remove elements: but which container to prefer

I am keeping the nonzeros of a sparse matrix representation in some triplets, known in the numerical community as Compressed Sparse Row storage, entries are stored row-wise, for instance a 4x4 matrix is represented as

r:0 0 1 1 2 2 3 3 3
c:0 3 2 3 2 3 1 2 3 
v:1 5 2 2 4 1 5 4 5

so 'r' gives row indices, 'c' gives column indices and 'v' are the values associated to the 2 indices above that value.

I would like to delete some rows and columns from my matrix representation, say rows and cols: 1 and 3. So I should remove 1s and 3s from the 'r' and 'c' arrays. I am also trying to learn more about the performance of the stl containers and read a bit more. As first try, created a multimap and delete开发者_运维技巧 the items by looping over them with the find method of multimap. This removes the found keys however might leave some of the searched values in the 'c' array then I swapped the key,value pairs and do the same operation for this second map, however this did not seem to be a very good solution to me, it seems to be pretty fast(on a problem with 50000 entries), though. So the question is what would be the most efficient way to do this with standard containers?

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You could use a map (between a pair of rows and columns) and the value, something like map<pair<int,int>, int>

If you then want to delete a row, you iterate over the elements and erase those with the to-be deleted row. The same can be done for columns.

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How are you accessing the matrix? Do you look up particular rows/columns and do things with them that way, or do you use the whole matrix at a time for operations like matrix-vector multiplications or factorization routines? If you're not normally indexing by row/column, then it may be more efficient to store your data in std::vector containers.

Your deletion operation is then a matter of iterating straight through the container, sliding down subsequent elements in place of the entries you wish to delete. Obviously, there are tradeoffs involved here. Your map/multimap approach will take something like O(k log n) time to delete k entries, but whole-matrix operations in that representation will be very inefficient (though hopefully still O(n) and not O(n log n)).

Using the array representation, deleting a single row or column would take O(n) time, but you could delete an arbitrary number of rows or columns in the same single pass, by keeping their indices in a pair of hash tables or splay trees and doing a lookup for each entry. After the deletion scan, you could either resize the vectors down to the number of elements you have left, which saves memory but might entail a copy, or just keep an explicit count of how many entries are valid, trading dead memory for saving time.