diff --git a/milli/src/search/criteria/exactness.rs b/milli/src/search/criteria/exactness.rs index b389a5d1e..d4a90576c 100644 --- a/milli/src/search/criteria/exactness.rs +++ b/milli/src/search/criteria/exactness.rs @@ -1,10 +1,10 @@ +use std::collections::btree_map::Entry; +use std::collections::BTreeMap; use std::convert::TryFrom; use std::mem::take; -use std::ops::BitOr; -use itertools::Itertools; use log::debug; -use roaring::RoaringBitmap; +use roaring::{MultiOps, RoaringBitmap}; use crate::search::criteria::{ resolve_phrase, resolve_query_tree, Context, Criterion, CriterionParameters, CriterionResult, @@ -20,6 +20,7 @@ pub struct Exactness<'t> { initial_candidates: InitialCandidates, parent: Box, query: Vec, + cache: Option, } impl<'t> Exactness<'t> { @@ -40,6 +41,7 @@ impl<'t> Exactness<'t> { initial_candidates: InitialCandidates::Estimated(RoaringBitmap::new()), parent, query, + cache: None, }) } } @@ -51,7 +53,6 @@ impl<'t> Criterion for Exactness<'t> { if let Some(state) = self.state.as_mut() { state.difference_with(params.excluded_candidates); } - loop { debug!("Exactness at state {:?}", self.state); @@ -60,9 +61,12 @@ impl<'t> Criterion for Exactness<'t> { // reset state self.state = None; self.query_tree = None; + // we don't need to reset the combinations cache since it only depends on + // the primitive query, which does not change } Some(state) => { - let (candidates, state) = resolve_state(self.ctx, take(state), &self.query)?; + let (candidates, state) = + resolve_state(self.ctx, take(state), &self.query, &mut self.cache)?; self.state = state; return Ok(Some(CriterionResult { @@ -166,12 +170,12 @@ impl Default for State { Self::Remainings(vec![]) } } - #[logging_timer::time("Exactness::{}")] fn resolve_state( ctx: &dyn Context, state: State, query: &[ExactQueryPart], + cache: &mut Option, ) -> Result<(RoaringBitmap, Option)> { use State::*; match state { @@ -186,7 +190,8 @@ fn resolve_state( let mut attribute_candidates_array = attribute_start_with_docids(ctx, id, query)?; attribute_candidates_array.push(attribute_allowed_docids); - candidates |= intersection_of(attribute_candidates_array.iter().collect()); + + candidates |= MultiOps::intersection(attribute_candidates_array); } } @@ -203,7 +208,7 @@ fn resolve_state( let attributes_ids = ctx.searchable_fields_ids()?; for id in attributes_ids { let attribute_candidates_array = attribute_start_with_docids(ctx, id, query)?; - candidates |= intersection_of(attribute_candidates_array.iter().collect()); + candidates |= MultiOps::intersection(attribute_candidates_array); } // only keep allowed candidates @@ -212,59 +217,26 @@ fn resolve_state( allowed_candidates -= &candidates; Ok((candidates, Some(ExactWords(allowed_candidates)))) } - ExactWords(mut allowed_candidates) => { - let number_of_part = query.len(); - let mut parts_candidates_array = Vec::with_capacity(number_of_part); - - for part in query { - let mut candidates = RoaringBitmap::new(); - use ExactQueryPart::*; - match part { - Synonyms(synonyms) => { - for synonym in synonyms { - if let Some(synonym_candidates) = ctx.word_docids(synonym)? { - candidates |= synonym_candidates; - } - } - } - // compute intersection on pair of words with a proximity of 0. - Phrase(phrase) => { - candidates |= resolve_phrase(ctx, phrase)?; - } - } - parts_candidates_array.push(candidates); - } - - let mut candidates_array = Vec::new(); - - // compute documents that contain all exact words. - let mut all_exact_candidates = intersection_of(parts_candidates_array.iter().collect()); - all_exact_candidates &= &allowed_candidates; - allowed_candidates -= &all_exact_candidates; - - // push the result of combinations of exact words grouped by the number of exact words contained by documents. - for c_count in (1..number_of_part).rev() { - let mut combinations_candidates = parts_candidates_array - .iter() - // create all `c_count` combinations of exact words - .combinations(c_count) - // intersect each word candidates in combinations - .map(intersection_of) - // union combinations of `c_count` exact words - .fold(RoaringBitmap::new(), RoaringBitmap::bitor); - // only keep allowed candidates - combinations_candidates &= &allowed_candidates; - // remove current candidates from allowed