# RabbitFarm

### 2021-01-03

#### Perl Weekly Challenge 093

## Part 1

*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.*

### Solution

```
use strict;
use warnings;
##
# 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 triangle_area{
my($i, $j, $k) = @_;
return ($i->[0] * ($j->[1] - $k->[1]))
+ ($j->[0] * ($k->[1] - $i->[1]))
+ ($k->[0] * ($i->[1] - $j->[1]));
}
sub collinear_points{
my(@points) = @_;
my @collinear;
for my $i (@points){
for my $j (@points){
for my $k (@points){
if(triangle_area($i, $j, $k) == 0){
my $i_string = join(",", @{$i});
my $j_string = join(",", @{$j});
my $k_string = join(",", @{$k});
if(($i_string ne $j_string) && ($i_string ne $k_string) && ($j_string ne $k_string)){
my $has_i = grep { $i_string eq join(",", @{$_}) } @collinear;
push @collinear, $i if !$has_i;
my $has_j = grep { $j_string eq join(",", @{$_}) } @collinear;
push @collinear, $j if !$has_j;
my $has_k = grep { $k_string eq join(",", @{$_}) } @collinear;
push @collinear, $k if !$has_k;
}
}
}
}
}
return @collinear;
}
MAIN:{
my @N;
@N = ([5,3], [1,1], [2,2], [3,1], [1,3]);
my @collinear = collinear_points(@N);
print "There are a maximum of " . @collinear . " collinear points.\n"
}
```

### Sample Run

```
$ perl perl/ch-1.pl
There are a maximum of 3 collinear points.
```

### Notes

Keep in mind that any two points determine a line. Therefore to consider all possible non-trivial lines we need to review all triples of points. This method will work in the most general case when the starting data may contain multiple lines with a larger number of points.

In determining collinearity I calculate the area of a triangle using the triple of points. If the area is zero we know that all the points lay on the same line.

## Part 2

*You are given a binary tree containing only the numbers 0-9. Write a script to sum all possible paths from root to leaf.*

### Solution

```
use strict;
use warnings;
##
# You are given a binary tree containing
# only the numbers 0-9.
# Write a script to sum all possible paths
# from root to leaf.
##
use Graph;
sub travserse_sum{
my($tree) = @_;
my @paths = build_paths($tree);
my $path_sum = 0;
for my $path (@paths){
$path_sum += unpack("%32C*", pack("C*", @{$path}));
}
return $path_sum;
}
sub build_paths {
my ($graph) = @_;
my @paths;
local *_helper = sub{
my $v = $_[-1];
my @successors = $graph->successors($v);
if(@successors){
_helper(@_, $_) for @successors;
}
else{
push @paths, [@_];
}
};
_helper($_) for $graph->source_vertices();
return @paths;
}
MAIN:{
my $Tree;
$Tree = new Graph();
$Tree->add_vertices(1, 2, 3, 4);
$Tree->add_edge(1, 2);
$Tree->add_edge(2, 3);
$Tree->add_edge(2, 4);
print travserse_sum($Tree) . "\n";
$Tree = new Graph();
$Tree->add_vertices(1, 2, 3, 4, 5, 6);
$Tree->add_edge(1, 2);
$Tree->add_edge(1, 3);
$Tree->add_edge(2, 4);
$Tree->add_edge(3, 5);
$Tree->add_edge(3, 6);
print travserse_sum($Tree) . "\n";
}
```

### Sample Run

```
$ perl perl/ch-2.pl
13
26
```

### Notes

This is straightforward enough, at a high level anyway: (1) Get all paths and then (2) sum all the nodes on the paths.

- I am always happy to have a chance to use the Graph module!
- The Graph module has a bunch of nice algorithms implemented but what we want here is not a
*shortest path*but*all paths*. The Graph module doesn’t have anything for us to use for that. Implementing a recursive*Depth First Search*and collecting all the paths is not such a hard thing to do, but in the**Holiday Spirit**(i.e. laziness) I just re-used Ikegami’s code. See the References section. - I first used the pack/unpack trick for summing array back in Challenge 007.

## References

posted at: 16:37 by: Adam Russell | path: /perl | permanent link to this entry