RogerBW's Blog

I’ve been doing the Weekly Challenges. The latest involved more binary trees and linked lists. (Note that this is open until 12 September 2021.)

TASK #1 › Root Distance

You are given a tree and a node of the given tree.

Write a script to find out the distance of the given node from the root.

Well, once more, this is made vastly easier by using a simple tree representation rather than some complex cross-linked structure. (If there were a bog-standard way of representing a binary tree I'd write code to convert between that format and this.) Here's a test case in Rust:

#[test]
fn test_ex1a() {
    assert_eq!(rd(vec![
               1,
           2,      3,
         0,  0,  0,  4,
        0,0,0,0,0,0,5,6
    ],6),3);
}

and here's how to do the work:

fn rd(tree: Vec<u64>,content: u64) -> i64 {

Initial variable setup. First node is at depth 0; the number of nodes at this level is 1.

    let mut depth: i64=0;
    let mut dl: u64=1;
    let mut db: u64=1;

Run down each member of the tree. If we find what we want, return the answer.

    for i in 0..tree.len() {
        if tree[i]==content {
            return depth;
        }

We didn't find it. Update the row length counter.

        dl -= 1;

If we've got to the end of the row:

• the next row will be twice as long as this one
• reset the row length counter
• the depth will be one greater than before

(This whole bit could also have been done by returning int(log2(i+1)) above, or successive right-shifts for the same effect without floating point.)

        if dl==0 {
            db *= 2;
            dl = db;
            depth += 1;
        }
    }
    return -1;
}

The same approach works in PostScript, though returning directly doesn't work as one might wish, so I introduce an extra variable for the case where the node value is not found. (The problem doesn't specify behaviour in that case, or if node values are not unique, which there's no need for them to be.)

/rd {
    /content exch def
    /tree exch def
    /ret -1 def
    /depth 0 def
    /dl 1 def
    /db 1 def
    tree {
        content eq { /ret depth def exit } if
        /dl dl 1 sub def
        dl 0 eq {
            /db db 2 mul def
            /dl db def
            /depth depth 1 add def
        } if
    } forall
    ret
} def

TASK #2 › Add Linked Lists

You are given two linked list having single digit positive numbers.

Write a script to add the two linked list and create a new linked [list] representing the sum of the two linked list numbers. The two linked lists may or may not have the same number of elements.

OK, perhaps I was feeling a bit peevish, but I really don't have any use for singly-linked lists like this; I'm not writing that kind of low-level code, and the data structures I already have in various languages are entirely suitable for the things I do. (Nothing here requires insertion anywhere other than at the end of the list, or deletion at all. Even if they did, Perl's native lists are reasonably good at that, enough that a custom data structure may mean more overhead than letting the language do the work until the data sets get fairly massive, and the double-ended queues in Python and especially Rust are great; and if ordering isn't needed much or at all, hashes are just fine too.) So I only answered this one in Perl, and it's a bit of a cheat.

Basic initialisation. My object substrate is itself a Perl list. But I'm not cheating yet: each node has a pointer to the next node, which I use.

package Local::LinkedList;

sub new {
  my $class=shift;
  my $self=[];
  bless $self,$class;
}

Return the index in the substrate of the last entry in the list (because that's the one I'm going to update when I append). (Or -1 if there aren't any entries.)

sub lastused {
  my $self=shift;
  if ($#{$self}==-1) {
    return -1;
  }
  my $i=0;
  while ($self->[$i]{next} != -1) {
    $i=$self->[$i]{next};
  }
  return $i;
}

Append a value (or, if given an arrayref, several values in order). Find the last-used node; push on a new node with an end-of-list marker; update the last-used node to point to the new node. (Yes, index 0 will always get a "next" pointer of 1, etc.; the question didn't require me to justify using a linked list, just to implement it.)

sub append {
  my $self=shift;
  my $elem=shift;
  if (ref $elem eq 'ARRAY') {
    map {$self->append($_)} @{$elem};
  } else {
    my $i=$self->lastused;
    push @{$self},{value => $elem,next => -1};
    if ($i > -1) {
      $self->[$i]{next}=$#{$self};
    }
  }
}

Dump the content of the list as an arrayref. (You can tell where this is going, right?)

sub as_arrayref {
  my $self=shift;
  my @a;
  my $i=0;
  while (defined $self->[$i]) {
    push @a,$self->[$i]{value};
    $i=$self->[$i]{next};
    if ($i == -1) {
      last;
    }
  }
  return \@a;
}

And finally, the piecewise addition (expanded somewhat from the definition in the question by the examples). I would obviously not choose a singly-linked list for this case which involves walking the list in reverse – and therefore I don't!

sub piecewise_add {
  my $self=shift;
  my $other=shift;

Grab the data from each list, and reverse them into proper Perl lists.

  my @a=reverse @{$self->as_arrayref};
  my @b=reverse @{$other->as_arrayref};

Even up the lengths. (Could get clever with references, but why?)

  while (scalar @a < scalar @b) {
    push @a,0;
  }
  while (scalar @b < scalar @a) {
    push @b,0;
  }

Do a piecewise addition with carry, into a new list.

  my @c;
  my $carry=0;
  foreach my $i (0..$#a) {
    my $d=$a[$i]+$b[$i]+$carry;
    push @c,$d % 10;
    $carry=int($d/10);
  }
  if ($carry) {
    push @c,1;
  }

And finally reverse the new list into the required linked-list structure.

  my $out=Local::LinkedList->new;
  $out->append([reverse @c]);
  return $out;
}

Full code on github.