Advent of Code 2023 Day 19

Day 19: Aplenty

https://adventofcode.com/2023/day/19

You arrive at the spot the machine part are forming a formidable pile. The elves are already very busy sorthing the parts, but could use your help.

Each part is rated on 4 categories:

x: Extremely cool looking
m: Musical (it makes a noise when you hit it)
a: Aerodynamic
s: Shiny

Then each part is sent through some workflows that ultimately decide whether to accept or reject the part.

Today’s input is a list of workflows, and parts. An example input looks like this:

px{a<2006:qkq,m>2090:A,rfg}
pv{a>1716:R,A}
lnx{m>1548:A,A}
rfg{s<537:gd,x>2440:R,A}
qs{s>3448:A,lnx}
qkq{x<1416:A,crn}
crn{x>2662:A,R}
in{s<1351:px,qqz}
qqz{s>2770:qs,m<1801:hdj,R}
gd{a>3333:R,R}
hdj{m>838:A,pv}

{x=787,m=2655,a=1222,s=2876}
{x=1679,m=44,a=2067,s=496}
{x=2036,m=264,a=79,s=2244}
{x=2461,m=1339,a=466,s=291}
{x=2127,m=1623,a=2188,s=1013}

Each named workflow has a list of rules.

If a part passes a rule, it moves to the destination that rule dictates (a new workflow, or a final accept/reject decision)
If a part fails a rule, it continues to the next rule in the current list of rules.

The rules are a pass/fail condition that checks if one of the xmas values is greater than, or smaller than a given number.

The last “rule” in a workflow has no condition, its destination always applies when that rule is reached.

An example workflow is ex{x>10:one,m<20:two,a>30:R,A}. It’s named ex, and has 4 rules.

Rule x>10:one: If the part’s x is more than 10, send the part to the workflow named one.
Rule m<20:two: Otherwise, if the part’s m is less than 20, send the part to the workflow named two.
Rule a>30:R: Otherwise, if the part’s a is more than 30, the part is immediately rejected (R).
Rule A: Otherwise, because no other rules matched the part, the part is immediately accepted (A).

An example part is {x=787,m=2655,a=1222,s=2876} It has these ratings:

x: Extremely cool looking: 787
m: Musical: 2655
a: Aerodynamic: 1222
s: Shiny: 2876

Each part starts at the workflow named in.

The example parts follow these paths through the workflows while being checked:

{x=787,m=2655,a=1222,s=2876}: in -> qqz -> qs -> lnx -> A
{x=1679,m=44,a=2067,s=496}: in -> px -> rfg -> gd -> R
{x=2036,m=264,a=79,s=2244}: in -> qqz -> hdj -> pv -> A
{x=2461,m=1339,a=466,s=291}: in -> px -> qkq -> crn -> R
{x=2127,m=1623,a=2188,s=1013}: in -> px -> rfg -> A

Parsing

Today was a heavy parsing day. I decided to put all data into neat data structures, preferring verbosity and clarity.

A part with the 4 ratings it has:

struct Part {
    x: usize,
    m: usize,
    a: usize,
    s: usize,
}

The final decision whether a part is accepted or rejected:

enum Final {
    Accept,
    Reject,
}

The destination a rule points to when it applies is either a new workflow, or a final decision:

enum Dest<'a> {
    WorkFlow(&'a str),
    Final(Final),
}

A rule in a workflow can either be a check, or if it’s the last one, only a new destination:

enum Rule<'a> {
    Check(Check<'a>),
    Last(Dest<'a>),
}

A ckeck tests if a single rating of a part is greater than or less than a given number:

struct Check<'a> {
    part: PartKind,
    operator: Operator,
    rhs: usize,
    dest: Dest<'a>,
}

To determine which ranking the check is for:

enum PartKind {
    X,
    M,
    A,
    S,
}

To determine which kind of comparison the check makes:

enum Operator {
    LessThan,
    GreaterThan,
}

The parsing is split into 2 parts, parsing a list of workflows, and parsing a list of parts:

fn parse(input: &str) -> (HashMap<&str, Vec<Rule>>, Vec<Part>) {
    let (workflows, parts) = input.split_once("\n\n").unwrap();
    (parse_workflows(workflows), parse_parts(parts))
}

