
But if these strings are sourced by human beings, and they're using long strings of the same letters, and not going insane trying to maintain that data, then when they complain that the algorithm is performing badly, you reply that "you're doing silly things, don't do that". But we don't know the source of these strings either.
So, you need to pick a problem space to target the algorithm. We have all sorts of algorithms that ostensibly do the same thing because they address different constraints and work better in different situations.
Hashing is expensive, laying out hashmaps is expensive. If there's not enough data involved, there are better techniques than hashing. If you have large memory budget, you could make an enormous state machine, based upon N states per node (N being your character set size -- which you don't specify -- BAUDOT? 7-bit ASCII? UTF-32?). That will run very quickly, unless the amount of memory consumed by the states smashes the CPU cache or squeezes out other things.
You could possibly generate code for all of this, but you may run in to code size limits (you don't say what language either -- Java has a 64K method byte code limit for example).
But you don't specify any of these constraints. So, it's kind of hard to get the most performant solution for your needs.
What you want is a look-up table of look-up tables.
If memory cost is not an issue you can go all out.
const int POSSIBLE_CHARCODES = 256; //256 for ascii //65536 for unicode 16bit
struct LutMap {
int value;
LutMap[POSSIBLE_CHARCODES] next;
}
int GetValue(string key) {
LutMap root = Global.AlreadyCreatedLutMap;
for(int x=0; x<key.length; x++) {
int c = key.charCodeAt(x);
if(root.next[c] == null) {
return root.value;
}
root = root.next[c];
}
}
I reckon that it's all about finding the right hash function. As long as you know what the key-value relationship is in advance, you can do an analysis to try and find a hash function to meet your requrements. Taking the example you've provided, treat the input strings as binary integers:
foo = 0x666F6F (hex value)
bar = 0x626172
bazz = 0x62617A7A
The last column present in all of them is different in each. Analyse further:
foo = 0xF = 1111
bar = 0x2 = 0010
bazz = 0xA = 1010
Bit-shift to the right twice, discarding overflow, you get a distinct value for each of them:
foo = 0011
bar = 0000
bazz = 0010
Bit-shift to the right twice again, adding the overflow to a new buffer:
foo = 0010
bar = 0000
bazz = 0001
You can use those to query a static 3-entry lookup table. I reckon this highly personal hash function would take 9 very basic operations to get the nibble (2), bit-shift (2), bit-shift and add (4) and query (1), and a lot of these operations can be compressed further through clever assembly usage. This might well be faster than taking run-time infomation into account.
Have you looked at TCB . Perhaps the algorithm used there can be used to retrieve your values. It sounds a lot like the problem you are trying to solve. And from experience I can say tcb is one of the fastest key store lookups I have used. It is a constant lookup time, regardless of the number of keys stored.
Consider using Knuth–Morris–Pratt algorithm.
Pre-process given map to a large string like below
String string = "{foo:1}{bar:42}{bazz:314159}";
int length = string.length();
According KMP preprocessing time for the string will take O(length).
For searching with any word/key will take O(w) complexity, where w is length of the word/key.
You will be needed to make 2 modification to KMP algorithm:
key should be appear ordered in the joined string
instead of returning true/false it should parse the number and return it
Wish it can give a good hints.
Here's a feasible approach to determine the smallest subset of chars to target for your hash routine:
let:
k be the amount of distinct chars across all your keywords
c be the max keyword length
n be the number of keywords
in your example (padded shorter keywords w/spaces):
"foo "
"bar "
"bazz"
k = 7 (f,o,b,a,r,z, ), c = 4, n = 3
We can use this to compute a lower bound for our search. We need at least log_k(n) chars to uniquely identify a keyword, if log_k(n) >= c then you'll need to use the whole keyword and there's no reason to proceed.
Next, eliminate one column at a time and check if there are still n distinct values remaining. Use the distinct chars in each column as a heuristic to optimize our search:
2 2 3 2
f o o .
b a r .
b a z z
Eliminate columns with the lowest distinct chars first. If you have <= log_k(n) columns remaining you can stop. Optionally you could randomize a bit and eliminate the 2nd lowest distinct col or try to recover if the eliminated col results in less than n distinct words. This algorithm is roughly O(n!) depending on how much you try to recover. It's not guaranteed to find an optimal solution but it's a good tradeoff.
