PWC125 - Binary Tree Diameter


On with TASK #2 from The Weekly Challenge #125. Enjoy!

The challenge

You are given binary tree as below:

   / \
  2   5
 / \ / \
3  4 6  7
       / \
      8  10

Write a script to find the diameter of the given binary tree.

The diameter of a binary tree is the length of the longest path between any two nodes in a tree. It doesn’t have to pass through the root.

For the above given binary tree, possible diameters (6) are:

3, 2, 1, 5, 7, 8, 9


4, 2, 1, 5, 7, 8, 9

The questions

Contrarily to what happened in the past, we’ll assume that we do not have to parse the tree but that we can somehow build it up in memory in some convenient way.

We will also assume that the diameter only is needed, not an actual sequence of nodes that make up that specific diameter.

The solution

I’ve been favoring Raku as first-attempt language lately, so it’s time to show Perl some love and start with it. By the way, it’s also the one with the comments about what’s going on.

sub visit_for_diameter ($root) {
   die "Ceci n'est pas une arbre\n" unless $root;

   # this keeps the length of the best diameter candidate passing through
   # the $root node itself
   my $subtree = 0;

   # this keeps the longest sub-leg starting from $root
   my $longest = 0;

   # this keeps the best diamater as found in some descendant but not
   # through $root
   my $best = 0;

   # iterate over the left and right sub-trees
   for my $children ($root->@[1, 2]) {

      # don't bother following dead ends
      next unless $children;

      # this gets the recursive sub-call, receiving the best diameter and
      # the longest leg length
      my ($c_best, $c_length) = visit_for_diameter($children);

      # keep the best between the left and the right sub-tree
      $best = $c_best if $c_best > $best;

      # the actual leg length from $root is one more step because we have
      # to reach the child with one step

      # keep the best sub-tree length
      $longest = $c_length if $c_length > $longest;

      # anyway, the best diameter passing through $root has to take into
      # account the length of the leg
      $subtree += $c_length;

   # the longest sub-tree length is established, but the best will have to
   # be established by comparing the best from the descendants and the
   # overall diameter passing through $root (i.e. $subtree)
   $best = $subtree if $subtree > $best;

   # return only the $best diameter in scalar context, and both in list
   # context so that we can properly recurse
   return $best unless wantarray;
   return ($best, $longest);

The input $root is assumed to be a reference to an array, where the first element is a label (which we ignore here), the second element is the left sub-tree (undef if there is none) and the third element is the right sub-tree (again, undef if there is none).

The idea is to perform a depth-first visit of the tree, emerging the best diameter in the descendants and comparing it with the best diameter passing through the specific node. Comments above provide the details step-by-step.

The Raku version is exceptionally similar, at least for one with such a strong Perl accent:

sub visit-for-diameter ($root) {
   die "Ceci n'est pas une arbre\n" unless $root;

   my ($subtree, $longest, $best) = (0, 0, 0);
   for $root[1, 2] -> $children {
      next unless $children;
      my ($c_best, $c_length) = visit-for-diameter($children);
      $best = $c_best if $c_best > $best;
      $longest = $c_length if $c_length > $longest;
      $subtree += $c_length;
   $best = $subtree if $subtree > $best;
   return ($best, $longest);

There is a big difference in the returned value: where I used wantarray to only return the best diameter in scalar context in the Perl code, Raku has nothing like that and I just return the pair. leaving for the printing function the taks of selecting the right slot in the answer.

And now… this is all for this week, stay safe and have -Ofun!

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