Eack workflow is represented by an entry into a map, the key is the workflow name, and the value is the list of rules in that workflow. The trickiest part was making sure to correctly handle that last rule that has no check:

fn parse_workflows(s: &str) -> HashMap<&str, Vec<Rule>> {
    s.lines()
        .map(|line| {
            let line = line.strip_suffix("}").unwrap();
            let (name, rules) = line.split_once("{").unwrap();
            let (checks, final_dest) = rules.rsplit_once(",").unwrap();
            let last_dest = match final_dest {
                "A" => Dest::Final(Final::Accept),
                "R" => Dest::Final(Final::Reject),
                name => Dest::WorkFlow(name),
            };

            let rules = checks
                .split(",")
                .map(|check| {
                    let (check, dest) = check.split_once(":").unwrap();
                    let part = match &check[0..1] {
                        "x" => PartKind::X,
                        "m" => PartKind::M,
                        "a" => PartKind::A,
                        "s" => PartKind::S,
                        _ => panic!("Invalid part kind"),
                    };
                    let operator = match &check[1..2] {
                        "<" => Operator::LessThan,
                        ">" => Operator::GreaterThan,
                        _ => panic!("Invalid operator"),
                    };
                    let rhs: usize = check[2..].parse().unwrap();
                    let dest = match dest {
                        "A" => Dest::Final(Final::Accept),
                        "R" => Dest::Final(Final::Reject),
                        name => Dest::WorkFlow(name),
                    };

                    Check {
                        part,
                        operator,
                        rhs,
                        dest,
                    }
                })
                .map(|check| Rule::Check(check))
                .chain(std::iter::once(match last_dest {
                    Dest::WorkFlow(_) => Rule::Last(last_dest),
                    Dest::Final(_) => Rule::Last(last_dest),
                }))
                .collect();

            (name, rules)
        })
        .collect()
}

The parsing of the parts is a lot more straightforward. For each line, I start with a part that has rating 0 in every category. I loop through every key=value pair, and set the appropriate rating.

fn parse_parts(s: &str) -> Vec<Part> {
    s.lines()
        .map(|line| {
            let line = line.strip_prefix("{").unwrap().strip_suffix("}").unwrap();
            line.split(",").map(|s| s.split_once("=").unwrap()).fold(
                Part {
                    x: 0,
                    m: 0,
                    a: 0,
                    s: 0,
                },
                |mut part, (xmas, n)| {
                    let n = n.parse().unwrap();
                    match xmas {
                        "x" => part.x = n,
                        "m" => part.m = n,
                        "a" => part.a = n,
                        "s" => part.s = n,
                        _ => panic!("Inval xmas part id"),
                    };
                    part
                },
            )
        })
        .collect()
}

Part 1

The question asks what you get if you add together all of the rating numbers for all of the parts that ultimately get accepted?

The code I want to work towards loops over every part, determines whether or not it gets accepted, and sums up all xmas ratings.

pub fn part_1(input: &str) -> usize {
    let (workflows, parts) = parse(input);

    parts
        .iter()
        .filter(|part| part.accepted(&workflows))
        .map(|part| part.x + part.m + part.a + part.s)
        .sum()
}

Helpers

A method on Part to determine if a part passes a Check:

impl Part {
    fn passes_check(&self, check: &Check) -> bool {
        let n = match check.part {
            PartKind::X => self.x,
            PartKind::M => self.m,
            PartKind::A => self.a,
            PartKind::S => self.s,
        };

        match check.operator {
            Operator::LessThan if n < check.rhs => true,
            Operator::GreaterThan if n > check.rhs => true,
            _ => false,
        }

        // less readable IMO variant:
        // matches!(check.operator, Operator::LessThan if n < check.rhs)
        // || matches!(check.operator, Operator::GreaterThan if n > check.rhs)
    }
}

I use that helper in both of my solutions (I like the recursive one most). The meat of the solution is that accepted method on Part.

Option 1: iteratively

The accepted method uses an infinite loop that gets broken when a part receives a final decision.

Outside of the loop I track which workflow the part is currently in (it starts off as the workflow named in) In the loop I track the current location the part is at (it starts off as the desination of the workflow named in).

