--- 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 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 quadcopter to generate a map with the height of each tree (your puzzle input). For example:
30373 25512 65332 33549 35390
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
5is visible from the left and top. (It isn't visible from the right or bottom since other trees of height
5are in the way.)
- The top-middle
5is visible from the top and right.
- The top-right
1is 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
5is visible, but only from the right.
- The center
3is not visible from any direction; for it to be visible, there would need to be only trees of at most height
2between it and an edge.
- The right-middle
3is visible from the right.
- In the bottom row, the middle
5is visible, but the
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?