I have algorithms that works with dynamically growing lists (contiguous memory like a C++ vector, Java ArrayList or C# List). Until recently, these algorithms would insert new values into the middle of the lists. Of course, this was usually a very slow operation. Every time an item was added, all the items after it needed to be shifted to a higher index. Do this a few times for each algorithm and things get really slow.
My realization was that I could add the new items to the end of the list and then rotate them into position later. That's one option!
Another option, when I know how many items I'm adding ahead of time, is to add that many items to the back, shift the existing items and then perform the algorithm in-place in the hole I've made for myself. The negative is that I have to add some default value to the end of the list and then just overwrite them.
I did a quick analysis of these options and concluded that the second option is more efficient. My reasoning was that the rotation with the first option would result in in-place swaps (requiring a temporary). My only concern with the second option is that I am creating a bunch of default values that just get thrown away. Most of the time, these default values will be null or a mem-filled value type.
However, I'd like someone else familiar with algorithms to tell me which approach would be faster. Or, perhaps there's an even more efficient solution I haven't considered.
Arrays aren't efficient for lots of insertions or deletions into anywhere other than the end of the array. Consider whether using a different data structure (such as one suggested in one of the other answers) may be more efficient. Without knowing the problem you're trying to solve, it's near-impossible to suggest a data structure (there's no one solution for all problems). That being said...
The second option is definitely the better option of the two. A somewhat better option (avoiding the default-value issue): simply copy 789 to the end and overwrite the middle 789 with 456. So the only intermediate step would be 0123789789.
Your default-value concern is, however, (generally) not a big issue:
In Java, for one, you cannot (to my knowledge) even assign memory for an array that's not 0- or null-filled. C++ STL containers also enforce this I believe (but not C++ itself).
The size of a pointer compared to any moderate-sized class is minimal (thus assigning it to a default value also takes minimal time) (in Java and C# everything is pointers, in C++ you can use pointers (something like boost::shared_ptr or a pointer-vector is preferred above straight pointers) (N/A to primitives, which are small to start, so generally not really a big issue either).
I'd also suggest forcing a reallocation to a specified size before you start inserting to the end of the array (Java's ArrayList::ensureCapacity or C++'s vector::reserve). In case you didn't know - varying-length-array implementations tend to have an internal array that's bigger than what size() returns or what's accessible (in order to prevent constant reallocation of memory as you insert or delete values).
Also note that there are more efficient methods to copy parts of an array than doing it manually with for loops (e.g. Java's System.arraycopy).
You might want to consider changing your representation of the list from using a dynamic array to using some other structure. Here are two options that allow you to implement these operations efficiently:
An order statistic tree is a modified type of binary tree that supports insertions and selections anywhere in O(log n) time, as well as lookups in O(log n) time. This will increase your memory usage quite a bit because of the overhead for the pointers and extra bookkeeping, but should dramatically speed up insertions. However, it will slow down lookups a bit.
If you always know the insertion point in advance, you could consider switching to a linked list instead of an array, and just keep a pointer to the linked list cell where insertions will occur. However, this slows down random access to O(n), which could possibly be an issue in your setup.
Alternatively, if you always know where insertions will happen, you could consider representing your array as two stacks - one stack holding the contents of the array to the left of the insert point and one holding the (reverse) of the elements to the right of the insertion point. This makes insertions fast, and if you have the right type of stack implementation could keep random access fast.
Hope this helps!
HashMaps and Linked Lists were designed for the problem you are having. Given a indexed data structure with numbered items, the difficulty of inserting items in the middle requires a renumbering of every item in the list.
You need a data structure which is optimized to make inserts a constant O(1) complexity. HashMaps were designed to make insert and delete operations lightning quick regardless of dataset size.
I can't pretend to do the HashMap subject justice by describing it. Here is a good intro: http://en.wikipedia.org/wiki/Hash_table
Related
I am working on a Task Schedule Simulator which needs to be programmed in Assembly language.
I've been struggling about Task sorting:
I am allocating new memory for each Task (user can insert the task and by using the sbrk instruction i allocate 20 byte that contain a word for Task's numeric ID, another word for it's priority expressed as an int, another word for the number of cycles to finish the task) and I'm storing the address of each new Task in the stack.
My problem is: i need to sort this tasks and the sorting can either be based on priority or number of cycles. When I pop these Tasks i can easily access the right field (since the structure is very rigid, i just need to type the right offset in the lw instruction and voilat), but then comparing and sorting gets complicated.