The infinite loop contains a loop that goes through every rule in the current workflow. When the part should go to a new destination, it breaks out of that for loop.

A new destination can happen:

if a check passed
if it was the final rule that has no condition

After breaking out of that for loop I check wich new destination the part went to:

If the new destination was a workflow, we update the current workflow and go through the outer (infinite) loop again.
If the new destination was a final decision, the whole function returns with that final decision.

impl Part {
    fn accepted(&self, workflows: &HashMap<&str, Vec<Rule>>) -> bool {
        let mut workflow = workflows.get("in").unwrap();
        loop {
            let mut dest = &Dest::WorkFlow("in");
            for rule in workflow {
                match rule {
                    Rule::Check(check) => {
                        if self.passes_check(check) {
                            dest = &check.dest;
                            break;
                        }
                    }
                    Rule::Last(last) => {
                        dest = last;
                        break;
                    }
                };
            }
            match dest {
                Dest::WorkFlow(name) => {
                    workflow = workflows.get(name).unwrap();
                }
                Dest::Final(accepted) => {
                    return *accepted == Final::Accept;
                }
            }
        }
    }
}

Option 2: recursively

A recursive function that takes in the current Part, the current Dest, and a map of all workflows.

If the dest is a final one, return the result from the function, this is the base case. If the dest is a workflow is when the recursing happens.

It loops through all rules of the workflow at the current destination.

It then returns the result of following that rule. (if it passes, recurse with the new destination, if it fails, move on to the next rule in the workflow by advancing the for loop)

impl Part {
    fn accepted(&self, dest: &Dest, workflows: &HashMap<&str, Vec<Rule>>) -> bool {
        match dest {
            Dest::Final(end) => *end == Final::Accept,
            Dest::WorkFlow(name) => {
                for rule in workflows.get(name).unwrap() {
                    match rule {
                        Rule::Check(check) => {
                            if self.passes_check(check) {
                                return self.accepted(&check.dest, workflows);
                            }
                        }
                        Rule::Last(dest) => return self.accepted(dest, workflows),
                    }
                }
                panic!("Could not determine if part is accepted")
            }
        }
    }
}

Code

Depending on whether or not you choose the recursive solution, the way you call the accepted helper on a part slightly changes. With the recursive version, you have to pass in the starting destination.

pub fn part_1(input: &str) -> usize {
    let (workflows, parts) = parse(input);

    parts
        .iter()
        // recursive version
        .filter(|part| part.accepted(&Dest::WorkFlow("in"), &workflows))
        // non-recursive version
        // .filter(|part| part.accepted(&workflows))
        .map(|part| part.x + part.m + part.a + part.s)
        .sum()
}

Part 2

The sorting still isn’t going quick enough, time to change strategies.

The elves want to figure out which combinations of ratings will be accepted or rejected.

Each of the 4 ratings (x, m, a, s) ranges from 1 up to, and including 4000.

In the example 167409079868000 combinations of ratings will be accepted.

The question asks how many distinct combinations of ratings will be accepted by the workflows?

Only consider the workflows, the list of individual part ratings is no longer relevant.

I represented all possible ranges for a part as a PartRange. A PartRange has 4 ranges, 1 for each rating:

struct PartRange {
    x: RangeInclusive<usize>,
    m: RangeInclusive<usize>,
    a: RangeInclusive<usize>,
    s: RangeInclusive<usize>,
}

The plan is to start with a single PartRange with ranges that go from 1 to 4000 in each category. Then apply the workflow named "in", and sum up all the distinct ranges that lead to a final accept decision.

This is the code I want to work towards, naming the main helper accepted again. Only this time, it does something different.

pub fn part_2(input: &str) -> usize {
    let (workflows, _) = input.split_once("\n\n").unwrap();
    let workflows = parse_workflows(workflows);

    let valid_ranges = PartRange {
        x: 1..=4_000,
        m: 1..=4_000,
        a: 1..=4_000,
        s: 1..=4_000,
    }
    .accepted(&Dest::WorkFlow("in"), &workflows);

    valid_ranges.into_iter().map(|range| range.combos()).sum()
}

Helpers

A the combos method that takes a PartRange and returns the amount of distinct combinations it represents. For every rating category, it takes the end of it’s range, subtracts the start, and adds 1 because that range was inclusive. Then it multiplies all those possibilities.

