# Polyglot Maxxie and Minnie

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Continuing my theme of learning all the languages, I took the opportunity of a programming puzzle to try out the same approach in a handful of different languages to compare how they work.

For an upcoming APL’ers meetup the challenge was set as posed at the end of in this post, namely

**Maxxie and Minnie**

The maxxie of a number n is the largest number you can achieve by swapping two of its digits (in decimal) (or choosing not to swap if it is already the largest possible). The minnie is the smallest with one swap (though you can’t swap a zero digit into the most significant position).

Your task is to write a function that takes an integer and returns a tuple of the maxxie and minnie.

Notes

- Swap any two decimal digits
- No leading zeroes
- Don’t swap if you can’t make it bigger/smaller

with the example solutions given in Clojure

(swapmaxmin 213) ;=> [312, 123] (swapmaxmin 12345) ;=> [52341, 12345] ;; the number was already the smallest (swapmaxmin 100) ;=> [100, 100] ;; no swap possible because of zeroes

This seems like fun – and I wanted to see how solutions might look across some of the different languages I know (including an APL, for the sake of the upcoming meetup).

I ended up using R, (Dyalog) APL, Julia, Haskell, Python, and Rust; someone provided a J solution; and I’ll add in any others shared with me. The site linked above collected Clojure solutions in this gist.

The common approach I used in all of these cases was:

- split the number into a vector of digits
- generate all possible combinations of indices to be swapped
- apply a swap function to perform all of those swaps
- append the unswapped vector, if not already included
- filter out any vectors which start with a
`0`

- recombine each vector into a single number
- return the maximum and minimum numbers

Here are my solutions in each language; it’s not so much for side-by-side comparison, but you can switch between the different ones. The full set of files is here if you’re interested.

R

I’m most familiar with R, so I like to start there. I created a

`swap`

function that swaps a vector at some indices, along with some helpers so that I could use`pmap_int()`

really cleanly.swap <- function(x, y, v) { xx <- v[x] yy <- v[y] v[x] <- yy v[y] <- xx v } chr_swap <- function(x, y, v) { paste0(swap(x, y, v), collapse = "") } toInt_swap <- function(x, y, v) { as.integer(chr_swap(x, y, v)) } maxmin <- function(num) { chars <- strsplit(as.character(num), "")[[1]] n <- nchar(num) s <- seq_len(n) opts <- expand.grid(x = s, y = s) opts$v <- list(chars) vals <- purrr::pmap_int(opts, toInt_swap) keeps <- vals[nchar(vals) == n] c(max(keeps), min(keeps)) } maxmin(213) [1] 312 123 maxmin(12345) [1] 52341 12345 maxmin(100) [1] 100 100 maxmin(11321) [1] 31121 11123

The

`expand.grid()`

does create some redundant combinations, but these fall out naturally so I didn’t bother filtering them out. Also, since this includes no-op swaps (e.g. swapping index`2`

and`2`

) it already contains the original vector. Rather than filtering to the vectors of integers*not*starting with 0, I filtered to those which contain the right number of digits after converting back to integer, which is equivalent.Try pasting the code into the {webr} online editor here; I’m not sure if it’s possible to link to an existing state, but when it asks if you want to install {purrr} to the interface, respond that you do.

APL

In Dyalog APL it’s easier to define a swap function; the

`@`

operator takes a function (reverse) so`s`

here performs a swap. The outer product is super handy for finding all the combinations of`x`

and`y`

:`x ∘., y`

.maxmin←{ ⎕IO←1 ⍝ so that x[1] is subset not x[0] n←⍎¨⍕⍵ ⍝ convert int to vec s←{⌽@⍵⊢⍺} ⍝ swap two elements swaps←{n s ⍵} ⍝ apply swaps to a vec n opts←,(⍳≢n)∘.,⍳≢n ⍝ combinations of 1..n new←swaps¨opts ⍝ perform the swaps keep←(~0=⊃¨new)/new ⍝ filter out values starting with 0 (⌈/,⌊/)10⊥¨keep ⍝ max and min of ints } maxmin 213 312 123 maxmin 12345 52341 12345 maxmin 100 100 100 maxmin 11321 31121 11123

