RogerBW's Blog

The Weekly Challenge 238: Running Persistence 15 October 2023

I’ve been doing the Weekly Challenges. The latest involved cumulative sums and complicated sorts. (Note that this ends today.)

Task 1: Running Sum

You are given an array of integers.

Write a script to return the running sum of the given array. The running sum can be calculated as sum[i] = num[0] + num[1] + …. + num[i].

There are two fairly obvious ways to do this. One is to start an accumulator at zero, add each entry, and copy the running total into a new list. That let me do it variable-free in PostScript:

/runningsum {

Push onto the stack, below the input array, the opening of a new array and a single member of velue zero.

    [ exch
      0 exch

For each member of the input array, add to the latest member of the new, and make another copy, which we'll add to with the next element.

          add dup
      } forall

The last entry will be duplicated, so drop that.


And end the array.

} bind def

But in other languages I made a copy of the input list and just added to each member (after the first) the value of the previous member. Thus in Raku:

sub runningsum(@a) {
    my @b = @a;
    for 1 .. @a.end -> $i {
        @b[$i] += @b[$i-1];
    return @b;

Task 2: Persistence Sort

You are given an array of positive integers.

Write a script to sort the given array in increasing order with respect to the count of steps required to obtain a single-digit number by multiplying its digits recursively for each array element. If any two numbers have the same count of steps, then print the smaller number first.

So there are two parts to this. One is a function to generate the persistence value, which is fairly straightforwawrd. Rust:

fn persistence(a: u32) -> u32 {
    let mut steps = 0;
    let mut b = a;
    while b > 9 {
        steps += 1;
        let mut p = 1;
        while b > 0 {
            p *= b % 10;
            b /= 10;
        b = p;

Then it's a two-stage sort, by persistence value and then by individual value, and different languages approach this in different ways. In Rust again, sort() is stable, and there's a sort_by_cached_key() which takes care of not calculating persistence more often than we have to. (While it doesn't matter with these small examples, it could clearly get quite expensive.)

fn persistencearray(a: Vec<u32>) -> Vec<u32> {
    let mut b = a;
    b.sort_by_cached_key(|i| persistence(*i));

Kotlin and Python also have stable sorting, but get a manual cache of persistence values. In Lua and most of the other languages, I build a manual cache and then do a sort with a custom comparator.

function persistencearray(a)
   local b = a

Build the cache (avoiding duplications):

   local c = {}
   for _, v in ipairs(b) do
      if c[v] == nil then
         c[v] = persistence(v)

Sort with comparator:

   table.sort(b, function(a, b)
                 if c[a] == c[b] then
                    return a < b
                    return c[a] < c[b]
   return b

Full code on github.

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