In math this is called permutations. Like for a 4 digit number the amount of permutations is 10 * 10 * 10 * 10, for 10 options per digit.

impl PartRange {
    fn combos(&self) -> usize {
        (self.x.end() - self.x.start() + 1)
            * (self.m.end() - self.m.start() + 1)
            * (self.a.end() - self.a.start() + 1)
            * (self.s.end() - self.s.start() + 1)
    }
}

A helper on PartRange that determines which relevant range passes a check, and which range fails a check.

Remember, a check looks at 1 specific range, either x, m, a, or s.

There are 3 different options:

The entire range passes a check
The entire range fails a check
The range is split in 2, a failing range, and a passing range

I represented these 3 options as an enum in code:

enum CheckedRange {
    FullPass,
    FullFail,
    Split { pass: PartRange, fail: PartRange },
}

The helper returns one of these three options.

Inside the method, it first extracts the range the check applies to. It stores the start and end of that range (start and end). It stores the number the check applies (called rhs).

Depending on the order of these 3 variables, and the operator (greater than or lessthan), the range falls in one of those 3 variants.

There are 3 different possible orderings of start, end, and rhs. When you order those 3 numbers from smallest to largest (start is always smaller than end):

start - end - rhs
rhs - start - end
start - rhs - end

Each of these options has 2 possible operators, greaterthan, or lessthan.

Covering every possibility, each one leads to one of those 3 CheckedRange variants. The ones where a range totally fails, or totally passes are not that interesting.

In the cases where a range should be split, 2 entirely new ranges are constructed from the original range:

A passing one
A failing one

impl PartRange {
    fn passes_check(&self, check: &Check) -> CheckedRange {
        let range = match check.part {
            PartKind::X => &self.x,
            PartKind::M => &self.m,
            PartKind::A => &self.a,
            PartKind::S => &self.s,
        };
        let start = *range.start();
        let end = *range.end();
        let rhs = check.rhs;

        match check.operator {
            // rhs -- start -- end
            Operator::LessThan if rhs <= start => CheckedRange::FullFail,
            Operator::GreaterThan if start > rhs => CheckedRange::FullPass,
            // start -- end -- rhs
            Operator::LessThan if end < rhs => CheckedRange::FullPass,
            Operator::GreaterThan if end <= rhs => CheckedRange::FullFail,
            // start -- rhs -- end
            Operator::LessThan => {
                CheckedRange::Split {
                    // passing: start..=rhs-1
                    pass: self.with_xmas(&check.part, start..=rhs - 1),
                    // failing: rhs..=end
                    fail: self.with_xmas(&check.part, rhs..=end),
                }
            }
            Operator::GreaterThan => {
                CheckedRange::Split {
                    // passing: rhs+1..=end
                    pass: self.with_xmas(&check.part, rhs + 1..=end),
                    // failing: start..=rhs
                    fail: self.with_xmas(&check.part, start..=rhs),
                }
            }
        }
    }
}

This uses a different helper that’s only there as convenience for me to make a new PartRange, but replace one of the x, m, a, s ranges with a new one.

impl PartRange {
    fn with_xmas(&self, kind: &PartKind, range: RangeInclusive<usize>) -> Self {
        let mut res = self.clone();
        match kind {
            PartKind::X => res.x = range,
            PartKind::M => res.m = range,
            PartKind::A => res.a = range,
            PartKind::S => res.s = range,
        };
        res
    }
}

Now the meat of the problem, the helper that returns a list of PartRanges that lead to a final accept decision. Again, it’s a recursive function that takes in the current destination.

If that destination is a final decision, the result is the entire range if it’s accepted, or nothing if it’s rejected. This is the base case of the recursion, eventually every PartRange is either accepted, or rejected.

If that destination is a workflow, a similar logic to part1 happens. I keep track of the current PartRange, and a list of all PartRanges in this workflow that eventually lead to an accept.

Then I loop through all rules in the workflow.