I’m quite pleased with this solution; performing a

`map`

is as simple as using each (`¨`

) and performing both`max`

and`min`

concatenated together with a fork (`(⌈/,⌊/)`

) is just so aesthetic. Conversion from a vector of numbers to a single number uses a base-10 decode (`10⊥`

) which is how one might need to do that in other languages, but with a loop.If I was to take some liberties with what one calls a ‘line’, I could say that this is a 1-line solution

maxmin←{⎕IO←1 ⋄ n←⍎¨⍕⍵ ⋄ s←{⌽@⍵⊢⍺} ⋄ swaps←{n s ⍵} ⋄ opts←,(⍳≢n)∘.,⍳≢n ⋄ new←swaps¨opts ⋄ keep←(~0=⊃¨new)/new ⋄ (⌈/,⌊/)10⊥¨keep }

Julia

In Julia the

`swap`

function can use destructuring which is nice, but since the language uses pass-by-reference semantics, I need to make a copy of the vector being swapped, otherwise I’ll just keep swapping it over and over. Note: this recent post of mine.using Combinatorics function swap(x, i, j) y = copy(x) y[i], y[j] = y[j], y[i] y end function maxmin(x) nvec = parse.(Int64, split(string(x), "")) opts = collect(combinations(1:length(nvec), 2)) new = [[nvec]; map(x -> swap(nvec, x...), opts)] keep = filter(x -> x[1] != 0, new) vals = parse.(Int64, join.(keep)) (maximum(vals), minimum(vals)) end maxmin(213) (312, 123) maxmin(12345) (52341, 12345) maxmin(100) (100, 100) maxmin(11321) (31121, 11123)

The part I probably had the most trouble with here was concatenating together the original vector with its swapped versions; it looks clean now, but figuring out how to get those all into the same vector-of-vectors took me a while.

The splatting of

`opts`

variants in the`map`

was nice; no need to define the swap in terms of a tuple. Overall, this is a very clean solution, in my opinion - Julia really does make for a lovely language.Haskell

Continuing my Haskell-learning journey, I figured it would be best to have a go at this. As a heavily functional language, one doesn’t do a lot of defining of variables, instead one writes a lot of functions which will pass data around. This makes it a bit tricky for testing, but I got there eventually. I did have to borrow the

`swapElts`

function, and`nub`

was a new one for me (essentially`unique()`

).import Data.List import Data.Digits uniq_pairs l = nub [(x,y) | x <- l, y <- l, x < y] opts n = uniq_pairs [0..n-1] -- https://gist.github.com/ijt/2010183 swapElts i j ls = [get k x | (k, x) <- zip [0..length ls - 1] ls] where get k x | k == i = ls !! j | k == j = ls !! i | otherwise = x doswap t v = swapElts (fst t) (snd t) v newlist v = v : map (\x -> doswap x v) (opts (length v)) keep v = filter (\x -> (head x /= 0)) (newlist v) maxmin n = (maximum(x), minimum(x)) where x = map (unDigits 10) (keep (digits 10 n)) maxmin 213 (312,123) maxmin 12345 (52341,12345) maxmin 100 (100,100) maxmin 11321 (31121,11123)

The

`Data.Digits`

package was very helpful here - having`digits`

and`unDigits`

, though if I was going to use these more I would have curried the required base 10 into something like`digits10`

and`unDigits10`

.There are likely improvements to be made here, and I’m interested in any you can spot!

Python

“Everyone” uses it, so I gotta learn it… is what I keep telling myself. I’m no stranger to the quirks of different languages, but every time I try to do something functional in python I end up angry that the print method for generators shows the memory address instead of, say, the first few elements. Printing a value and seeing

`<map at 0x7fb928d4a2c0>`

gets me every. single. time. Yes, yes,`list(value)`

“collects” it, but grrr…Python has the destructuring syntax which is nice in the

`swap`

function, but again it’s pass-by-reference so I need to make a copy first.import itertools def swap(x, t): y = x.copy() i, j = t y[i], y[j] = y[j], y[i] return y def minmax(num): nums = [int(i) for i in str(num)] opts = itertools.combinations(range(len(nums)), 2) new = map(lambda x: swap(nums, x), list(opts)) keeps = list(filter(lambda x: x[0] != 0, new)) keeps.append(nums) vals = list(map(lambda x: int(''.join(map(str, x))), keeps)) return (max(vals), min(vals)) minmax(213) (312, 123) minmax(12345) (52341, 12345) minmax(100) (100, 100) minmax(11321) (31121, 11123)

