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Added Solution for 2021 day 17

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Burnus 2023-04-28 14:50:13 +02:00
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2021/day17_trick_shot/challenge.txt Normal file
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You finally decode the Elves' message. `HI`, the message says. You continue searching for the sleigh keys.
Ahead of you is what appears to be a large [ocean trench](https://en.wikipedia.org/wiki/Oceanic_trench). Could the keys have fallen into it? You'd better send a probe to investigate.
The probe launcher on your submarine can fire the probe with any [integer](https://en.wikipedia.org/wiki/Integer) velocity in the `x` (forward) and `y` (upward, or downward if negative) directions. For example, an initial `x,y` velocity like `0,10` would fire the probe straight up, while an initial velocity like `10,-1` would fire the probe forward at a slight downward angle.
The probe's `x,y` position starts at `0,0`. Then, it will follow some trajectory by moving in *steps*. On each step, these changes occur in the following order:
* The probe's `x` position increases by its `x` velocity.
* The probe's `y` position increases by its `y` velocity.
* Due to drag, the probe's `x` velocity changes by `1` toward the value `0`; that is, it decreases by `1` if it is greater than `0`, increases by `1` if it is less than `0`, or does not change if it is already `0`.
* Due to gravity, the probe's `y` velocity decreases by `1`.
For the probe to successfully make it into the trench, the probe must be on some trajectory that causes it to be within a *target area* after any step. The submarine computer has already calculated this target area (your puzzle input). For example:
```
target area: x=20..30, y=-10..-5
```
This target area means that you need to find initial `x,y` velocity values such that after any step, the probe's `x` position is at least `20` and at most `30`, *and* the probe's `y` position is at least `-10` and at most `-5`.
Given this target area, one initial velocity that causes the probe to be within the target area after any step is `7,2`:
```
.............#....#............
.......#..............#........
...............................
S........................#.....
...............................
...............................
...........................#...
...............................
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTT#TT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
```
In this diagram, `S` is the probe's initial position, `0,0`. The `x` coordinate increases to the right, and the `y` coordinate increases upward. In the bottom right, positions that are within the target area are shown as `T`. After each step (until the target area is reached), the position of the probe is marked with `#`. (The bottom-right `#` is both a position the probe reaches and a position in the target area.)
Another initial velocity that causes the probe to be within the target area after any step is `6,3`:
```
...............#..#............
...........#........#..........
...............................
......#..............#.........
...............................
...............................
S....................#.........
...............................
...............................
...............................
.....................#.........
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................T#TTTTTTTTT
....................TTTTTTTTTTT
```
Another one is `9,0`:
```
S........#.....................
.................#.............
...............................
........................#......
...............................
....................TTTTTTTTTTT
....................TTTTTTTTTT#
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
```
One initial velocity that *doesn't* cause the probe to be within the target area after any step is `17,-4`:
```
S..............................................................
...............................................................
...............................................................
...............................................................
.................#.............................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT..#.............................
....................TTTTTTTTTTT................................
...............................................................
...............................................................
...............................................................
...............................................................
................................................#..............
...............................................................
...............................................................
...............................................................
...............................................................
...............................................................
...............................................................
..............................................................#
```
The probe appears to pass through the target area, but is never within it after any step. Instead, it continues down and to the right - only the first few steps are shown.
If you're going to fire a highly scientific probe out of a super cool probe launcher, you might as well do it with *style*. How high can you make the probe go while still reaching the target area?
In the above example, using an initial velocity of `6,9` is the best you can do, causing the probe to reach a maximum `y` position of `*45*`. (Any higher initial `y` velocity causes the probe to overshoot the target area entirely.)
Find the initial velocity that causes the probe to reach the highest `y` position and still eventually be within the target area after any step. *What is the highest `y` position it reaches on this trajectory?*
To begin, [get your puzzle input](17/input).
Answer: