dynamic programming
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name = "day12"
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version = "0.1.0"
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edition = "2021"
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default-run = "dp"
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# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
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[dependencies]
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[[bin]]
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name = "old"
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path= "src/main.rs"
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[[bin]]
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name = "dp"
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path= "src/main_dp.rs"
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243
day12/src/main_dp.rs
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243
day12/src/main_dp.rs
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use std::fs::read_to_string;
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use std::time::Instant;
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use std::iter;
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const PRINT_VALUES: bool = false;
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const PRINT_VISUALISATION: bool = false;
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// Counts all options by advancing through the spring layout from left to right, splitting at
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// possible uncertainities. Groups sequences of uncertain values and uses combinatorics.
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fn count_options_dp(layout: &[u8], broken_sequences: &[u32], sum_broken: u32) -> u64 {
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// Indexed with [a][b], storing results for computation, last a elements of layout
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// and last b elements of broken_sequences
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// u64::MAX marks values that will never be used and don't need to be computed
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let mut cache: Vec<Vec<u64>> = vec![vec![u64::MAX; broken_sequences.len() + 1]; layout.len() + 1];
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// For empty layout and empty broken sequences there's one option
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cache[0][0] = 1;
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cache[0][1..].iter_mut().for_each(|x| *x = 0);
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// Get the result
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let result = count_options_with_cache(layout, broken_sequences, sum_broken, &mut cache);
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// Visualise
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if PRINT_VISUALISATION {
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cache[layout.len()][broken_sequences.len()] = result;
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println!("{}", std::str::from_utf8(layout).unwrap());
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for j in 0..broken_sequences.len() + 1 {
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let row = cache.iter().map(|row| row[j]).collect::<Vec<_>>();
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println!("{} {:?}", row.iter().map(
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|&x| match x {
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0 => '0', u64::MAX => '.', _ => 'X'
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}).rev().collect::<String>(), &broken_sequences[broken_sequences.len() - j..]);
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}
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}
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if PRINT_VALUES {
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cache[layout.len()][broken_sequences.len()] = result;
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println!("{}", std::str::from_utf8(layout).unwrap());
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for j in 0..broken_sequences.len() + 1 {
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let row = cache.iter().map(|row| row[j]).collect::<Vec<_>>();
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println!("{:?} {:?}", row.iter().map(
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|&x| x as i64).rev().collect::<Vec<_>>(), &broken_sequences[broken_sequences.len() - j..]);
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}
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}
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result
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}
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fn use_or_update<F: Fn(&mut Vec<Vec<u64>>) -> u64>(cache: &mut Vec<Vec<u64>>, idx1: usize, idx2: usize, update_func: F) -> u64 {
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if cache[idx1][idx2] == u64::MAX {
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cache[idx1][idx2] = update_func(cache);
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}
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cache[idx1][idx2]
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}
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// Counts all options by advancing through the spring layout from left to right, splitting at
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// possible uncertainities. Groups sequences of uncertain values and uses combinatorics.
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fn count_options_with_cache(layout: &[u8], broken_sequences: &[u32], sum_broken: u32, cache: &mut Vec<Vec<u64>>) -> u64 {
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// Assuming sum_broken must be sum of broken_sequences
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// If no more broken need to be placed, the remaining are all unbroken
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if sum_broken == 0 {
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// If the remaining data contains a surely broken spring, the configuration is impossible
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if layout.contains(&b'#') {
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return 0;
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}
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// The rest are not broken, 1 option
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return 1;
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}
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// Go ahead in the layout to find place where a split of options is
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let mut split_position = 0;
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// Skip through all unbroken
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while split_position < layout.len() && layout[split_position] == b'.' {
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split_position += 1;
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}
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// Found no place to fit remaining broken springs, impossible
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if layout.len() - split_position < sum_broken as usize + broken_sequences.len() - 1 {
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return 0;
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}
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// Count amount of uncertain springs (can be zero)
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let mut num_uncertain: usize = 0;
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while split_position < layout.len() && layout[split_position] == b'?' {
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split_position += 1;
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num_uncertain += 1;
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}
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if split_position == layout.len() || layout[split_position] == b'.' {
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// Block of 1 or more uncertain springs followed by a unbroken spring
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let mut sum_options = 0;
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// Initially try assuming all the question marks will be unbroken
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if split_position < layout.len() {
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sum_options += use_or_update(
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cache, layout.len() - (split_position + 1), broken_sequences.len(),
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|cache|
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count_options_with_cache(&layout[split_position + 1..], broken_sequences, sum_broken, cache));
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}
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// Taking some number of elements from broken sequences
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let mut num_elems_taken = 1;
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let mut sum_elems_taken = broken_sequences[0];
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while num_elems_taken <= broken_sequences.len() && sum_elems_taken as usize + num_elems_taken - 1 <= num_uncertain {
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// If the split was done due to end of input, it's the length, otherwise advance by 1
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let corrected_split_position = std::cmp::min(split_position + 1, layout.len());
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// Multiplying the combination of elements before with recursive options after
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let pre_split_options = count_options_in_uncertain(num_uncertain as u64, sum_elems_taken as u64, num_elems_taken as u64);
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let post_split_options = use_or_update(
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cache, layout.len() - corrected_split_position, broken_sequences.len() - num_elems_taken,
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|cache| count_options_with_cache(
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&layout[corrected_split_position..],
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&broken_sequences[num_elems_taken..], sum_broken - sum_elems_taken, cache));
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// let post_split_options = count_options_with_cache(
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// &layout[corrected_split_position..],
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// &broken_sequences[num_elems_taken..], sum_broken - sum_elems_taken);
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sum_options += pre_split_options * post_split_options;
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// Prepare for the next iteration
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if num_elems_taken < broken_sequences.len() {
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sum_elems_taken += broken_sequences[num_elems_taken];
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}
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num_elems_taken += 1;
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}
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return sum_options;
