So bit arrays and hash tables don't seem to inherently allow for a find-max type operation, but there are ways around it. I'm wondering if there's a way using the bit array alone without extra variables, pointers, or manipulating the start/end of the array, in some scenarios. For example...
I have integers {1,...,n} and a n-bit bit array. To keep a subset of the integers, I use the integer itself as the key in the bit array and set the bit to 1 if it is in the subset, or 0 if it is not.
For example for integers {1,2,3,4} and subset {1,3), the bit array would look like {1,0,1,0}.
It seems like there's no way to do this without somehow moving the bits around which leads me to believe the O(1) dream is dead and perhaps the bit array won't work. Is something like this possible in O(log n)?
Thanks
Finding the highest set bit on a bit array of length n is O(n). If you need better, then you'll need to choose another data structure, or keep a high-water mark along with your bitmap.
Related
I have a slice that contains pointers to values. In a performance-critical part of my program, I'm adding or removing values from this slice. For the moment, inserting a value is just an append (O(1) complexity), and removal consists in searching the slice for the corresponding pointer value, from 0 to n-1, until the pointer is found (O(n)). To improve performance, I'd like to sort values in the slice, so that searching can be done using dichotomy (so O(log(n)).
But how can I compare pointer values? Pointer arithmetic is forbidden in go, so AFAIK to compare pointer values p1 and p2 I have to use the unsafe package and do something like
uintptr(unsafe.Pointer(p1)) < uintptr(unsafe.Pointer(p2))
Now, I'm not comfortable using unsafe, at least because of its name. So, is that method correct? Is it portable? Are there potential pitfalls? Is there a better way to define an order on pointer values? I know I could use maps, but maps are slow as hell.
As said by others, don't do this. Performance can't be that critical to resort to pointer arithmetic in Go.
Pointers are comparable, Spec: Comparison operators:
Pointer values are comparable. Two pointer values are equal if they point to the same variable or if both have value nil. Pointers to distinct zero-size variables may or may not be equal.
Just use a map with the pointers as keys. Simple as that. Yes, indexing maps is slower than indexing slices, but then again, if you'd want to keep your slice sorted and you wanted to perform binary searches in that, then the performance gap decreases, as the (hash) map implementation provides you O(1) lookup while binary search is only O(log n). In case of big data set, the map might even be faster than searching in the slice.
If you anticipate a big number of pointers in the map, then pre-allocate a big one with make() passing an estimated upper size, and until your map exceeds this size, no reallocation will occur.
m := make(map[*mytype]struct{}, 1<<20) // Allocate map for 1 million entries
I want to create a divide and conquer algorithm (O(nlgn) runtime) to determine if there exists a number in an array that occurs k times. A constraint on this problem is that only a equality/inequality comparison method is defined on the objects of the array (i.e can't use <, >).
So I have tried a number of approaches including splitting the array into k pieces of equal size (approximately). The approach is similar to finding the majority item in an array, however in the majority case when you split the array, you know that one half must have a majority item if such an item exists. Any pointers or tips that one could provide to put me in the right direction ?
EDIT: To clear up a little, I am wondering whether the problem of finding the majority item by splitting the array in half and using a recursive solution can be extended to other situations where k may be n/4 or n/5 etc.
Maybe I should of phrased the question using n/k instead.
This is impossible. As a simple example of why this is impossible, consider an input with a length-n array, all elements distinct, and k=2. The only way to be sure no element appears twice is to compare every element against every other element, which takes O(n^2) time. Until you perform all possible comparisons, you cannot be sure that some pair you didn't compare isn't actually equal.
I am parallelizing a certain dynamic programming problem using AVX2/SSE instructions.
In the main iteration of my calculation, I calculate column in matrix where each cell is a structure of AVX2 registers (_m256i). I use values from the previous matrix column as input values for calculating the current column. Columns can be big, so what I do is I have an array of structures (on stack), where each structure has two _m256i elements.
Structure:
struct Cell {
_m256i first;
_m256i second;
};
An then I have array like this: Cell prevColumn [N]. N will tipically be few hundreds.
I know that _m256i basically represents an avx2 register, so I am wondering how should I think about this array, how does it behave, since N is much larger than 16 (which is number of avx registers)? Is it a good practice to create such an array, or is there some better approach that i should use when storing a lot of _m256i values that are going to be reused real soon?
Also, is there any aligning I should be doing with this structures? I read a lot about aligning, but I am still not sure how and when to do it exactly.
