On 22 Mar 2017, at 18:48, David Turner <dct25-561bs@mythic-beasts.com> wrote:

I think the space must be O(m+n) since you are using strict Text values. But even if you weren't, you're using s1 and s2 in more than one place so they will be shared, leading to them both being fully in memory at once.

The minimum possible space complexity could well be O(1) if using String or lazy Text.

The time complexity looks like O(min(m,n)), because that's the cost of `zip`/`filter`, not counting the cost of loading the two Texts into memory in the first place (which will be O(m+n)). If you used String, it'd be O(m+n) since that's the cost of the two calls to `length`. I think the minimum possible time complexity will be O(min(m,n)), and that could include the cost of loading the strings too.

On 22 Mar 2017 18:32, "Michael Litchard" <litchard.michael@gmail.com> wrote:

Problem spec from CareerCup.

Given two strings, return boolean True/False if they are only one edit apart. Edit can be insert/delete/update of only one character in the string. Eg.

-True

xyz,xz

xyz,xyk

xy,xyz

-False

xyz,xyz

xyz,xzy

x,xyz

module Strings.OneLetter where`

import Prelude
import qualified Data.Text as T`

oneLetter :: T.Text -> T.Text -> Bool
oneLetter s1 s2
  | s1 == s2 = False
  | max_l > (min_l + 1) = False
  | max_l == min_l = diff_size == 1
  | otherwise = diff_size == 0
  where
    length_s1 = T.length s1
    length_s2 = T.length s2
    max_l = max length_s1 length_s2
    min_l = min length_s1 length_s2
    diff_size = length $ filter (\(a,b) -> a /= b) zipped
    zipped = T.zip s1 s2`

So, I used Text instead of String, hoping I could take advantage of fusion. I have the following questions and my initial attempt to answer them.

What is the time complexity of oneLetter 0(m+n) where m is the length of s1 and n is the length of s2

what is the space complexity of oneLetter? I'm thinking due to laziness it's O(1), only two Chars are in memory at any one time, or two Ints. But I'm hazy on why. If this is wrong, please articulate why. If I'm right, and my reasoning is wrong or incomplete, please say why.

I don't think I can improve the time complexity. Am I right? Can the space complexity be improved?

What if I changed from Text to String? I don't think the time complexity changes, but how does this change the space complexity?

_______________________________________________
Haskell-Cafe mailing list
To (un)subscribe, modify options or view archives go to:
http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
Only members subscribed via the mailman list are allowed to post

_______________________________________________
Haskell-Cafe mailing list
To (un)subscribe, modify options or view archives go to:
http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
Only members subscribed via the mailman list are allowed to post.