Day 6 initial solution

input/2023/day6.txt

@@ -0,0 +1,2 @@
+Time:        46     68     98     66
+Distance:   358   1054   1807   1080

src/day06.rs

@@ -0,0 +1,93 @@
+use aoc_runner_derive::{aoc_generator, aoc};
+use nom::{sequence::{preceded, separated_pair, pair}, bytes::complete::tag, IResult, character::complete::{multispace0, line_ending}, multi::separated_list0};
+
+
+fn parse_number_list(start_tag: &str) -> impl Fn(&str) -> IResult<&str, Vec<u64>> + '_ {
+    move |input| {
+        preceded(pair(tag(start_tag), multispace0), separated_list0(pair(tag(" "), multispace0), nom::character::complete::u64))(input)
+    }
+}
+
+fn parse_input(input: &str) -> IResult<&str, (Vec<u64>, Vec<u64>)> {
+    separated_pair(parse_number_list("Time:"), line_ending, parse_number_list("Distance:"))(input)
+}
+
+#[aoc_generator(day6, part1)]
+fn input_generator_part1(input: &str) -> (Vec<u64>, Vec<u64>) {
+    parse_input(input).unwrap().1
+}
+
+#[aoc_generator(day6, part2)]
+fn input_generator_part2(input: &str) -> (u64, u64) {
+    let mut lines = input.split('\n');
+    let time_line = lines.next().unwrap();
+    let dist_line = lines.next().unwrap();
+    let time_line = time_line.replace(' ', "");
+    let dist_line = dist_line.replace(' ', "");
+    let time = time_line[5..].parse().unwrap();
+    let dist = dist_line[9..].parse().unwrap();
+    (time, dist)
+}
+
+
+fn race_dist(speed: u64, total_time: u64) -> u64 {
+    speed*(total_time-speed)
+}
+
+// let n be the number of ms you hold the button
+// let t be the race time
+// let d be the record distance
+// time units is ms unless specified, distance is mm unless specified
+// n(t-n)>d
+// nt-n^2>d
+// nt-n^2-d>0
+//
+// nt-n^2-d=0
+// -n^2+tn-d=0
+//
+// n=-t(+-)sqrt(t^2-4*1*-d)/2
+// n=-t(+-)sqrt(t^2+4d)/2
+//
+// Let the two values be n_1 and n_2
+//
+// d/dn(nt-n^2-d)=t-2n
+// d/dn(t-2n)=-2
+//
+// Function is always concave down
+// Concave down parabolas are >0 between their roots
+//
+// Range of winning times are ceil(n_1) to floor(n_2)
+// Excluding an n value if distance is = record distance
+fn ways_to_win_race(time: u64, dist: u64) -> u64 {
+    let f_time = time as f64;
+    let f_dist = dist as f64;
+    let sqr_discr = ((f_time * f_time) - (4.0 * f_dist)).sqrt();
+    let n_1 = (((-f_time) + sqr_discr)/(-2.0)).ceil() as u64;
+    let n_2 = (((-f_time) - sqr_discr)/(-2.0)).floor() as u64;
+    let (n_1, n_2) = if n_1 > n_2 {
+        (n_2, n_1)
+    } else {
+        (n_1, n_2)
+    };
+    let excl_n1 = race_dist(n_1, time) == dist;
+    let excl_n2 = race_dist(n_2, time) == dist;
+    let total_offset = match (excl_n1, excl_n2) {
+       (false, false) => 0, 
+       (false, true) => 1, 
+       (true, false) => 1, 
+       (true, true) => 2, 
+    };
+    ((n_2 - n_1) + 1) - total_offset
+}
+
+#[aoc(day6, part1)]
+fn part1((times, dists): &(Vec<u64>, Vec<u64>)) -> u64 {
+    times.iter().zip(dists.iter()).map(|(&time, &dist)| {
+        ways_to_win_race(time, dist)
+    }).product()
+}
+
+#[aoc(day6, part2)]
+fn part2(&(time, dist): &(u64, u64)) -> u64 {
+    ways_to_win_race(time, dist)
+}

src/lib.rs

@@ -5,5 +5,6 @@ mod day02;
 mod day03;
 mod day04;
 mod day05;
+mod day06;
 
 aoc_lib! { year = 2023 }