I am working on the pseudocode for this part of the program and can't find any way to untie the knot.
Let me first try and paraphrase what you have indicate as the problem.
You have a stack, that has "records" of the structure
{ word : id, word : priority, word : cycle_count, dword : address}
Since the end objective is to "pop" these in desired order, we have to execute an in-place sort. There are many choices of algorithms, but to keep matters simple (also taking a cue from an underlying assumption that the count of tasks is not that many), I am explaining using bubble-sort. There exist a vast cornucopia of literature comparing each probable sort algorithm to their finest details, and if relevant, you may consider wikipedia as the perfect starting point.
Step 1 : Make the data pointer = stack pointer+count_of_records*20 - effectively, for next few steps, the data pointer points to the top of the "table of records" which happens to be located at the stack. An advanced consideration but not required in MIPS, is to assert DS=SS.
Step 2 : Next, identify which record pair needs to be swapped, and use the appropriate index within a record to identify the field that defines the swapping order.
Step 3: Allocate a 20 byte space as temporary, and use that space to temporarily hold the swapped record. An advanced consideration here is whether the environment can do an interrupt while the swap is going on. MIPS does not seem to have an atomic lock so this memory move needs to be carefully done.
Once the requisite number of passes are completed, the table will appear sorted, and will remain in place. The temporary buffer to store a record may be released.
The vital statistics for Bubble-Sort is that its O(n^2), responds well to almost sorted situations (not very likely in your example), and will handle the fact well that in midst of sorting, some records may find the processor free to start running, and therefore, will have to be removed from the queue by a POP and the sort needs to be restarted. This restart, however, will find the table almost sorted, and therefore, on a continuous basis, the table will display fairly strong pre-sorted behavior. Most importantly, has the perhaps most efficient code footprint among all in-situ algorithms.
Trust this helps
You might want to introduce a level of indirection, and sort pointers to your structs based on comparing the pointed-to data.
If your sort keys are all integers of the same size at different offsets within the structs, your sort function could take an offset as a parameter. e.g. lw from base + off to get the integer that you're going to compare.
Insertion sort is probably easiest to code, and much better that BubbleSort in the not-almost-sorted case. If you care about having a result ready to pop ASAP, before the whole array is sorted, then use Selection Sort.
It wasn't clear if your code is itself going to be multi-threaded, or if you can just write a normal sort function. #qasar66's answer seems to be suggesting a BubbleSort with atomic swaps, so other threads can safely look at the partially-sorted array while its being sorted.
If you only ever need to pop the min element, one of the best data structures is a Heap. It takes more code to implement, so if ease of implementation is your top goal, use a simple sort. Heapifying an un-sorted array is cheaper than doing a full sort: the full O(n log n) cost of extracting all elements in order is amortized over the extracts. So it's great if you want to be able to change the sort key, since you don't have to do all the work of fully sorting.
I'm just wondering, would the speed of selection sort change depending on the TYPE of data? So like would the speed change depending on if it were words or numbers? why or why not?. Also, would the speed of insertion sort change depending on the TYPE of data?
I personally don't think they do change the speed of the sorting but I'm not 100% sure.
A comparison-based sort algorithm needs to know, among other things:
how to tell if element a is "smaller" than element b or not
how to swap two elements in the array,
ie. moving one element to the position of another and vice-versa.
Other than this two things, no part of the algorithm depends on the actual type and/or content of the data elements. The only possible speed difference is in this parts.
Yes, comparing eg. strings is usually slower than comparing integer, and the longer the strings get, the more noticable the difference will be. The same is valid for swapping, altough there are some C++ things to remedy that (depending on the implementation of the data type, swapping could be done by copying everything (slow) or just by swapping eg. a pointer (faster))
I was wondering why many languages (Java, C++, Python, Perl etc) implement hash tables using linked lists to avoid collisions instead of arrays?
I mean instead of buckets of linked lists, we should use arrays.
If the concern is about the size of the array then that means that we have too many collisions so we already have a problem with the hash function and not the way we address collisions. Am I misunderstanding something?
I mean instead of buckets of linked lists, we should use arrays.
Pros and cons to everything, depending on many factors.