candidates - allowed_candidates -= &combinations_candidates; - candidates_array.push(combinations_candidates); + ExactWords(allowed_candidates) => { + // Retrieve the cache if it already exist, otherwise create it. + let owned_cache = if let Some(cache) = cache.take() { + cache + } else { + compute_combinations(ctx, query)? + }; + // The cache contains the sets of documents which contain exactly 1,2,3,.. exact words + // from the query. It cannot be empty. All the candidates in it are disjoint. + + let mut candidates_array = owned_cache.combinations.clone(); + for candidates in candidates_array.iter_mut() { + *candidates &= &allowed_candidates; } + *cache = Some(owned_cache); - // push remainings allowed candidates as the worst valid candidates - candidates_array.push(allowed_candidates); - // reverse the array to be able to pop candidates from the best to the worst. - candidates_array.reverse(); + let best_candidates = candidates_array.pop().unwrap(); - Ok((all_exact_candidates, Some(Remainings(candidates_array)))) + candidates_array.insert(0, allowed_candidates); + Ok((best_candidates, Some(Remainings(candidates_array)))) } // pop remainings candidates until the emptiness Remainings(mut candidates_array) => { @@ -317,15 +289,6 @@ fn attribute_start_with_docids( Ok(attribute_candidates_array) } -fn intersection_of(mut rbs: Vec<&RoaringBitmap>) -> RoaringBitmap { - rbs.sort_unstable_by_key(|rb| rb.len()); - let mut iter = rbs.into_iter(); - match iter.next() { - Some(first) => iter.fold(first.clone(), |acc, rb| acc & rb), - None => RoaringBitmap::new(), - } -} - #[derive(Debug, Clone)] pub enum ExactQueryPart { Phrase(Vec>), @@ -363,3 +326,441 @@ impl ExactQueryPart { Ok(part) } } + +struct ExactWordsCombinationCache { + // index 0 is only 1 word + combinations: Vec, +} + +fn compute_combinations( + ctx: &dyn Context, + query: &[ExactQueryPart], +) -> Result { + let number_of_part = query.len(); + let mut parts_candidates_array = Vec::with_capacity(number_of_part); + for part in query { + let mut candidates = RoaringBitmap::new(); + use ExactQueryPart::*; + match part { + Synonyms(synonyms) => { + for synonym in synonyms { + if let Some(synonym_candidates) = ctx.word_docids(synonym)? { + candidates |= synonym_candidates; + } + } + } + // compute intersection on pair of words with a proximity of 0. + Phrase(phrase) => { + candidates |= resolve_phrase(ctx, phrase)?; + } + } + parts_candidates_array.push(candidates); + } + let combinations = create_disjoint_combinations(parts_candidates_array); + + Ok(ExactWordsCombinationCache { combinations }) +} + +/// Given a list of bitmaps `b0,b1,...,bn` , compute the list of bitmaps `X0,X1,...,Xn` +/// such that `Xi` contains all the elements that are contained in **at least** `i+1` bitmaps among `b0,b1,...,bn`. +/// +/// The returned vector is guaranteed to be of length `n`. It is equal to `vec![X0, X1, ..., Xn]`. +/// +/// ## Implementation +/// +/// We do so by iteratively building a map containing the union of all the different ways to intersect `J` bitmaps among `b0,b1,...,bn`. +/// - The key of the map is the index `i` of the last bitmap in the intersections +/// - The value is the union of all the possible intersections of J bitmaps such that the last bitmap in the intersection is `bi` +/// +/// For example, with the bitmaps `b0,b1,b2,b3`, this map should look like this +/// ```text +/// Map 0: (first iteration, contains all the combinations of 1 bitmap) +/// // What follows are unions of intersection of bitmaps asscociated with the index of their last component +/// 0: [b0] +/// 1: [b1] +/// 2: [b2] +/// 3: [b3] +/// Map 1: (second iteration, combinations of 2 bitmaps) +/// 1: [b0&b1] +/// 2: [b0&b2 | b1&b2] +/// 3: [b0&b3 | b1&b3 | b2&b3] +/// Map 2: (third iteration, combinations of 3 bitmaps) +/// 2: [b0&b1&b2] +/// 3: [b0&b2&b3 | b1&b2&b3] +/// Map 3: (fourth iteration, combinations of 4 bitmaps) +/// 3: [b0&b1&b2&b3] +/// ``` +/// +/// These maps are built one by one from the content of the preceding map. +/// For example, to create Map 2, we look at each line of Map 1, for example: +/// ```text +/// 2: [b0&b2 | b1&b2] +/// ``` +/// And then for each i > 2, we compute `(b0&b2 | b1&b2) & bi = b0&b2&bi | b1&b2&bi` +/// and then add it