82 lines
4.3 KiB
Markdown
82 lines
4.3 KiB
Markdown
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# 2022 Day 08: Treetop Tree House
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Copyright (c) Eric Wastl
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#### [Direct Link](https://adventofcode.com/2022/day/8)
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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](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Quadcopter) to generate a map with the height of each tree (your puzzle input). For example:
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```
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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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```
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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](https://en.wikipedia.org/wiki/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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```
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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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```
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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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```
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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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```
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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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