# Advent of Code 2023 Day 6

## Day 6: Wait For It

https://adventofcode.com/2023/day/6

A ferry brings you to a boat race.
The prize for winning the race is a trip to desert island, you want to go there, because you heard some sand is needed to fix the snow issue.
A island named **Desert Island** will surely have a lot of that annoying, course, stuff.

This race is slightly unusual, the amount of **time everyone gets is fixed**.
Whoever gets the **furthest in that time wins**.

Todayâ€™s input is a report of previous races.

An example input looks like this:

Time: 7 15 30Distance: 9 40 200

It maps time-limits of races to the current furthest distance.

This document describes three races:

- Race 1 lasts 7 milliseconds. The record distance in this race is 9 millimeters.
- Race 2 lasts 15 milliseconds. The record distance in this race is 40 millimeters.
- Race 3 lasts 30 milliseconds. The record distance in this race is 200 millimeters.

The boats are toy boats.

Before they start moving, you have to charge them by holding a button. The longer you charge them, the larger the boatâ€™s speed.

- The moment you start charging, the time starts
- The moment you stop charging, the boat starts moving (and doesnâ€™t lose speed, apparently they were made by a physics teacher elf that assumed a frictionless vaccuum)

## Part 1

For each race, determine the amount of ways you can beat the current record.

For the first race in the example (that lasts 7 milliseconds), there are 4 ways to beat the record of 9 millimeters:

- Hold the button for 2 milliseconds at the start of the race.
- Hold the button for 3 milliseconds at the start of the race.
- Hold the button for 4 milliseconds at the start of the race.
- Hold the button for 5 milliseconds at the start of the race.

The question asks you to multiply the number of ways you can win each race.

### Parsing

Getting 2 lists of numbers, and combining them.

For my own convenience, I used a `Race`

structure to represent each race, so I donâ€™t confuse myself by accessing things by index.

struct Race {time: u32,dist: u32,}

I chose to create a list of times and a list of distances, then zip those 2 lists together to get a list of races.

let (time, dist) = input.split_once("\n").unwrap();let time = time.strip_prefix("Time: ").unwrap().split_whitespace().map(|s| s.parse::<u32>().unwrap());let dist = dist.strip_prefix("Distance: ").unwrap().split_whitespace().map(|s| s.parse::<u32>().unwrap());let races = time.zip(dist).map(|(time, dist)| Race { time, dist });

### Code

The logic then loops over each race and determines how many ways I can win for each one. At the end, those counts are multiplied.

For every race: I determined the distance I would travel for every possible time I held the button. If the resulting final distance was greater than the current record, I won.

struct Race {time: u32,dist: u32,}pub fn part_1(input: &str) -> usize {let (time, dist) = input.split_once("\n").unwrap();let time = time.strip_prefix("Time: ").unwrap().split_whitespace().map(|s| s.parse::<u32>().unwrap());let dist = dist.strip_prefix("Distance: ").unwrap().split_whitespace().map(|s| s.parse::<u32>().unwrap());let races = time.zip(dist).map(|(time, dist)| Race { time, dist });races.map(|race| {(0..=race.time).map(|elapsed| {let speed = elapsed;speed * (race.time - elapsed)}).filter(|&dist| dist > race.dist).count()}).product::<usize>()}

## Part 2

It turns out the input had really bad keming. Each line is one number.

The question stays the same, but this time there is only 1 race.

### Parsing

For both time, and distance, I made a list of single digits. For each digit I encountered, I concatenate it to the end of the current number with math.

In the example input:

Time: 7 15 30Distance: 9 40 200

For time:

- The first digit is 7, the current number becomes 7
- The second digit is 1, the current number becomes 71
- The third digit is 5, the current number becomes 715
- The fourth digit is 3, the current number becomes 7153
- The final digit is 0, the current number becomes 71530

let (time, dist) = input.split_once("\n").unwrap();let race_time = time.strip_prefix("Time: ").unwrap().chars().filter_map(|c| c.to_digit(10)).fold(0u64, |curr, digit| curr * 10 + digit as u64);let race_dist = dist.strip_prefix("Distance: ").unwrap().chars().filter_map(|c| c.to_digit(10)).fold(0u64, |curr, digit| curr * 10 + digit as u64);

### Option 1: brute-force

The code from part 1 can largely be reused.

And joy, oh joy, I could even **remove** some code!