The two biggest problem with arrays:
changing capacity involves copying all content to another memory area
you have to choose between:
a) arrays of Element*s, adding one extra indirection during table operations, and one extra memory allocation per non-empty bucket with associated heap management overheads
b) arrays of Elements, such that the pre-existing Elements iterators/pointers/references are invalidated by some operations on other nodes (e.g. insert) (the linked list approach - or 2a above for that matter - needn't invalidate these)
...will ignore several smaller design choices about indirection with arrays...
Practical ways to reduce copying from 1. include keeping excess capacity (i.e. currently unused memory for anticipated or already-erased elements), and - if sizeof(Element) is much greater than sizeof(Element*) - you're pushed towards arrays-of-Element*s (with "2a" problems) rather than Element[]s/2b.
There are a couple other answers claiming erasing in arrays is more expensive than for linked lists, but the opposite's often true: searching contiguous Elements is faster than scanning a linked list (less steps in code, more cache friendly), and once found you can copy the last array Element or Element* over the one being erased then decrement size.
If the concern is about the size of the array then that means that we have too many collisions so we already have a problem with the hash function and not the way we address collisions. Am I misunderstanding something?
To answer that, let's look at what happens with a great hash function. Packing a million elements into a million buckets using a cryptographic strength hash, a few runs of my program counting the number of buckets to which 0, 1, 2 etc. elements hashed yielded...
0=367790 1=367843 2=184192 3=61200 4=15370 5=3035 6=486 7=71 8=11 9=2
0=367664 1=367788 2=184377 3=61424 4=15231 5=2933 6=497 7=75 8=10 10=1
0=367717 1=368151 2=183837 3=61328 4=15300 5=3104 6=486 7=64 8=10 9=3
If we increase that to 100 million elements - still with load factor 1.0:
0=36787653 1=36788486 2=18394273 3=6130573 4=1532728 5=306937 6=51005 7=7264 8=968 9=101 10=11 11=1
We can see the ratios are pretty stable. Even with load factor 1.0 (the default maximum for C++'s unordered_set and -map), 36.8% of buckets can be expected to be empty, another 36.8% handling one Element, 18.4% 2 Elements and so on. For any given array resizing logic you can easily get a sense of how often it will need to resize (and potentially copy elements). You're right that it doesn't look bad, and may be better than linked lists if you're doing lots of lookups or iterations, for this idealistic cryptographic-hash case.
But, good quality hashing is relatively expensive in CPU time, such that general purpose hash-table supporting hash functions are often very weak: e.g. it's very common for C++ Standard library implementations of std::hash<int> to return their argument, and MS Visual C++'s std::hash<std::string> picks 10 characters evently spaced along the string to incorporate in the hash value, regardless of how long the string is.
Clearly implementation's experience has been that this combination of weak-but-fast hash functions and linked lists (or trees) to handle the greater collision proneness works out faster on average - and has less user-antagonising manifestations of obnoxiously bad performance - for everyday keys and requirements.
Strategy 1
Use (small) arrays which get instantiated and subsequently filled once collisions occur. 1 heap operation for the allocation of the array, then room for N-1 more. If no collision ever occurs again for that bucket, N-1 capacity for entries is wasted. List wins, if collisions are rare, no excess memory is allocated just for the probability of having more overflows on a bucket. Removing items is also more expensive. Either mark deleted spots in the array or move the stuff behind it to the front. And what if the array is full? Linked list of arrays or resize the array?
One potential benefit of using arrays would be to do a sorted insert and then binary search upon retrieval. The linked list approach cannot compete with that. But whether or not that pays off depends on the write/retrieve ratio. The less frequently writing occurs, the more could this pay off.
Strategy 2
Use lists. You pay for what you get. 1 collision = 1 heap operation. No eager assumption (and price to pay in terms of memory) that "more will come". Linear search within the collision lists. Cheaper delete. (Not counting free() here). One major motivation to think of arrays instead of lists would be to reduce the amount of heap operations. Amusingly the general assumption seems to be that they are cheap. But not many will actually know how much time an allocation requires compared to, say traversing the list looking for a match.
Strategy 3
Use neither array nor lists but store the overflow entries within the hash table at another location. Last time I mentioned that here, I got frowned upon a bit. Benefit: 0 memory allocations. Probably works best if you have indeed low fill grade of the table and only few collisions.
