# RogerBW's Blog

Perl Weekly Challenge 93: Max Path 30 December 2020

I’ve been doing the Perl Weekly Challenges. The latest involved colinear points and binary tree sums. (Note that this is open until 3 January 2021.)

# TASK #1 › Max Points

You are given set of co-ordinates @N.

Write a script to count maximum points on a straight line when given co-ordinates plotted on 2-d plane.

``````sub mp {
my @c=@_;
my \$epsilon=0.0001;
my \$mxp=0;
``````

So I do a nested search: for each (ordered) pair of coordinates A and B, see how many of the others fall on the line they form.

``````  foreach my \$a (0..\$#c-2) {
foreach my \$b (\$a+1..\$#c-1) {
my @d=map {\$c[\$b][\$_]-\$c[\$a][\$_]} (0,1);
``````

Any two points are in a straight line…

``````      my \$pil=2;
foreach my \$c (\$b+1..\$#c) {
my \$tp=0;
my @v=map {\$c[\$c][\$_]-\$c[\$a][\$_]} (0,1);
``````

A bit of special-casing deals with the situation where A and B are on the same horizontal or vertical coordinate.

``````        if (\$d==0) {
if (\$v==0) {
\$tp=1;
}
} elsif (\$d==0) {
if (\$v==0) {
\$tp=1;
}
``````

Then it's time for floating-point. Yeah, probably could have done it all in integer. `max(v,d) % min(v,d) == 0` and so on, but it starts getting into special cases quite quickly. So I got lazy. `epsilon` is there because you can never trust floating-point equality. Python has a `Fraction` class, Raku has `Rat`, Ruby has `Rational` and Rust has `fraction`, but I basically just implemented this same system again.

``````        } elsif (abs(\$v/\$d-\$v/\$d)<\$epsilon) {
\$tp=1;
}
if (\$tp) {
\$pil++;
}
}
if (\$pil > \$mxp) {
\$mxp=\$pil;
}
}
}
return \$mxp;
}
``````

Raku is basically the same.

Python should have explicit conversion to float (though the test cases don't check for this).

``````                elif abs(float(v)/float(d)-float(v)/float(d)) < epsilon:
``````

Ruby is much the same again. Rust gets more fun, not least because the copy of the book I have uses `...` for inclusive range but the compiler has `..=`. (And people complained about Ruby changing its syntax.)

You are given binary tree containing numbers `0-9` only.

Write a script to sum all possible paths from root to leaf.

Rather than parse an ASCII diagram, I started with an array representation of the tree, with non-existing nodes represented by `undef`.

``````is(sp(1,2,undef,3,4),13,'example 1');
is(sp(1,2,3,4,undef,5,6),26,'example 2');
``````

Then it's back to good old FIFO buffer code. Which in Perl is trivial (if sluggish); in other languages, a bit less so. See, the great thing is that a Perl array isn't a first-class type: if I say [@array,\$variable] that's simply a reference to a new array consisting of all the values of the old `array` plus `variable` on the end. Which is what I want. Each entry in `@path` is a simple list of all the array indices needed to get to this point. If it has no child nodes, I add the sum of entries to the total.

``````sub sp {
my @t=@_;
my \$s=0;
my @path=();
while (my \$a=shift @path) {
my \$c=(\$a->[-1])*2+1;
my \$tn=1;
foreach my \$ac (\$c,\$c+1) {
if (\$ac <= \$#t && defined \$t[\$ac]) {
push @path,[@{\$a},\$ac];
\$tn=0;
}
}
if (\$tn) {
\$s+=sum(map {\$t[\$_]} @{\$a});
}
}
return \$s;
}
``````

This is the sort of thing that did my head in in Raku a few months back. And even here it's a bit dodgy; if I called my temporary variable `@a` rather than `\$a` it behaved differently. Also note the double `flat` plus `list`; all of those are necessary in order to get what seems to me the simple result. Raku doesn't like this use of `undef` so I substituted `-1`.

``````sub sp (**@t) {
my \$s=0;
my @path=((0));
while (@path) {
my \$a=shift @path;
my \$c=(\$a[\$a.end])*2+1;
my \$tn=1;
for (\$c,\$c+1) -> \$ac {
if (\$ac <= @t.end && @t[\$ac] != -1) {
push @path,(\$a.flat,\$ac).flat.list;
\$tn=0;
}
}
if (\$tn) {
\$s+=sum(map {@t[\$_]},\$a.list);
}
}
return \$s;
}
``````

For Python I used the `deque` type for the main buffer. It's happy with `None` though. I did end up using a temporary array variable, which I suppose is what the other languages are doing internally.

``````def sp(*t):
s=0
path=collections.deque([])
while len(path)>0:
a=path.popleft()
c=a[-1]*2+1
tn=1
for ac in range(c,c+2):
if ac < len(t) and t[ac] is not None:
b=a.copy()
b.append(ac)
path.append(b)
tn=0
if tn:
s += sum(t[i] for i in a)
return s
``````

Ruby has `nil`, though it doesn't need a `deque` type.

``````def sp(*t)
s=0
path=[]
while (a=path.shift) do
c=a[-1]*2+1
tn=true
c.upto(c+1) do |ac|
if ac <= t.length && !t[ac].nil? then
path.push([a,ac].flatten)
tn=false
end
end
if tn
s += a.map{|i| t[i]}.sum()
end
end
return s
end
``````

And Rust, ah, beautiful Rust… which gets the `deque` and type conversions, as well as the explicit temporary variable.

``````fn sp(t: Vec<i32>) -> i32 {
let mut s: i32=0;
let mut path: VecDeque<Vec<i32>>=VecDeque::new();
path.push_back(vec!);
while path.len() > 0 {
let a=path.pop_front().unwrap();
let c=((a.last().unwrap())*2+1) as usize;
let mut tn=true;
for ac in c..=c+1 {
if ac < t.len() && t[ac]>-1 {
let mut b=a.clone();
b.push(ac as i32);
path.push_back(b);
tn=false;
}
}
if tn {
s+=a.iter().map(|i| t[*i as usize]).sum::<i32>();
}
}
return s;
}
``````

But this is feeling increasingly like the right way to do things.

Full code on github.

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