我如何在 haskell 中进行检查 O(1)，而不是 O(n)？

Question

get1 [] n = error "List is too small"
get1 xs n|n<0 = error "Use positive numbers"          
get1 (x:xs) 0 = x
get1 (x:xs) n = get1 xs (n-1)

I have get function made myself, but my check for positive numbers goes for O(n). What should i do to make this O(1)? I'm new in haskell, so recommend me something simple, please

Answer 1

If you stay with linked lists, you cannot do better than O(n). So if you want better, you'll have to use a different data structure; for O(1) essentially your only choice is an array, though there are many options if you allow yourself to relax to O(log n). And remember, for all n, log n < 30.

Answer 2

[Int] is a linked list type. Using this data structure, there's no faster way to access the Nth element than traveling through the first N ones.

In the case you are using get1 in another function f and you find that to be too slow, you either need to switch to a new data structure or (very commonly) rewrite f to avoid get1 . For instance, this is a common beginner mistake:

-- add 10 to each element in the list
add10 :: [Int] -> [Int]
add10 xs = [ 10 + get1 xs i | i <- [0 .. length xs-1] ]

This function "works" but is rather inefficient. For a list of length N, we pay O(N) for each get1 , and we make O(N) such calls, for a total of O(N^2) where, intuitively, O(N) would suffice.

The solution, in this case, is to avoid working with indices i but directly scan the list.

-- add 10 to each element in the list
add10 :: [Int] -> [Int]
add10 xs = [ 10 + x | x <- xs ]

In some other languages, to scan a list/array/sequence we need to work with indices. In Haskell, that's not the proper way to do it.

As a thumb rule, if you are a beginner and start working with lists, you should avoid functions like length, !! in most cases. I'd also recommend to avoid partial functions like head, tail . In general, many problems can be efficiently solved with lists using recursion and pattern matching, folds, maps, zip / zipWith , list comprehensions, and the like.