Summary
There are indeed many options and trade-offs to choose from. Generic hash table implementations such as those in standard libraries cannot make any assumption regarding write/read ratio, quality of hash key, use cases, etc. If, on the other hand all those traits of a hash table application are known (and if it is worth the effort), it is well possible to create an optimized implementation of a hash table which is tailored for the set of trade offs the application requires.
The reason is, that the expected length of these lists is tiny, with only zero, one, or two entries in the vast majority of cases. Yet these lists may also become arbitrarily long in the worst case of a really bad hash function. And even though this worst case is not the case that hash tables are optimized for, they still need to be able to handle it gracefully.
Now, for an array based approach, you would need to set a minimal array size. And, if that initial array size is anything other then zero, you already have significant space overhead due to all the empty lists. A minimal array size of two would mean that you waste half your space. And you would need to implement logic to reallocate the arrays when they become full because you cannot put an upper limit to the list length, you need to be able to handle the worst case.
The list based approach is much more efficient under these constraints: It has only the allocation overhead for the node objects, most accesses have the same amount of indirection as the array based approach, and it's easier to write.
I'm not saying that it's impossible to write an array based implementation, but its significantly more complex and less efficient than the list based approach.
why many languages (Java, C++, Python, Perl etc) implement hash tables using linked lists to avoid collisions instead of arrays?
I'm almost sure, at least for most from that "many" languages:
Original implementors of hash tables for these languages just followed classic algorithm description from Knuth/other algorithmic book, and didn't even consider such subtle implementation choices.
Some observations:
Even using collision resolution with separate chains instead of, say, open addressing, for "most generic hash table implementation" is seriously doubtful choice. My personal conviction -- it is not the right choice.
When hash table's load factor is pretty low (that should chosen in nearly 99% hash table usages), the difference between the suggested approaches hardly could affect overall data structure perfromance (as cmaster explained in the beginning of his answer, and delnan meaningfully refined in the comments). Since generic hash table implementations in languages are not designed for high density, "linked lists vs arrays" is not a pressing issue for them.
Returning to the topic question itself, I don't see any conceptual reason why linked lists should be better than arrays. I can easily imagine, that, in fact, arrays are faster on modern hardware / consume less memory with modern momory allocators inside modern language runtimes / operating systems. Especially when the hash table's key is primitive, or a copied structure. You can find some arguments backing this opinion here: http://en.wikipedia.org/wiki/Hash_table#Separate_chaining_with_other_structures
But the only way to find the correct answer (for particular CPU, OS, memory allocator, virtual machine and it's garbage collection algorithm, and the hash table use case / workload!) is to implement both approaches and compare them.
Am I misunderstanding something?
No, you don't misunderstand anything, your question is legal. It's an example of fair confusion, when something is done in some specific way not for a strong reason, but, largely, by occasion.
If is implemented using arrays, in case of insertion it will be costly due to reallocation which in case of linked list doesn`t happen.
Coming to the case of deletion we have to search the complete array then either mark it as delete or move the remaining elements. (in the former case it makes the insertion even more difficult as we have to search for empty slots).
To improve the worst case time complexity from o(n) to o(logn), once the number of items in a hash bucket grows beyond a certain threshold, that bucket will switch from using a linked list of entries to a balanced tree (in java).
Given two files containing list of words(around million), We need to find out the words that are in common.
Use Some efficient algorithm, also not enough memory availble(1 million, certainly not).. Some basic C Programming code, if possible, would help.
The files are not sorted.. We can use some sort of algorithm... Please support it with basic code...
Sorting the external file...... with minimum memory available,, how can it be implement with C programming.
Anybody game for external sorting of a file... Please share some code for this.
Yet another approach.
General. first, notice that doing this sequentially takes O(N^2). With N=1,000,000, this is a LOT. Sorting each list would take O(N*log(N)); then you can find the intersection in one pass by merging the files (see below). So the total is O(2N*log(N) + 2N) = O(N*log(N)).
Sorting a file. Now let's address the fact that working with files is much slower than with memory, especially when sorting where you need to move things around. One way to solve this is - decide the size of the chunk that can be loaded into memory. Load the file one chunk at a time, sort it efficiently and save into a separate temporary file. The sorted chunks can be merged (again, see below) into one sorted file in one pass.
Merging. When you have 2 sorted lists (files or not), you can merge them into one sorted list easily in one pass: have 2 "pointers", initially pointing to the first entry in each list. In each step, compare the values the pointers point to. Move the smaller value to the merged list (the one you are constructing) and advance its pointer.
