dynamic programming

day12/Cargo.toml

@@ -2,7 +2,16 @@
 name = "day12"
 version = "0.1.0"
 edition = "2021"
+default-run = "dp"
 
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
+
+[[bin]]
+name = "old"
+path= "src/main.rs"
+
+[[bin]]
+name = "dp"
+path= "src/main_dp.rs"

day12/src/main_dp.rs

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