If a check passes for the full current range, I recurse to it’s destination and add the result to that list of valid PartRanges.
If a check fails for the full current range, I do nothing and move on to the next rule in the workflow.
If a check splits a range, I recurse with the passing part, and set the current PartRange to the failing part before moving on to the next rule in this workflow. (If I don’t do this, I’d never reach the next rule in a workflow, but I would have passed the check that just happened)

impl PartRange {
    fn accepted(&self, dest: &Dest, workflows: &HashMap<&str, Vec<Rule>>) -> Vec<Self> {
        match dest {
            Dest::Final(end) => match end {
                Final::Accept => vec![self.clone()],
                Final::Reject => vec![],
            },
            Dest::WorkFlow(name) => {
                // keep track of a valid range inside this workflow
                let mut curr_range = self.clone();
                // keep track of all ranges that lead to a final accept
                let mut valid_ranges = Vec::new();

                for rule in workflows.get(name).unwrap() {
                    match rule {
                        Rule::Check(check) => {
                            match curr_range.passes_check(check) {
                                CheckedRange::FullPass => {
                                    let passing = curr_range.accepted(&check.dest, workflows);
                                    valid_ranges.extend(passing);
                                }
                                CheckedRange::FullFail => (),
                                CheckedRange::Split { pass, fail } => {
                                    // move onto new destination with passing range
                                    let passing = pass.accepted(&check.dest, workflows);
                                    valid_ranges.extend(passing);
                                    // move onto next check in this workflow with failing range
                                    curr_range = fail;
                                }
                            }
                        }
                        Rule::Last(dest) => {
                            let passing = curr_range.accepted(dest, workflows);
                            valid_ranges.extend(passing);
                        }
                    }
                }

                valid_ranges
            }
        }
    }
}

But it’s not necessary to keep track of all the PartRanges that eventually pass. More efficient would be to immediately calculate the distinct combinations of that PartRange and add it to a sum.

So here is the same helper, only this time, it returns that sum instead of a list of PartRange. I also rewrote the for loop as a fold. An operation that’s called reduce in many languages. It takes a list of something, and condenses it down into a single thing.

Inside that fold the accumulator (the thing that’s reused every loop and ultimately returned) has 2 parts:

The current PartRange
The sum so far

When it’s done, the thing that interests me is the final value of the sum.

impl PartRange {
    fn accepted(&self, dest: &Dest, workflows: &HashMap<&str, Vec<Rule>>) -> usize {
        match dest {
            Dest::Final(end) => match end {
                Final::Accept => self.combos(),
                Final::Reject => 0,
            },
            Dest::WorkFlow(name) => {
                workflows
                    .get(name)
                    .unwrap()
                    .iter()
                    // keep track of a valid range inside this workflow
                    // keep track of the sum of all range combos that lead to an accept
                    .fold((self.clone(), 0), |(mut curr, sum), rule| {
                        let accepted = match rule {
                            Rule::Check(check) => {
                                match curr.passes_check(check) {
                                    CheckedRange::FullFail => 0,
                                    CheckedRange::FullPass => curr.accepted(&check.dest, workflows),
                                    CheckedRange::Split { pass, fail } => {
                                        // move onto next check in this workflow with failing range
                                        curr = fail;
                                        // count accepted combos with passing range
                                        pass.accepted(&check.dest, workflows)
                                    }
                                }
                            }
                            Rule::Last(dest) => curr.accepted(dest, workflows),
                        };

                        (curr, sum + accepted)
                    })
                    .1
            }
        }
    }
}

Code

The variant that does not keep track of all passing PartRanges:

pub fn part_2(input: &str) -> usize {
    let (workflows, _) = input.split_once("\n\n").unwrap();
    let workflows = parse_workflows(workflows);

    PartRange {
        x: 1..=4_000,
        m: 1..=4_000,
        a: 1..=4_000,
        s: 1..=4_000,
    }
    .accepted(&Dest::WorkFlow("in"), &workflows)
}