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} else {
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// Block of 0 or more uncertain springs followed by at least one broken spring
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let mut sum_options = 0;
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// Count how many known broken elements there are after the uncertain
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let mut last_min_length = 0;
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while split_position < layout.len() && layout[split_position] == b'#' {
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split_position += 1;
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last_min_length += 1;
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}
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let extended_num_uncertain = num_uncertain + last_min_length;
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// Taking some number of elements from broken sequences
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let mut last_taken_index = 0;
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let mut sum_elems_taken_no_last: u32 = 0;
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while last_taken_index < broken_sequences.len() {
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// Length of last element that is taken, we need to fit it around the end of the region
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let last_length = broken_sequences[last_taken_index];
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// Putting the last elem at some offset, subtracted from split_position
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let mut last_offset = last_min_length;
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while last_offset <= last_length as usize && last_offset <= extended_num_uncertain {
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// If sum of taken elements with free spaces (last_taken_index) doesn't fit in the
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// uncertainity region
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if sum_elems_taken_no_last as usize + last_taken_index > extended_num_uncertain - last_offset {
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break;
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}
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// Multiplying the combination of elements before with recursive options after
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let pre_split_options;
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if extended_num_uncertain > last_offset + 1 {
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pre_split_options = count_options_in_uncertain(
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(extended_num_uncertain - last_offset - 1) as u64, sum_elems_taken_no_last as u64, last_taken_index as u64);
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} else {
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pre_split_options = 1;
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}
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let post_split_options = count_options_consume_sequence_with_cache(
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&layout[split_position - last_offset..], &broken_sequences[last_taken_index..],
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sum_broken - sum_elems_taken_no_last, cache);
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sum_options += pre_split_options * post_split_options;
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// Prepare for the next iteration
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last_offset += 1;
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}
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// Prepare for the next iteration
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sum_elems_taken_no_last += broken_sequences[last_taken_index];
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last_taken_index += 1;
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}
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return sum_options;
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}
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}
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fn choose(n: u64, k: u64) -> u64 {
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let mut prod = 1;
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let mut n_copy = n;
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for i in 1..=k {
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prod *= n_copy;
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n_copy -= 1;
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prod /= i;
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}
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prod
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}
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fn count_options_in_uncertain(length_uncertain: u64, sum_broken: u64, num_broken: u64) -> u64 {
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let slots = length_uncertain - sum_broken + 1;
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// slots choose num_broken
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if slots == 0 || num_broken == 0 {
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return 1;
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}
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choose(slots, num_broken)
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}
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// Helper function for count_options, assuming that a sequence of broken springs starts at
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// the beginning of the slice and that sum_broken is sum of broken_sequences and is not 0
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fn count_options_consume_sequence_with_cache(layout: &[u8], broken_sequences: &[u32], sum_broken: u32, cache: &mut Vec<Vec<u64>>) -> u64 {
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let mut sequence_position = 0usize;
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let target_position = sequence_position + broken_sequences[0] as usize;
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// If we'd run out of space trying to process this option, impossible
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if target_position > layout.len() {
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return 0;
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}
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// Go through all potentially broken elements
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while sequence_position < target_position && layout[sequence_position] != b'.' {
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sequence_position += 1;
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}
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// If found a surely unbroken element before end of sequence, impossible
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if sequence_position < target_position {
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return 0;
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}
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// If we aren't at the end of sequence
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if sequence_position < layout.len() {
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// If there's yet another surely broken spring, the sequence would be too long, impossible
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if layout[sequence_position] == b'#' {
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return 0;
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}
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// If there's a following unbroken element, advance through that because count_options
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// assumes with each call that we're starting from a fresh potential sequence
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sequence_position += 1;
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}
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// Call count_options recursively with advanced layout options and consumed one sequence
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use_or_update(
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cache, layout.len() - sequence_position, broken_sequences.len() - 1,
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|cache|
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count_options_with_cache(&layout[sequence_position..], &broken_sequences[1..],
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sum_broken - broken_sequences[0], cache))
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}
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fn main() {
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let time_start = Instant::now();
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let input_str = read_to_string("input.txt").unwrap();
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let time_start_no_io = Instant::now();
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let mut sum1 = 0u64;
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let mut sum2 = 0u64;
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for line in input_str.lines() {
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let mut split_whitespace = line.split_whitespace();
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let layout_str = split_whitespace.next().unwrap();
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let layout = layout_str.bytes().collect::<Vec<_>>();
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let layout2 = layout_str.bytes().chain(iter::once(b'?')).cycle().take(layout.len() * 5 + 4).collect::<Vec<_>>();
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let numbers = split_whitespace.next().unwrap()
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.split(',').map(|str| str.parse::<u32>().unwrap()).collect::<Vec<_>>();
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let numbers2 = numbers.iter().cycle().take(numbers.len() * 5).copied().collect::<Vec<_>>();
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let sum_numbers = numbers.iter().sum::<u32>();
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let sum_numbers2 = sum_numbers * 5;
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let options = count_options_dp(&layout, &numbers, sum_numbers) as u64;
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sum1 += options;
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sum2 += count_options_dp(&layout2, &numbers2, sum_numbers2) as u64;
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}
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let elapsed = time_start.elapsed().as_micros();
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let elapsed_no_io = time_start_no_io.elapsed().as_micros();
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println!("Time: {}us", elapsed);
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println!("Time without file i/o: {}us", elapsed_no_io);
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println!("Sum1: {}", sum1);
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println!("Sum2: {}", sum2);
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}
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