** --- Day 8: Treetop Tree House ---
The expedition comes across a peculiar patch of tall trees all planted
carefully in a grid. The Elves explain that a previous expedition
planted these trees as a reforestation effort. Now, they're curious if
this would be a good location for a
[[https://en.wikipedia.org/wiki/Tree_house][tree house]].

First, determine whether there is enough tree cover here to keep a tree
house /hidden/. To do this, you need to count the number of trees that
are /visible from outside the grid/ when looking directly along a row or
column.

The Elves have already launched a
[[https://en.wikipedia.org/wiki/Quadcopter][quadcopter]] to generate a
map with the height of each tree (your puzzle input). For example:

#+begin_example
30373
25512
65332
33549
35390
#+end_example

Each tree is represented as a single digit whose value is its height,
where =0= is the shortest and =9= is the tallest.

A tree is /visible/ if all of the other trees between it and an edge of
the grid are /shorter/ than it. Only consider trees in the same row or
column; that is, only look up, down, left, or right from any given tree.

All of the trees around the edge of the grid are /visible/ - since they
are already on the edge, there are no trees to block the view. In this
example, that only leaves the /interior nine trees/ to consider:

- The top-left =5= is /visible/ from the left and top. (It isn't visible
  from the right or bottom since other trees of height =5= are in the
  way.)
- The top-middle =5= is /visible/ from the top and right.
- The top-right =1= is not visible from any direction; for it to be
  visible, there would need to only be trees of height /0/ between it
  and an edge.
- The left-middle =5= is /visible/, but only from the right.
- The center =3= is not visible from any direction; for it to be
  visible, there would need to be only trees of at most height =2=
  between it and an edge.
- The right-middle =3= is /visible/ from the right.
- In the bottom row, the middle =5= is /visible/, but the =3= and =4=
  are not.

With 16 trees visible on the edge and another 5 visible in the interior,
a total of =21= trees are visible in this arrangement.

Consider your map; /how many trees are visible from outside the grid?/

To begin, [[file:8/input][get your puzzle input]].