PWC151 - Binary Tree Depth

TL;DR

Here we are with TASK #1 from The Weekly Challenge #151. Enjoy!

The challenge

You are given binary tree.

Write a script to find the minimum depth.

The minimum depth is the number of nodes from the root to the nearest leaf node (node without any children).

Example 1:

Input: '1 | 2 3 | 4 5'

                1
               / \
              2   3
             / \
            4   5

Output: 2

Example 2:

Input: '1 | 2 3 | 4 *  * 5 | * 6'

                1
               / \
              2   3
             /     \
            4       5
             \
              6
Output: 3

The questions

I’m a paranoid bastard and, as everyone, I project that a lot. But I’m also bayesian, and experience has shown time and again that our fine host is indeed a kind and honest person.

And yet, my mind can’t possibly avoid to think for a tiny teensy split second that maybe the choice of the input representation for the binary tree is a big bait for totally disregarding that this is supposed to indeed represent a binary tree and be treated as such, instead of just playing with strings and find a solution that technically solves the problem, but it would be otherwise garbage.

But I’ll resist, and eat the bait 😂

And wait! Missing stuff and * mean the same, right? And a space can never be a node’s content, right?

The solution

So well, yeah, find… a binary tree. Given in input in a weird but so subtly useful way - no less than by layers. So I read the challenge as: don’t bother with any layer below the first one that provides a solution to the challenge. We will not end up with the complete binary tree (as a matter of fact, with any tree at all), but we will have fun on the way.

So where’s the “first” (by depth/level) leaf located? Well, just look for missing stuff in the layer immediately below, of course. The slots corresponding to its children will either be missing, or filled with an asterisk *.

There’s more: the two children will always be located in two consecutive places, namely an even position and the odd position immediately after. So we only need to find the first level with two such empty positions, and the answer will be the level immediately before.

We’ll start with Raku first, in a sort of strong Perl accent. I’ve been doing a lot of Perl lately, and like with natural language I tend to regress when I don’t exercise much with the new one.

#!/usr/bin/env raku
use v6;
sub MAIN (Str $input = '1 | 2 3 | 4 5') {
   if ($input.chars == 0) {
      put 0;
      return 0;
   }
   my @levels = $input.split(/\s*\|\s*/)».comb(/\S+/)».Array;
   for 1 ..^ @levels -> $depth {
      for 0 .. @levels[$depth - 1].end -> $i {
         next if (@levels[$depth - 1][$i] eq '*')
            || ((@levels[$depth][$i * 2] // '*') ne '*')
            || ((@levels[$depth][$i * 2 + 1] // '*') ne '*');
         put $depth;
         return 0;
      }
   }
   put @levels.elems;
   return 0;
}

The input is split into parts using the pipe character | as separator. I’m very used to Perl’s split and Raku’s rendition is… different:

$ perl -E 'my @x = split /\|/, ""; say scalar @x'
0

$ raku -e 'my @x = split /\|/, ""; put @x.elems'
1

So we have to keep this in mind. This is why there’s an explicit check for an empty input at the beginning, by the way.

The challenge is then solved by comparing consecutive layers of the tree, directly from the input. In the “previous” one we consider all items that are not empty; for them we check if either child is filled with something. When this does not apply any more… bingo! We have a solution.

If we run out of layers, then the last layer is the solution (hence the put @levels.elems at the end).

The Perl version is quite similar:

#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';

my $input = shift // '1 | 2 3 | 4 5';
my @levels = map { [ split m{\s+}mxs ] } split m{\s*\|\s*}mxs, $input;
for my $depth (1 .. $#levels) {
   for my $i (0 .. $levels[$depth - 1]->$#*) {
      next if $levels[$depth - 1][$i] eq '*'
         || ($levels[$depth][$i * 2] // '*') ne '*'
         || ($levels[$depth][$i * 2 + 1] // '*') ne '*';
      say $depth;
      exit 0;
   }
}
say scalar @levels;
exit 0;

I have to admit that I like Perl’s split better, although it’s probably just a matter of taste and muscle memory. I also have to admit that having less built-in container types plays in favor of Perl in these situations: we only have arrays, while the default type provided by comb as output is not good in our case, and we have to put the thing in an Array explicitly:

my @levels = $input.split(/\s*\|\s*/)».comb(/\S+/)».Array;

Anyway, this is really nitpicking - Raku is a lot of fun to use and learn!

Stay safe people, see you next time!


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