You can modify the merge algorithm easily to make it find the intersection - if pointed values are equal move it to the results (consider how do you want to deal with duplicates).
For merging more than 2 lists (as in sorting the file above) you can generalize the algorithm for using k pointers.
If you had enough memory to read the first file completely into RAM, I would suggest reading it into a dictionary (word -> index of that word ), loop over the words of the second file and test if the word is contained in that dictionary. Memory for a million words is not much today.
If you have not enough memory, split the first file into chunks that fit into memory and do as I said above for each of that chunk. For example, fill the dictionary with the first 100.000 words, find every common word for that, then read the file a second time extracting word 100.001 up to 200.000, find the common words for that part, and so on.
And now the hard part: you need a dictionary structure, and you said "basic C". When you are willing to use "basic C++", there is the hash_map data structure provided as an extension to the standard library by common compiler vendors. In basic C, you should also try to use a ready-made library for that, read this SO post to find a link to a free library which seems to support that.
Your problem is: Given two sets of items, find the intersaction (items common to both), while staying within the constraints of inadequate RAM (less than the size of any set).
Since finding an intersaction requires comparing/searching each item in another set, you must have enough RAM to store at least one of the sets (the smaller one) to have an efficient algorithm.
Assume that you know for a fact that the intersaction is much smaller than both sets and fits completely inside available memory -- otherwise you'll have to do further work in flushing the results to disk.
If you are working under memory constraints, partition the larger set into parts that fit inside 1/3 of the available memory. Then partition the smaller set into parts the fit the second 1/3. The remaining 1/3 memory is used to store the results.
Optimize by finding the max and min of the partition for the larger set. This is the set that you are comparing from. Then when loading the corresponding partition of the smaller set, skip all items outside the min-max range.
First find the intersaction of both partitions through a double-loop, storing common items to the results set and removing them from the original sets to save on comparisons further down the loop.
Then replace the partition in the smaller set with the second partition (skipping items outside the min-max). Repeat. Notice that the partition in the larger set is reduced -- with common items already removed.
After running through the entire smaller set, repeat with the next partition of the larger set.
Now, if you do not need to preserve the two original sets (e.g. you can overwrite both files), then you can further optimize by removing common items from disk as well. This way, those items no longer need to be compared in further partitions. You then partition the sets by skipping over removed ones.
I would give prefix trees (aka tries) a shot.
My initial approach would be to determine a maximum depth for the trie that would fit nicely within my RAM limits. Pick an arbitrary depth (say 3, you can tweak it later) and construct a trie up to that depth, for the smaller file. Each leaf would be a list of "file pointers" to words that start with the prefix encoded by the path you followed to reach the leaf. These "file pointers" would keep an offset into the file and the word length.
Then process the second file by reading each word from it and trying to find it in the first file using the trie you constructed. It would allow you to fail faster on words that don't match. The deeper your trie, the faster you can fail, but the more memory you would consume.
Of course, like Stephen Chung said, you still need RAM to store enough information to describe at least one of the files, if you really need an efficient algorithm. If you don't have enough memory -- and you probably don't, because I estimate my approach would require approximately the same amount of memory you would need to load a file whose words were 14-22 characters long -- then you have to process even the first file by parts. In that case, I would actually recommend using the trie for the larger file, not the smaller. Just partition it in parts that are no bigger than the smaller file (or no bigger than your RAM constraints allow, really) and do the whole process I described for each part.
Despite the length, this is sort of off the top of my head. I might be horribly wrong in some details, but this is how I would initially approach the problem and then see where it would take me.
If you're looking for memory efficiency with this sort of thing you'll be hard pushed to get time efficiency. My example will be written in python, but should be relatively easy to implement in any language.
with open(file1) as file_1:
current_word_1 = read_to_delim(file_1, delim)
while current_word_1:
with open(file2) as file_2:
current_word_2 = read_to_delim(file_2, delim)
while current_word_2:
if current_word_2 == current_word_1:
print current_word_2
current_word_2 = read_to_delim(file_2, delim)
current_word_1 = read_to_delim(file_1, delim)
I leave read_to_delim to you, but this is the extreme case that is memory-optimal but time-least-optimal.
depending on your application of course you could load the two files in a database, perform a left outer join, and discard the rows for which one of the two columns is null
Can somebody explain the main differences between (advantages / disadvantages) the two implementations?
