Stefan Müller
258 lines
8.0 KiB
Rust
258 lines
8.0 KiB
Rust
use crate::solvers::Solver;
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use primes::{PrimeSet, Sieve};
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use std::collections::HashMap;
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use std::io::BufRead;
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pub struct GiftShop {}
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impl GiftShop {
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const RANGES_SPLIT_CHAR: char = ',';
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}
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impl Solver for GiftShop {
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const PUZZLE_INDEX: u8 = 2;
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const PUZZLE_NAME: &'static str = "Gift Shop";
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fn process_data<R: BufRead>(&self, reader: R) -> (u64, u64) {
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// Cache of part configuration data for number of digits.
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let mut cache = Cache::new();
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let mut result = (0, 0);
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for line in reader.lines().map_while(Result::ok) {
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let ranges = line.split(Self::RANGES_SPLIT_CHAR);
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for range in ranges {
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for range in Range::from_str(range) {
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let invalid_id_sums = range.sum_invalid_ids(&mut cache);
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result.0 += invalid_id_sums.0;
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result.1 += invalid_id_sums.1;
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}
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}
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}
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result
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}
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}
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struct Range {
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first: u64,
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last: u64,
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digits: u32,
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}
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impl Range {
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const SPLIT_CHAR: char = '-';
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// Returns a vector of Range from a string, such that each element describes an interval of
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// integers with the same number of digits (base 10), and the intervals combined describe the
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// full range.
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fn from_str(s: &str) -> Vec<Self> {
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// Parses first and last IDs from range string.
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let ids: Vec<u64> = s
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.split(Self::SPLIT_CHAR)
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.map(|s| {
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s.parse()
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.expect("could not parse id range, must be integers")
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})
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.collect();
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assert_eq!(ids.len(), 2, "could not parse id range, must be two values");
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// Calculates the logs of first and last IDs and checks the size of the range.
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let (a_log, b_log) = (ids[0].ilog10(), ids[1].ilog10());
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assert!(b_log < a_log + 2, "id range is unexpectedly large");
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if a_log != 0 {
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if a_log == b_log {
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vec![Range {
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first: ids[0],
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last: ids[1],
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digits: a_log + 1,
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}]
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} else {
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vec![
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// Last ID becomes the largest ID with a number of digits equal to 'a_log + 1'.
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Range {
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first: ids[0],
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last: 10_u64.pow(b_log) - 1,
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digits: b_log,
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},
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// First ID becomes the smallest ID with a number of digits equal to 'a_log + 2'.
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Range {
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first: 10_u64.pow(b_log),
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last: ids[1],
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digits: b_log + 1,
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},
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]
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}
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} else {
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// There are no invalid IDs with one digit.
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if a_log == b_log {
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vec![]
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} else {
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vec![Range {
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first: 10,
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last: ids[1],
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digits: 2,
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}]
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}
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}
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}
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// Calculates the sum of invalid IDs contained in this Range. The first number in the returned
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// tuple is the sum of invalid IDs made from some sequence of digits repeated exactly twice,
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// while the second number results from considering sequences repeated twice or more.
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fn sum_invalid_ids(&self, cache: &mut Cache) -> (u64, u64) {
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let parts_configs = cache.entry(self.digits);
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// Determines sum of invalid IDs.
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let mut result = (0, 0);
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let mut duplicate_correction = 0;
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for config in parts_configs {
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let invalid_id_sum = self.sum_invalid_ids_fixed_parts(&config);
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if config.parts == 2 {
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result.0 += invalid_id_sum;
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}
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result.1 += invalid_id_sum;
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if config.parts == self.digits {
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duplicate_correction = invalid_id_sum;
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}
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}
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// This correction ensures that invalid IDs that are composed of a repetition of a single
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// digit, e.g. '111111' are counted only once.
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result.1 -= duplicate_correction * (parts_configs.len() as u64 - 1);
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result
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}
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// Calculates the sum of invalid IDs contained in this Range made from a fixed, given number of
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// repetitions of a sequence of digits.