Final code

use std::{collections::HashMap, ops::RangeInclusive};

enum Rule<'a> {
    Check(Check<'a>),
    Last(Dest<'a>),
}

#[derive(PartialEq, Eq)]
enum Final {
    Accept,
    Reject,
}

struct Check<'a> {
    part: PartKind,
    operator: Operator,
    rhs: usize,
    dest: Dest<'a>,
}

enum Dest<'a> {
    WorkFlow(&'a str),
    Final(Final),
}

enum Operator {
    LessThan,
    GreaterThan,
}

enum PartKind {
    X,
    M,
    A,
    S,
}

struct Part {
    x: usize,
    m: usize,
    a: usize,
    s: usize,
}

#[derive(Clone)]
struct PartRange {
    x: RangeInclusive<usize>,
    m: RangeInclusive<usize>,
    a: RangeInclusive<usize>,
    s: RangeInclusive<usize>,
}

#[derive(Clone)]
enum CheckedRange {
    FullPass,
    FullFail,
    Split { pass: PartRange, fail: PartRange },
}

impl Part {
    fn passes_check(&self, check: &Check) -> bool {
        let n = match check.part {
            PartKind::X => self.x,
            PartKind::M => self.m,
            PartKind::A => self.a,
            PartKind::S => self.s,
        };

        match check.operator {
            Operator::LessThan if n < check.rhs => true,
            Operator::GreaterThan if n > check.rhs => true,
            _ => false,
        }
    }

    fn accepted(&self, dest: &Dest, workflows: &HashMap<&str, Vec<Rule>>) -> bool {
        match dest {
            Dest::Final(end) => *end == Final::Accept,
            Dest::WorkFlow(name) => {
                for rule in workflows.get(name).unwrap() {
                    match rule {
                        Rule::Check(check) => {
                            if self.passes_check(check) {
                                return self.accepted(&check.dest, workflows);
                            }
                        }
                        Rule::Last(dest) => return self.accepted(dest, workflows),
                    }
                }
                panic!("Could not determine if part is accepted")
            }
        }
    }
}

fn parse_workflows(s: &str) -> HashMap<&str, Vec<Rule>> {
    s.lines()
        .map(|line| {
            let line = line.strip_suffix("}").unwrap();
            let (name, rules) = line.split_once("{").unwrap();
            let (checks, final_dest) = rules.rsplit_once(",").unwrap();
            let last_dest = match final_dest {
                "A" => Dest::Final(Final::Accept),
                "R" => Dest::Final(Final::Reject),
                name => Dest::WorkFlow(name),
            };

            let rules = checks
                .split(",")
                .map(|check| {
                    let (check, dest) = check.split_once(":").unwrap();
                    let part = match &check[0..1] {
                        "x" => PartKind::X,
                        "m" => PartKind::M,
                        "a" => PartKind::A,
                        "s" => PartKind::S,
                        _ => panic!("Invalid part kind"),
                    };
                    let operator = match &check[1..2] {
                        "<" => Operator::LessThan,
                        ">" => Operator::GreaterThan,
                        _ => panic!("Invalid operator"),
                    };
                    let rhs: usize = check[2..].parse().unwrap();
                    let dest = match dest {
                        "A" => Dest::Final(Final::Accept),
                        "R" => Dest::Final(Final::Reject),
                        name => Dest::WorkFlow(name),
                    };

                    Check {
                        part,
                        operator,
                        rhs,
                        dest,
                    }
                })
                .map(|check| Rule::Check(check))
                .chain(std::iter::once(match last_dest {
                    Dest::WorkFlow(_) => Rule::Last(last_dest),
                    Dest::Final(_) => Rule::Last(last_dest),
                }))
                .collect();

            (name, rules)
        })
        .collect()
}

fn parse_parts(s: &str) -> Vec<Part> {
    s.lines()
        .map(|line| {
            let line = line.strip_prefix("{").unwrap().strip_suffix("}").unwrap();
            line.split(",").map(|s| s.split_once("=").unwrap()).fold(
                Part {
                    x: 0,
                    m: 0,
                    a: 0,
                    s: 0,
                },
                |mut part, (xmas, n)| {
                    let n = n.parse().unwrap();
                    match xmas {
                        "x" => part.x = n,
                        "m" => part.m = n,
                        "a" => part.a = n,
                        "s" => part.s = n,
                        _ => panic!("Inval xmas part id"),
                    };
                    part
                },
            )
        })
        .collect()
}