For a library, what implementation is recommended?
Wikipedia's article on hash tables gives a distinctly better explanation and overview of different hash table schemes that people have used than I'm able to off the top of my head. In fact you're probably better off reading that article than asking the question here. :)
That said...
A chained hash table indexes into an array of pointers to the heads of linked lists. Each linked list cell has the key for which it was allocated and the value which was inserted for that key. When you want to look up a particular element from its key, the key's hash is used to work out which linked list to follow, and then that particular list is traversed to find the element that you're after. If more than one key in the hash table has the same hash, then you'll have linked lists with more than one element.
The downside of chained hashing is having to follow pointers in order to search linked lists. The upside is that chained hash tables only get linearly slower as the load factor (the ratio of elements in the hash table to the length of the bucket array) increases, even if it rises above 1.
An open-addressing hash table indexes into an array of pointers to pairs of (key, value). You use the key's hash value to work out which slot in the array to look at first. If more than one key in the hash table has the same hash, then you use some scheme to decide on another slot to look in instead. For example, linear probing is where you look at the next slot after the one chosen, and then the next slot after that, and so on until you either find a slot that matches the key you're looking for, or you hit an empty slot (in which case the key must not be there).
Open-addressing is usually faster than chained hashing when the load factor is low because you don't have to follow pointers between list nodes. It gets very, very slow if the load factor approaches 1, because you end up usually having to search through many of the slots in the bucket array before you find either the key that you were looking for or an empty slot. Also, you can never have more elements in the hash table than there are entries in the bucket array.
To deal with the fact that all hash tables at least get slower (and in some cases actually break completely) when their load factor approaches 1, practical hash table implementations make the bucket array larger (by allocating a new bucket array, and copying elements from the old one into the new one, then freeing the old one) when the load factor gets above a certain value (typically about 0.7).
There are lots of variations on all of the above. Again, please see the wikipedia article, it really is quite good.
For a library that is meant to be used by other people, I would strongly recommend experimenting. Since they're generally quite performance-crucial, you're usually best off using somebody else's implementation of a hash table which has already been carefully tuned. There are lots of open-source BSD, LGPL and GPL licensed hash table implementations.
If you're working with GTK, for example, then you'll find that there's a good hash table in GLib.
My understanding (in simple terms) is that both the methods has pros and cons, though most of the libraries use Chaining strategy.
Chaining Method:
Here the hash tables array maps to a linked list of items. This is efficient if the number of collision is fairly small. The worst case scenario is O(n) where n is the number of elements in the table.
Open Addressing with Linear Probe:
Here when the collision occurs, move on to the next index until we find an open spot. So, if the number of collision is low, this is very fast and space efficient. The limitation here is the total number of entries in the table is limited by the size of the array. This is not the case with chaining.
There is another approach which is Chaining with binary search trees. In this approach, when the collision occurs, they are stored in binary search tree instead of linked list. Hence, the worst case scenario here would be O(log n). In practice, this approach is best suited when there is a extremely nonuniform distribution.
Since excellent explanation is given, I'd just add visualizations taken from CLRS for further illustration:
Open Addressing:
Chaining:
Open addressing vs. separate chaining
Linear probing, double and random hashing are appropriate if the keys are kept as entries in the hashtable itself...
doing that is called "open addressing"
it is also called "closed hashing"
Another idea: Entries in the hashtable are just pointers to the head of a linked list (“chain”); elements of the linked list contain the keys...
this is called "separate chaining"
it is also called "open hashing"
Collision resolution becomes easy with separate chaining: just insert a key in its linked list if it is not already there
(It is possible to use fancier data structures than linked lists for this; but linked lists work very well in the average case, as we will see)
Let’s look at analyzing time costs of these strategies
Source: http://cseweb.ucsd.edu/~kube/cls/100/Lectures/lec16/lec16-25.html
If the number of items that will be inserted in a hash table isn’t known when the table is created, chained hash table is preferable to open addressing.
Increasing the load factor(number of items/table size) causes major performance penalties in open addressed hash tables, but performance degrades only linearly in chained hash tables.
If you are dealing with low memory and want to reduce memory usage, go for open addressing. If you are not worried about memory and want speed, go for chained hash tables.
When in doubt, use chained hash tables. Adding more data than you anticipated won’t cause performance to slow to a crawl.