Aside from my grumbles while writing it, the solution is still pretty clean. The calls to

`list()`

interspersed throughout might be avoidable, but the need to do that while developing at least slowed me down.Rust

I almost didn’t do a Rust solution because I thought I’d done enough. It ended up being the most complicated, though - I’m not sure if that’s because of me, or Rust.

use itertools::Itertools; fn swap(v: Vec<u32>, t1: usize, t2: usize) -> Vec<u32> { let mut vv = v; let tmp1 = vv[t1]; let tmp2 = vv[t2]; vv[t1] = tmp2; vv[t2] = tmp1; return vv; } fn maxmin(num: u32) -> (u32, u32) { let numc = num.to_string(); let n = numc.len(); let numv: Vec<u32> = numc .to_string() .chars() .map(|c| c.to_digit(10).unwrap()) .collect(); let mut opts = Vec::new(); for (a, b) in (0..n).tuple_combinations() { opts.push((a, b)); } let mut new: Vec<Vec<u32>> = Vec::new(); new.push(numv.clone()); for o in opts { new.push(swap(numv.clone(), o.0, o.1)); } let keeps: Vec<Vec<u32>> = new.into_iter().filter(|x| x[0] != 0).collect(); let mut vals = Vec::new(); for v in keeps { let tmp: u32 = v .clone() .into_iter() .map(|x| x.to_string()) .collect::<String>() .parse() .unwrap(); vals.push(tmp); } let min = *vals.iter().min().unwrap(); let max = *vals.iter().max().unwrap(); (max, min) } fn main() { println!("{:?}", maxmin(213)); println!("{:?}", maxmin(12345)); println!("{:?}", maxmin(100)); println!("{:?}", maxmin(11321)) } (312, 123) (52341, 12345) (100, 100) (31121, 11123)

This solution reminded me why I like working with array (or at least vector-supporting) languages; not needing to explicitly loop over every element of a vector to do something. I had to write a lot of

`push()`

loops to move data around.`max()`

doesn’t work on a vector (in the sense of finding the maximum of n elements); it works that way on an iterator, and may fail, hence the longer`min`

and`max`

lines.Having to

`clone()`

various values explicitly because they can’t be re-used was a bit annoying, but I understand*why*it complains about those.This took longer than I would have liked, but of course I learned more by doing it.

J

At the APL meetup we discussed one partial J solution which used a slightly different approach to the ‘swap’ algorithm. I’m not sure that there

*is*a way in J that’s as elegant as the APL solution, but I’d be interested if there is.Justus Perlwitz offered this solution, the essence of which is

digits =: 10&#.^:_1 sd =: {{ amend =. (|.y)} swap =. (y { ]) amend ] swap &.: digits x }} cart =: {{ all =. ,/ (,"0)/~ y uniq =. ~. /:~"1 all l =. 0{"1 uniq r =. 1{"1 uniq (l ~: r) # uniq }} swapmaxmin =: {{ ndigits =. [: # digits combs =. cart i. ndigits y constr =. ((ndigits y) <: [: ndigits"0 ]) # ] swaps =. constr y, y sd"1 combs (>./ , <./) swaps }} swapmaxmin 213 312 123 swapmaxmin 12345 52341 12345 swapmaxmin 100 100 100 swapmaxmin 11321 31121 11123

and which you can run in the J playground

There’s a lot I want to learn about J, so I’ll be digging through this solution myself.

## Summary

I was most pleased with the APL solution; it does what it says on the box without ambiguity because it’s constructed entirely from primitives (or utility functions defined in terms of those). The Julia solution also feels very clean, while the Haskell solution, defined entirely from functions, nicely demonstrates the functional principle.

I found it to be an interesting example of where pass-by-reference is *not* so
helpful. For packaged Julia functions that distinction is made clear with the
`!`

suffix to denote mutating functions, and it’s common to write both a
mutating and non-mutating version wherever possible.

Writing these taught me more and more about using each of these languages, and I’m of the opinion that just reading solutions is no substitute for getting your hands dirty in some actual code.

Comments, improvements, or your own solutions are most welcome. I can be found on Mastodon or use the comments below.

##
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