It's better to structure your code to do everything it can with a value before moving on. Small buffers that fit in L1 cache aren't going to be too bad for performance, but don't do that unless you need to.
I think it's more typical to write your code with buffers of int [] type, rather than __m256i type, but I'm not sure. Either way works, and should get the compile to generate efficient code. But the int [] way means less code has to be different for the SSE, AVX2, and AVX512 version. And it might make it easier to examine things with a debugger, to have your data in an array with a type that will get the data formatted nicely.
As I understand it, the load/store intrinsics are partly there as a cast between _m256i and int [], since AVX doesn't fault on unaligned, just slows down on cacheline boundaries. Assigning to / from an array of _m256i should work fine, and generate load/store instructions where needed, otherwise generate vector instructions with memory source operands. (for more compact code and fewer fused-domain uops.)
Assuming you want a list of arrays, each having the same size. Is it better performance-wise to use a 2D array :
integer, allocatable :: data(:,:)
or an array of derived types :
type test
integer, allocatable :: content(:)
end type
type(test), allocatable :: data(:)
Of course, for arrays of different sizes, we don't have a choice. But how is the memory managed between the 2 cases ? Also, is one of them good code practice ?
Choose the implementation which minimises the conceptual distance that your mind has to leap between the problem in your head and the solution in your code. The force of this approach increases with age, both the age of your code (good conceptual design is a solid foundation for future development) and your own age (the less effort understanding your code demands the longer you'll remain mentally competent enough to understand it).
As to the non-opinion-determined part of your question concerning the way that the memory is managed ... My naive expectation is that most compilers will, under most circumstances, allocate contiguous memory for the first of your outlines, and may not for the second. But I don't care enough about this to check, and I do not think that you should either. I don't, by this, suggest that you should not be interested in what is going on under the hood, but rather that you should be more concerned with the matters referred to in the first paragraph.
In general, you want to use the simplest data structure that suits your problem. If a 2d rectangular array meets your needs - and for a huge number of scientific computing problems, problems for which Fortran is a good choice, it does - then that's the choice you want.
The 2d array will be contiguous in memory, which will normally make accessing it faster both due to caching and one fewer level of indirection; the 2d array will also allow you to do things like data = data * 2 or data = 0. which the array-of-array approach doesn't [Edited to add: though as IanH points out in comments you can create a defined type and defined operations on those types to allow this]. Those advantages are great enough that even when you have "ragged arrays", if the range of expected row lengths isn't that large, implementing it as a rectangular 2d array is sometimes a choice worth considering.
Suppose I have a set of tuples like this (each tuple will have 1,2 or 3 items):
Master Set:
{(A) (A,C) (B,C,E)}
and suppose I have another set of tuples like this:
Real Set: {(BOB) (TOM) (ERIC,SALLY,CHARLIE) (TOM,SALLY) (DANNY) (DANNY,TOM) (SALLY) (SALLY,TOM,ERIC) (BOB,SALLY) }
What I want to do is to extract all subsets of Tuples from the Real Set where the tuple members can be substituted to become the same as the Master Set.
In the example above, two sets would be returned:
{(BOB) (BOB,SALLY) (ERIC,SALLY,CHARLIE)}
(let BOB=A,ERIC=B,SALLY=C,CHARLIE=E)
and
{(DANNY) (DANNY,TOM) (SALLY,TOM,ERIC)}
(let DANNY=A,SALLY=B,TOM=C,ERIC=E)
Its sort of pattern matching, sort of combinatorics I guess. I really don't know how to classify this problem and what common plans of attack there are for it. What would the stackoverflow experts suggest?
Seperate your tuples into sets by size. Within each set, create a data structure that allows you to efficiently query for tuples containing a given element. The first part of this structure is your tuples as an array (so that each tuple has a cannonical index). The second set is: Map String (Set Int). This is somewhat space intensive but hopefully not prohibative.
Then, you, essentially, brute force it. For all assignments to the first master set, restrict all assignments to other master sets. For all remaining assignments to the second, restrict all assignments to the third and beyond, etc. The algorithm is basically inductive.
I should add that I don't think the problem is NP-complete so much as just flat worst-case exponential. It's not a decision problem, but an enumeration problem. And it's fairly easy to imagine scenarios of inputs that blow up exponentially.
It will be difficult to do efficiently since your problem is probably NP-complete (it includes subgraph isomorphism as a special case). That assumes the patterns and database both vary in size, though. How much data are you searching? How complicated will your patterns be? I would recommend the brute force solution first, then test if that is too slow and you need something fancier.