Re: [Haskell-cafe] Time and space complexity of "take k . sort"
Unless of course you use a GHC RULE to rewrite the RHS into the LHS, which should always be a valid transformation. Ketil Malde wrote: Paul Johnson writes: takeLargest k = take k . sort But of equal practical interest is the space complexity. The optimum algorithm is to take the first k items, sort them, and then iterate through the remaining items by adding each item to the sorted list and then throwing out the highest one. That has space complexity O(k). What does the function above do? Well - 'sort' doesn't know the value of 'k', so it needs to retain all elements, just in case 'k' might be 'n'. So I don't see how you can use space less than 'n' for a construct like the above. -k ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Time and space complexity of "take k . sort"
Paul Johnson writes: >> takeLargest k = take k . sort > But of equal practical interest is the space complexity. The optimum > algorithm is to take the first k items, sort them, and then iterate > through the remaining items by adding each item to the sorted list and > then throwing out the highest one. That has space complexity O(k). > What does the function above do? Well - 'sort' doesn't know the value of 'k', so it needs to retain all elements, just in case 'k' might be 'n'. So I don't see how you can use space less than 'n' for a construct like the above. -k -- If I haven't seen further, it is by standing in the footprints of giants ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Time and space complexity of "take k . sort"
On 22/10/09 15:31, Paul Johnson wrote: > takeLargest k = take k . sort Because "sort" is lazily evaluated this only does enough sorting to find the first k elements. I guess the complexity is something like O(n*k*log(k)). Correction: O(n*log(k)) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Time and space complexity of "take k . sort"
This question on StackOverflow asked about how to find the largest 100 items in a very long list: http://stackoverflow.com/questions/1602998/fastest-way-to-obtain-the-largest-x-numbers-from-a-very-large-unsorted-list/1603198#1603198 I replied that you could do it with something like this (but here taking the k smallest to strip out some irrelevant complications): > takeLargest k = take k . sort Because "sort" is lazily evaluated this only does enough sorting to find the first k elements. I guess the complexity is something like O(n*k*log(k)). But of equal practical interest is the space complexity. The optimum algorithm is to take the first k items, sort them, and then iterate through the remaining items by adding each item to the sorted list and then throwing out the highest one. That has space complexity O(k). What does the function above do? Paul. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
