73 lines
4.0 KiB
Markdown
73 lines
4.0 KiB
Markdown
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# Day 8: Treetop Tree House
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## Part 1
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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.
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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.
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The Elves have already launched a quadcopter to generate a map with the height of each tree (your puzzle input). For example:
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30373
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25512
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65332
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33549
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35390
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Each tree is represented as a single digit whose value is its height, where 0 is the shortest and 9 is the tallest.
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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.
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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:
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* 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.)
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* The top-middle 5 is **visible** from the top and right.
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* 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.
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* The left-middle 5 is **visible**, but only from the right.
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* 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.
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* The right-middle 3 is **visible** from the right.
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* In the bottom row, the middle 5 is **visible**, but the 3 and 4 are not.
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With 16 trees visible on the edge and another 5 visible in the interior, a total of 21 trees are visible in this arrangement.
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**Consider your map; how many trees are visible from outside the grid?**
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## Part 2
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Content with the amount of tree cover available, the Elves just need to know the best spot to build their tree house: they would like to be able to see a lot of trees.
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To measure the viewing distance from a given tree, look up, down, left, and right from that tree; stop if you reach an edge or at the first tree that is the same height or taller than the tree under consideration. (If a tree is right on the edge, at least one of its viewing distances will be zero.)
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The Elves don't care about distant trees taller than those found by the rules above; the proposed tree house has large eaves to keep it dry, so they wouldn't be able to see higher than the tree house anyway.
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In the example above, consider the middle 5 in the second row:
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30373
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25512
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65332
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33549
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35390
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* Looking up, its view is not blocked; it can see 1 tree (of height 3).
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* Looking left, its view is blocked immediately; it can see only 1 tree (of height 5, right next to it).
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* Looking right, its view is not blocked; it can see 2 trees.
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* Looking down, its view is blocked eventually; it can see 2 trees (one of height 3, then the tree of height 5 that blocks its view).
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A tree's scenic score is found by multiplying together its viewing distance in each of the four directions. For this tree, this is 4 (found by multiplying 1 * 1 * 2 * 2).
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However, you can do even better: consider the tree of height 5 in the middle of the fourth row:
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30373
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25512
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65332
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33549
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35390
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* Looking up, its view is blocked at 2 trees (by another tree with a height of 5).
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* Looking left, its view is not blocked; it can see 2 trees.
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* Looking down, its view is also not blocked; it can see 1 tree.
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* Looking right, its view is blocked at 2 trees (by a massive tree of height 9).
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This tree's scenic score is 8 (2 * 2 * 1 * 2); this is the ideal spot for the tree house.
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Consider each tree on your map. **What is the highest scenic score possible for any tree?**
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