# ETOOBUSY š minimal blogging for the impatient

# PWC152 - Triangle Sum Path

**TL;DR**

Here we are with TASK #1 from The Weekly Challenge #152. Enjoy!

# The challenge

You are given a triangle array.

Write a script to find the minimum sum path from top to bottom.

Example 1:`Input: $triangle = [ [1], [5,3], [2,3,4], [7,1,0,2], [6,4,5,2,8] ] 1 5 3 2 3 4 7 1 0 2 6 4 5 2 8 Output: 8 Minimum Sum Path = 1 + 3 + 2 + 0 + 2 => 8`

Example 2:`Input: $triangle = [ [5], [2,3], [4,1,5], [0,1,2,3], [7,2,4,1,9] ] 5 2 3 4 1 5 0 1 2 3 7 2 4 1 9 Output: 9 Minimum Sum Path = 5 + 2 + 1 + 0 + 1 => 9`

# The questions

Oh my how many questions I have.

The most basic one is *what is a path from top to bottom*. By the
arrangement of the numbers in the triangle, I was assuming that itās
some kind of graph where each node is connected to up to two nodes above
and up to two nodes below, e.g. the `3`

at the very center of the first
example would be connected to the `5`

and `3`

above of it, and to the
`1`

and `0`

immediately below. On the other hand, *both* examples make
it clear that this is not the case: in the first example we go from the
`2`

in third row to the `0`

in the fourth, and they are definitely not
ācloseā by the definition above.

Soā¦ Iāll assume that everything in a tier is connected to everything in the tier below.

I would also ask whatās the domain of the numbers in the nodes. In this
ātotal connection between two adjacent tiersā this question is kind of
moot butā¦ I only figured that there is the total connection at a
second read of the input, so it *initially* mattered a lot!
Additionally, I think itās a good information to have around (especially
if negative numbers would be allowed).

# The solution

I initially totally misunderstood the task at hand and didnāt think that
each tier was totally connected to its adjacent tiersā¦ I only figured
this *after* botching both examplesā result.

So my initial take was to consider this a graph, add a `goal`

node at
the end (connected to all nodes in the bottom tier) and put my A*
implementation to work the best path and its cost:

```
sub triangle-restricted-sum-path (@triangle) {
class Astar { ... }
my $max-last = @triangle[*-1].max;
my $astar = Astar.new(
distance => sub ($u, $v) {
return $v<goal> ?? 0 !! @triangle[$v<tier>][$v<index>];
},
successors => sub ($v) {
my $tier = $v<tier> + 1;
return hash(goal => 1) unless $tier <= @triangle.end;
my @retval = gather {
for 0 .. 1 -> $delta {
my $index = $v<index> + $delta;
take hash(tier => $tier, index => $index)
if $index <= @triangle[$tier].end;
}
};
return @retval;
},
heuristic => sub ($u, $v) {
return $u<goal> ?? 0 !! $u<tier> < @triangle.end ?? $max-last !! 0;
},
identifier => sub ($v) {
return $v<goal> ?? 'goal' !! $v<tier index>.join(',');
},
);
my $triangle-sum-path = $astar.best-path(
hash(tier => 0, index => 0),
hash(goal => 1),
);
my $sum = 0;
for $triangle-sum-path.List -> $v {
last if $v<goal>;
$sum += @triangle[$v<tier>][$v<index>];
}
return $sum;
}
```

Butā¦ butā¦ it turns out that life is *extremely* simpler in this
challenge, and it seems that taking the minimum value out of every tier
and summing them up does the trick, soā¦

```
sub triangle-sum-path (@triangle) { @triangleĀ».min.sum }
```

I confess that this has been a bit of anti-climax, but the challenge is the challenge. Itās also a nice place to show off a bit of hyperoperators!

When translating into Perl, though, I didnāt do the same error, so hereās the full solution:

```
#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';
use List::Util qw< sum min >;
my @triangle = map { [split m{,}mxs] } @ARGV;
say triangle_sum_path(@triangle);
sub triangle_sum_path (@triangle) { sum map { min $_->@* } @triangle }
```

No hyperoperators here, but still Perl rocks a lot with all the needed batteries in CORE.

This, and a `-r`

flag, are all I ask to be happy š

Stay safe folks!

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