the new map (Map 3) under the key `i` (if it is not empty): +/// ```text +/// 3: [b0&b2&b3 | b1&b2&b3] +/// 4: [b0&b2&b4 | b1&b2&b4] +/// 5: [b0&b2&b5 | b1&b2&b5] +/// etc. +/// ``` +/// We only keep two maps in memory at any one point. As soon as Map J is built, we flatten Map J-1 into +/// a single bitmap by taking the union of all of its values. This union gives us Xj-1. +/// +/// ## Memory Usage +/// This function is expected to be called on a maximum of 10 bitmaps. The worst case thus happens when +/// 10 identical large bitmaps are given. +/// +/// In the context of Meilisearch, let's imagine that we are given 10 bitmaps containing all +/// the document ids. If the dataset contains 16 million documents, then each bitmap will take +/// around 2MB of memory. +/// +/// When creating Map 3, we will have, in memory: +/// 1. The 10 original bitmaps (20MB) +/// 2. X0 : 2MB +/// 3. Map 1, containing 9 bitmaps: 18MB +/// 4. Map 2, containing 8 bitmaps: 16MB +/// 5. X1: 2MB +/// for a total of around 60MB of memory. This roughly represents the maximum memory usage of this function. +/// +/// ## Time complexity +/// Let N be the size of the given list of bitmaps and M the length of each individual bitmap. +/// +/// We need to create N new bitmaps. The most expensive one to create is the second one, where we need to +/// iterate over the N keys of Map 1, and for each of those keys `k_i`, we perform `N-k_i` bitmap unions. +/// Unioning two bitmaps is O(M), and we need to do it O(N^2) times. +/// +/// Therefore the time complexity is O(N^3 * M). +fn create_non_disjoint_combinations(bitmaps: Vec) -> Vec { + let nbr_parts = bitmaps.len(); + if nbr_parts == 1 { + return bitmaps; + } + let mut flattened_levels = vec![]; + let mut last_level: BTreeMap = + bitmaps.clone().into_iter().enumerate().collect(); + + for _ in 2..=nbr_parts { + let mut new_level = BTreeMap::new(); + for (last_part_index, base_combination) in last_level.iter() { + #[allow(clippy::needless_range_loop)] + for new_last_part_index in last_part_index + 1..nbr_parts { + let new_combination = base_combination & &bitmaps[new_last_part_index]; + if !new_combination.is_empty() { + match new_level.entry(new_last_part_index) { + Entry::Occupied(mut b) => { + *b.get_mut() |= new_combination; + } + Entry::Vacant(entry) => { + entry.insert(new_combination); + } + } + } + } + } + // Now flatten the last level to save memory + let flattened_last_level = MultiOps::union(last_level.into_values()); + flattened_levels.push(flattened_last_level); + last_level = new_level; + } + // Flatten the last level + let flattened_last_level = MultiOps::union(last_level.into_values()); + flattened_levels.push(flattened_last_level); + flattened_levels +} + +/// Given a list of bitmaps `b0,b1,...,bn` , compute the list of bitmaps `X0,X1,...,Xn` +/// such that `Xi` contains all the elements that are contained in **exactly** `i+1` bitmaps among `b0,b1,...,bn`. +/// +/// The returned vector is guaranteed to be of length `n`. It is equal to `vec![X0, X1, ..., Xn]`. +fn create_disjoint_combinations(parts_candidates_array: Vec) -> Vec { + let non_disjoint_combinations = create_non_disjoint_combinations(parts_candidates_array); + let mut disjoint_combinations = vec![]; + let mut combinations = non_disjoint_combinations.into_iter().peekable(); + while let Some(mut combination) = combinations.next() { + if let Some(forbidden) = combinations.peek() { + combination -= forbidden; + } + disjoint_combinations.push(combination) + } + + disjoint_combinations +} + +#[cfg(test)] +mod tests { + use big_s::S; + use roaring::RoaringBitmap; + + use crate::index::tests::TempIndex; + use crate::search::criteria::exactness::{ + create_disjoint_combinations, create_non_disjoint_combinations, + }; + use crate::snapshot_tests::display_bitmap; + use crate::SearchResult; + + #[test] + fn test_exact_words_subcriterion() { + let index = TempIndex::new(); + + index + .update_settings(|settings| { + settings.set_primary_key(S("id")); + settings.set_criteria(vec!["exactness".to_owned()]); + }) + .unwrap(); + + index + .add_documents(documents!