#### Code

pub fn part_2(input: &str) -> usize {let (time, dist) = input.split_once("\n").unwrap();let race_time = time.strip_prefix("Time: ").unwrap().chars().filter_map(|c| c.to_digit(10)).fold(0u64, |curr, digit| curr * 10 + digit as u64);let race_dist = dist.strip_prefix("Distance: ").unwrap().chars().filter_map(|c| c.to_digit(10)).fold(0u64, |curr, digit| curr * 10 + digit as u64);(0..=race_time).map(|elapsed| {let speed = elapsed;speed * (race_time - elapsed)}).filter(|&dist| dist > race_dist).count()}

### Option 2: math

This question was describing a quadratic graph. The answer is the difference between the two intersections with the y-axis on that graph.

Time to dust of the highschool math!

The equation we used to determine the distance we travel:

Written differently, that looks more familiar:

To find the 2 intersections of the second degree function with the x-axis, we set y to 0 and solve for x:

A refresher on the quadratic equation from Khan Academy.

The answer is the difference between the two points where the graph intersects with the x-axis.

I can only hold the button for an integer amount, so I need to round up the lowest value, and round down the highest value.

Then add 1 to the difference between those 2, because I want to include that last point where I can win the race.

#### Code

pub fn part_two_math(input: &str) -> u32 {let (time, dist) = input.split_once("\n").unwrap();let race_time = time.strip_prefix("Time: ").unwrap().chars().filter_map(|c| c.to_digit(10)).fold(0u64, |curr, digit| curr * 10 + digit as u64);let race_dist = dist.strip_prefix("Distance: ").unwrap().chars().filter_map(|c| c.to_digit(10)).fold(0u64, |curr, digit| curr * 10 + digit as u64);// time to dust off the math I learned in high school, a refresher: https://youtu.be/i7idZfS8t8w?si=FHnYI6--op32fkdk// x * (time - x) = dist// y = x^2 - time*x + dist// find the 2 intersections of the second degree function with the x-axis// so we set y to 0 and solve for x// 0 = x^2 - time*x + dist// The answer is the difference between the two points the graph intersects with the x-axis// x1 = (-b - SQRT(b^2 - 4*a*c)) / (2 * a)// x2 = (-b + SQRT(b^2 - 4*a*c)) / (2 * a)let a = 1.0;let b = 0.0 - race_time as f64;let c = race_dist as f64;let x1 = ((0.0 - b) - (b.powf(2.0) - (4.0 * a * c)).sqrt()) / (2.0 * a);let x2 = ((0.0 - b) + (b.powf(2.0) - (4.0 * a * c)).sqrt()) / (2.0 * a);// Because you can only hold the button for integer amounts, round up the lower value and round down the upper value// And add 1 since |x2 - x1| gives you the amount from x1 to below x2 but we want to include x2.let lower_bound = x1.ceil() as u32;let upper_bound = x2.floor() as u32 + 1;upper_bound - lower_bound}

## Final code

1struct Race {2 time: u32,3 dist: u32,4}56pub fn part_1(input: &str) -> usize {7 let (time, dist) = input.split_once("\n").unwrap();8 let time = time9 .strip_prefix("Time: ")10 .unwrap()11 .split_whitespace()12 .map(|s| s.parse::<u32>().unwrap());13 let dist = dist14 .strip_prefix("Distance: ")15 .unwrap()16 .split_whitespace()17 .map(|s| s.parse::<u32>().unwrap());18 let races = time.zip(dist).map(|(time, dist)| Race { time, dist });1920 races21 .map(|race| {22 (0..=race.time)23 .map(|elapsed| {24 let speed = elapsed;25 speed * (race.time - elapsed)26 })27 .filter(|&dist| dist > race.dist)28 .count()29 })30 .product::<usize>()31}3233pub fn part_2(input: &str) -> u32 {34 let (time, dist) = input.split_once("\n").unwrap();35 let race_time = time36 .strip_prefix("Time: ")37 .unwrap()38 .chars()39 .filter_map(|c| c.to_digit(10))40 .fold(0u64, |curr, digit| curr * 10 + digit as u64);41 let race_dist = dist42 .strip_prefix("Distance: ")43 .unwrap()44 .chars()45 .filter_map(|c| c.to_digit(10))46 .fold(0u64, |curr, digit| curr * 10 + digit as u64);4748 let a = 1.0;49 let b = 0.0 - race_time as f64;50 let c = race_dist as f64;5152 let x1 = ((0.0 - b) - (b.powf(2.0) - (4.0 * a * c)).sqrt()) / (2.0 * a);53 let x2 = ((0.0 - b) + (b.powf(2.0) - (4.0 * a * c)).sqrt()) / (2.0 * a);5455 let lower_bound = x1.ceil() as u32;56 let upper_bound = x2.floor() as u32 + 1;5758 upper_bound - lower_bound59}

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