Partially smart, partially brute-force day 17

2021/inputs/17.txt

@@ -0,0 +1 @@
+target area: x=14..50, y=-267..-225

2021/src/day17.rs

@@ -1,9 +1,179 @@
 use std::io::Read;
+use std::ops::RangeInclusive;
 
-pub fn part1(_input: &mut dyn Read) -> String {
+use itertools::Itertools;
-    todo!()
+use itertools::MinMaxResult;
+use nom::bytes::complete::tag;
+use nom::combinator::map;
+use nom::sequence::preceded;
+use nom::sequence::separated_pair;
+use nom::Finish;
+use nom::IResult;
+
+#[inline]
+fn solve_quadratic(a: f64, b: f64, c: f64) -> Option<f64> {
+    let d = b * b - 4. * a * c;
+
+    if d < 0. {
+        None
+    } else {
+        // Don't care about the smaller solution due to problem statement
+        Some((-b - d.sqrt()) / 2. / a)
+    }
 }
 
-pub fn part2(_input: &mut dyn Read) -> String {
+fn position(initial: i32, time: i32) -> i32 {
-    todo!()
+    time * (2 * initial - time + 1) / 2
+}
+
+fn find_hit(initial: i32, range: &RangeInclusive<i32>) -> Option<RangeInclusive<i32>> {
+    // y position at time x: f(x) = x * (1 + initial + initial - x) / 2
+    //                            = -1/2x^2 + (initial + 0.5)x
+    //
+    // to hit, find x := (max(box) + min(box)) / 2 = f(x)
+    //                                             = -1/2x^2 + (initial + 0.5)x
+    // -1/2x^2 + (initial + 0.5)x - (max(box) + min(box)) / 2 = 0
+    let middle = (*range.start() + *range.end()) as f64 / 2.;
+    let b = initial as f64 + 0.5;
+    let hit = solve_quadratic(-0.5, b, -middle)? as i32;
+
+    if hit < 0 {
+        // Should not happen because of the shape but for correctness
+        None
+    } else {
+        let min_hit = (0..=hit)
+            .rev()
+            .take_while(|&n| range.contains(&position(initial, n)))
+            .min();
+
+        let max_hit = ((hit + 1)..)
+            .take_while(|&n| range.contains(&position(initial, n)))
+            .max();
+
+        match (min_hit, max_hit) {
+            (Some(min), Some(max)) => Some(min..=max),
+            (Some(val), None) | (None, Some(val)) => Some(val..=val),
+            _ => None,
+        }
+    }
+}
+
+fn find_speed(x: i32, range: &RangeInclusive<i32>) -> Option<RangeInclusive<i32>> {
+    let mut min = 0;
+    let mut max = *range.end();
+
+    // Need to tweak the formula as x slows down
+    let x_pos = |speed| position(speed, speed.min(x));
+
+    while max >= min {
+        let speed = (max + min) / 2;
+
+        let pos = x_pos(speed);
+
+        if range.contains(&x_pos(speed)) {
+            let min_speed = (0..speed)
+                .rev()
+                .take_while(|&speed| range.contains(&x_pos(speed)))
+                .min()
+                .unwrap_or(speed);
+
+            let max_speed = ((speed + 1)..)
+                .take_while(|&speed| range.contains(&x_pos(speed)))
+                .max()
+                .unwrap_or(speed);
+            return Some(min_speed..=max_speed);
+        } else if pos < *range.start() {
+            min = speed + 1;
+        } else {
+            max = speed - 1;
+        }
+    }
+
+    None
+}
+
+fn parse_range(input: &[u8]) -> IResult<&[u8], RangeInclusive<i32>> {
+    use nom::character::complete::i32;
+
+    map(separated_pair(i32, tag(".."), i32), |(start, end)| {
+        start..=end
+    })(input)
+}
+
+fn parse_input(input: &[u8]) -> IResult<&[u8], (RangeInclusive<i32>, RangeInclusive<i32>)> {
+    preceded(
+        tag("target area: x="),
+        separated_pair(parse_range, tag(", y="), parse_range),
+    )(input)
+}
+
+pub fn part1(input: &mut dyn Read) -> String {
+    let mut buffer = Vec::new();
+    input.read_to_end(&mut buffer).unwrap();
+
+    let (x_range, y_range) = parse_input(&buffer).finish().unwrap().1;
+
+    let check_value = |y_speed| {
+        let mut time = find_hit(y_speed, &y_range)?;
+
+        if time.any(|time| find_speed(time, &x_range).is_some()) {
+            Some(position(y_speed, y_speed))
+        } else {
+            None
+        }
+    };
+
+    (0..1000).filter_map(check_value).max().unwrap().to_string()
+}
+
+pub fn part2(input: &mut dyn Read) -> String {
+    let mut buffer = Vec::new();
+    input.read_to_end(&mut buffer).unwrap();
+
+    let (x_range, y_range) = parse_input(&buffer).finish().unwrap().1;
+
+    let num_options = |y_speed| {
+        let time = find_hit(y_speed, &y_range)?;
+        let range = time
+            .filter_map(|time| find_speed(time, &x_range))
+            .flat_map(|x| [*x.start(), *x.end()])
+            .minmax();
+
+        Some(match range {
+            MinMaxResult::NoElements => 0,
+            MinMaxResult::OneElement(_) => 1,
+            MinMaxResult::MinMax(min, max) => max - min + 1,
+        })
+    };
+
+    (-1000..1000)
+        .filter_map(num_options)
+        .sum::<i32>()
+        .to_string()
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::test_implementation;
+
+    use super::*;
+
+    const SAMPLE: &[u8] = &*b"target area: x=20..30, y=-10..-5";
+
+    #[test]
+    fn test_find_hit() {
+        assert_eq!(find_hit(2, &(-10..=-5)), Some(7..=7));
+        assert_eq!(find_hit(3, &(-10..=-5)), Some(9..=9));
+        assert_eq!(find_hit(0, &(-10..=-5)), Some(4..=5));
+    }
+
+    #[test]
+    fn sample_part1() {
+        test_implementation(part1, SAMPLE, 45);
+    }
+
+    #[test]
+    fn sample_part2() {
+        test_implementation(part2, SAMPLE, 112);
+    }
 }

2021/src/samples/17.txt

@@ -0,0 +1 @@
+target area: x=20..30, y=-10..-5