Once you have your subset of chars, proceed with the usual routines for generating a perfect hash. The result should be an optimal perfect hash.
If I have an ArrayList<Double> dblList and a Predicate<Double> IS_EVEN I am able to remove all even elements from dblList using:
Collections2.filter(dblList, IS_EVEN).clear()
if dblList however is a result of a transformation like
dblList = Lists.transform(intList, TO_DOUBLE)
this does not work any more as the transformed list is immutable :-)
Any solution?
Lists.transform() accepts a List and helpfully returns a result that is RandomAccess list. Iterables.transform() only accepts an Iterable, and the result is not RandomAccess. Finally, Iterables.removeIf (and as far as I see, this is the only one in Iterables) has an optimization in case that the given argument is RandomAccess, the point of which is to make the algorithm linear instead of quadratic, e.g. think what would happen if you had a big ArrayList (and not an ArrayDeque - that should be more popular) and kept removing elements from its start till its empty.
But the optimization depends not on iterator remove(), but on List.set(), which is cannot be possibly supported in a transformed list. If this were to be fixed, we would need another marker interface, to denote that "the optional set() actually works".
So the options you have are:
Call Iterables.removeIf() version, and run a quadratic algorithm (it won't matter if your list is small or you remove few elements)
Copy the List into another List that supports all optional operations, then call Iterables.removeIf().
The following approach should work, though I haven't tried it yet.
Collection<Double> dblCollection =
Collections.checkedCollection(dblList, Double.class);
Collections2.filter(dblCollection, IS_EVEN).clear();
The checkCollection() method generates a view of the list that doesn't implement List. [It would be cleaner, but more verbose, to create a ForwardingCollection instead.] Then Collections2.filter() won't call the unsupported set() method.
The library code could be made more robust. Iterables.removeIf() could generate a composed Predicate, as Michael D suggested, when passed a transformed list. However, we previously decided not to complicate the code by adding special-case logic of that sort.
Maybe:
Collection<Double> odds = Collections2.filter(dblList, Predicates.not(IS_EVEN));
or
dblList = Lists.newArrayList(Lists.transform(intList, TO_DOUBLE));
Collections2.filter(dblList, IS_EVEN).clear();
As long as you have no need for the intermediate collection, then you can just use Predicates.compose() to create a predicate that first transforms the item, then evaluates a predicate on the transformed item.
For example, suppose I have a List<Double> from which I want to remove all items where the Integer part is even. I already have a Function<Double,Integer> that gives me the Integer part, and a Predicate<Integer> that tells me if it is even.
I can use these to get a new predicate, INTEGER_PART_IS_EVEN
Predicate<Double> INTEGER_PART_IS_EVEN = Predicates.compose(IS_EVEN, DOUBLE_TO_INTEGER);
Collections2.filter(dblList, INTEGER_PART_IS_EVEN).clear();
After some tries, I think I've found it :)
final ArrayList<Integer> ints = Lists.newArrayList(1, 2, 3, 4, 5);
Iterables.removeIf(Iterables.transform(ints, intoDouble()), even());
System.out.println(ints);
[1,3,5]
I don't have a solution, instead I found some kind of a problem with Iterables.removeIf() in combination with Lists.TransformingRandomAccessList.
The transformed list implements RandomAccess, thus Iterables.removeIf() delegates to Iterables.removeIfFromRandomAccessList() which depends on an unsupported List.set() operation.
Calling Iterators.removeIf() however would be successful, as the remove() operation IS supported by Lists.TransformingRandomAccessList.
see: Iterables: 147
Conclusion: instanceof RandomAccess does not guarantee List.set().
Addition:
In special situations calling removeIfFromRandomAccessList() even works:
if and only if the elements to erase form a compact group at the tail of the List or all elements are covered by the Predicate.