fn parse(input: &str) -> (HashMap<&str, Vec<Rule>>, Vec<Part>) {
    let (workflows, parts) = input.split_once("\n\n").unwrap();
    (parse_workflows(workflows), parse_parts(parts))
}

pub fn part_1(input: &str) -> usize {
    let (workflows, parts) = parse(input);

    parts
        .iter()
        .filter(|part| part.accepted(&Dest::WorkFlow("in"), &workflows))
        .map(|part| part.x + part.m + part.a + part.s)
        .sum()
}

impl PartRange {
    fn combos(&self) -> usize {
        (self.x.end() - self.x.start() + 1)
            * (self.m.end() - self.m.start() + 1)
            * (self.a.end() - self.a.start() + 1)
            * (self.s.end() - self.s.start() + 1)
    }

    fn with_xmas(&self, kind: &PartKind, range: RangeInclusive<usize>) -> Self {
        let mut res = self.clone();
        match kind {
            PartKind::X => res.x = range,
            PartKind::M => res.m = range,
            PartKind::A => res.a = range,
            PartKind::S => res.s = range,
        };
        res
    }

    fn passes_check(&self, check: &Check) -> CheckedRange {
        let range = match check.part {
            PartKind::X => &self.x,
            PartKind::M => &self.m,
            PartKind::A => &self.a,
            PartKind::S => &self.s,
        };
        let start = *range.start();
        let end = *range.end();
        let rhs = check.rhs;

        match check.operator {
            // rhs -- start -- end
            Operator::LessThan if rhs <= start => CheckedRange::FullFail,
            Operator::GreaterThan if start > rhs => CheckedRange::FullPass,
            // start -- end -- rhs
            Operator::LessThan if end < rhs => CheckedRange::FullPass,
            Operator::GreaterThan if end <= rhs => CheckedRange::FullFail,
            // start -- rhs -- end
            Operator::LessThan => {
                CheckedRange::Split {
                    // passing: start..=rhs-1
                    pass: self.with_xmas(&check.part, start..=rhs - 1),
                    // failing: rhs..=end
                    fail: self.with_xmas(&check.part, rhs..=end),
                }
            }
            Operator::GreaterThan => {
                CheckedRange::Split {
                    // passing: rhs+1..=end
                    pass: self.with_xmas(&check.part, rhs + 1..=end),
                    // failing: start..=rhs
                    fail: self.with_xmas(&check.part, start..=rhs),
                }
            }
        }
    }

    fn accepted(&self, dest: &Dest, workflows: &HashMap<&str, Vec<Rule>>) -> usize {
        match dest {
            Dest::Final(end) => match end {
                Final::Accept => self.combos(),
                Final::Reject => 0,
            },
            Dest::WorkFlow(name) => {
                workflows
                    .get(name)
                    .unwrap()
                    .iter()
                    // keep track of a valid range inside this workflow
                    // keep track of the sum of all range combos that lead to an accept
                    .fold((self.clone(), 0), |(mut curr, sum), rule| {
                        let accepted = match rule {
                            Rule::Check(check) => {
                                match curr.passes_check(check) {
                                    CheckedRange::FullFail => 0,
                                    CheckedRange::FullPass => curr.accepted(&check.dest, workflows),
                                    CheckedRange::Split { pass, fail } => {
                                        // move onto next check in this workflow with failing range
                                        curr = fail;
                                        // count accepted combos with passing range
                                        pass.accepted(&check.dest, workflows)
                                    }
                                }
                            }
                            Rule::Last(dest) => curr.accepted(dest, workflows),
                        };

                        (curr, sum + accepted)
                    })
                    .1
            }
        }
    }
}

pub fn part_2(input: &str) -> usize {
    let (workflows, _) = input.split_once("\n\n").unwrap();
    let workflows = parse_workflows(workflows);

    PartRange {
        x: 1..=4_000,
        m: 1..=4_000,
        a: 1..=4_000,
        s: 1..=4_000,
    }
    .accepted(&Dest::WorkFlow("in"), &workflows)
}

Date

Tagged

Part of series

Older post

Newer post

Advent of Code 2023 Day 19

Day 19: Aplenty

Parsing

Part 1

Helpers

Option 1: iteratively

Option 2: recursively

Code

Part 2

Helpers

Code

Final code