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fn sum_invalid_ids_fixed_parts(&self, config: &PartsConfig) -> u64 {
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let mut sum = 0;
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let first_left = self.first / config.base;
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let last_left = self.last / config.base;
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let first_right = self.first % config.base;
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let last_right = self.last % config.base;
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// Checks, for a given range 'ABC...-DEF...', whether invalid ID 'AAA...' is in the range.
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let target_right = first_left * config.part_base_repeat;
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if target_right >= first_right && (first_left < last_left || target_right <= last_right) {
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sum += first_left;
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}
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// Calculates the sum of the in-between invalid IDs directly without loop, but we need to
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// explicitly check whether there are any values.
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if first_left + 1 < last_left {
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sum += (first_left + last_left) * (last_left - first_left - 1) / 2;
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}
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// Checks, for a given range 'ABC...-DEF...', whether invalid ID 'DDD...' is in the range.
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let target_right = last_left * config.part_base_repeat;
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if first_left != last_left && target_right <= last_right {
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sum += last_left;
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}
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sum * (config.base + config.part_base_repeat)
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}
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}
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struct Cache {
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map: HashMap<u32, Vec<PartsConfig>>,
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primes: Sieve,
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}
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impl Cache {
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fn new() -> Self {
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Cache {
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map: HashMap::new(),
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primes: Sieve::new(),
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}
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}
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// Gets cached or inserts new parts configurations for number of digits.
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fn entry(&mut self, digits: u32) -> &Vec<PartsConfig> {
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self.map
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.entry(digits)
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.or_insert_with(|| Self::build_cache_entry(digits, &mut self.primes))
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}
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fn build_cache_entry(digits: u32, primes: &mut Sieve) -> Vec<PartsConfig> {
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let mut result = Vec::new();
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result.push(PartsConfig::new(digits, digits));
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let max = digits / 2;
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for i in primes.iter().take_while(|&p| p <= u64::from(max)) {
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let i = u32::try_from(i).unwrap();
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if digits % i == 0 {
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result.push(PartsConfig::new(digits, i));
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}
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}
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result
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}
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}
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struct PartsConfig {
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parts: u32,
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base: u64,
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part_base_repeat: u64,
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}
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impl PartsConfig {
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fn new(digits: u32, parts: u32) -> Self {
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let part_digits = digits / parts;
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PartsConfig {
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parts,
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base: 10_u64.pow(digits - part_digits),
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part_base_repeat: Self::repeat_base(part_digits, parts - 1),
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}
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}
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fn repeat_base(part_digits: u32, repeat: u32) -> u64 {
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let base = 10_u64.pow(part_digits);
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let mut result = 1;
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for _ in 1..repeat {
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result = result * base + 1;
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}
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result
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn part1() {
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test_fixed_parts(11, 22, 2, 2, 33);
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test_fixed_parts(11, 21, 2, 2, 11);
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test_fixed_parts(12, 22, 2, 2, 22);
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test_fixed_parts(12, 32, 2, 2, 22);
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}
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#[test]
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fn part2() {
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test_fixed_parts(111, 333, 3, 3, 666);
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test_fixed_parts(565653, 565659, 6, 3, 565656);
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test_fixed_parts(56565300, 56565900, 8, 4, 56565656);
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}
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fn test_fixed_parts(first: u64, last: u64, digits: u32, parts: u32, expected: u64) {
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assert_eq!(
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Range {
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first,
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last,
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digits
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}
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.sum_invalid_ids_fixed_parts(&PartsConfig::new(digits, parts)),
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expected
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);
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}
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#[test]
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fn ignore_duplicates() {
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assert_eq!(
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Range {
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first: 222222,
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last: 222222,
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digits: 6
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}
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.sum_invalid_ids(&mut Cache::new()),
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(222222, 222222)
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);
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}
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}
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