([ + // not relevant + { "id": "0", "text": "cat good dog bad" }, + // 1 exact word + { "id": "1", "text": "they said: cats arebetter thandogs" }, + // 3 exact words + { "id": "2", "text": "they said: cats arebetter than dogs" }, + // 5 exact words + { "id": "3", "text": "they said: cats are better than dogs" }, + // attribute starts with the exact words + { "id": "4", "text": "cats are better than dogs except on Saturday" }, + // attribute equal to the exact words + { "id": "5", "text": "cats are better than dogs" }, + ])) + .unwrap(); + + let rtxn = index.read_txn().unwrap(); + + let SearchResult { matching_words: _, candidates: _, documents_ids } = + index.search(&rtxn).query("cats are better than dogs").execute().unwrap(); + + insta::assert_snapshot!(format!("{documents_ids:?}"), @"[5, 4, 3, 2, 1]"); + } + + fn print_combinations(rbs: &[RoaringBitmap]) -> String { + let mut s = String::new(); + for rb in rbs { + s.push_str(&format!("{}\n", &display_bitmap(rb))); + } + s + } + + // In these unit tests, the test bitmaps always contain all the multiple of a certain number. + // This makes it easy to check the validity of the results of `create_disjoint_combinations` by + // counting the number of dividers of elements in the returned bitmaps. + fn assert_correct_combinations(combinations: &[RoaringBitmap], dividers: &[u32]) { + for (i, set) in combinations.iter().enumerate() { + let expected_nbr_dividers = i + 1; + for el in set { + let nbr_dividers = dividers.iter().map(|d| usize::from(el % d == 0)).sum::(); + assert_eq!( + nbr_dividers, expected_nbr_dividers, + "{el} is divisible by {nbr_dividers} elements, not {expected_nbr_dividers}." + ); + } + } + } + + #[test] + fn compute_combinations_1() { + let b0: RoaringBitmap = (0..).into_iter().map(|x| 2 * x).take_while(|x| *x < 150).collect(); + + let parts_candidates = vec![b0]; + + let combinations = create_disjoint_combinations(parts_candidates); + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, ] + "###); + + assert_correct_combinations(&combinations, &[2]); + } + + #[test] + fn compute_combinations_2() { + let b0: RoaringBitmap = (0..).into_iter().map(|x| 2 * x).take_while(|x| *x < 150).collect(); + let b1: RoaringBitmap = (0..).into_iter().map(|x| 3 * x).take_while(|x| *x < 150).collect(); + + let parts_candidates = vec![b0, b1]; + + let combinations = create_disjoint_combinations(parts_candidates); + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [2, 3, 4, 8, 9, 10, 14, 15, 16, 20, 21, 22, 26, 27, 28, 32, 33, 34, 38, 39, 40, 44, 45, 46, 50, 51, 52, 56, 57, 58, 62, 63, 64, 68, 69, 70, 74, 75, 76, 80, 81, 82, 86, 87, 88, 92, 93, 94, 98, 99, 100, 104, 105, 106, 110, 111, 112, 116, 117, 118, 122, 123, 124, 128, 129, 130, 134, 135, 136, 140, 141, 142, 146, 147, 148, ] + [0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, ] + "###); + } + + #[test] + fn compute_combinations_4() { + let b0: RoaringBitmap = (0..).into_iter().map(|x| 2 * x).take_while(|x| *x < 150).collect(); + let b1: RoaringBitmap = (0..).into_iter().map(|x| 3 * x).take_while(|x| *x < 150).collect(); + let b2: RoaringBitmap = (0..).into_iter().map(|x| 5 * x).take_while(|x| *x < 150).collect(); + let b3: RoaringBitmap = (0..).into_iter().map(|x| 7 * x).take_while(|x| *x < 150).collect(); + + let parts_candidates = vec![b0, b1, b2, b3]; + + let combinations = create_disjoint_combinations(parts_candidates); + + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [2, 3, 4, 5, 7, 8, 9, 16, 22, 25, 26, 27, 32, 33, 34, 38, 39, 44, 46, 49, 51, 52, 55, 57, 58, 62, 64, 65, 68, 69, 74, 76, 77, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99, 104, 106, 111, 115, 116, 117, 118, 119, 122, 123, 124, 125, 128, 129, 133, 134, 136, 141, 142, 145, 146, 148, ] + [6, 10, 12, 14, 15, 18, 20, 21, 24, 28, 35, 36, 40, 45, 48, 50, 54, 56, 63, 66, 72, 75, 78, 80, 96, 98, 100, 102, 108, 110, 112, 114, 130, 132, 135, 138, 144, 147, ] + [30, 42, 60, 70, 84, 90, 105, 120, 126, 140, ] + [0, ] + "###); + + // But we also check it programmatically + assert_correct_combinations(&combinations, &[2, 3, 5, 7]); + } + #[test] + fn compute_combinations_4_with_empty_results_at_end() { + let b0: RoaringBitmap = (1..).into_iter().map(|x| 2 * x).take_while(|x| *x < 150).collect(); + let b1: RoaringBitmap = (1..).into_iter().map(|x| 3 * x).take_while(|x| *x < 150).collect(); + let b2: RoaringBitmap = (1..).into_iter().map(|x| 5 * x).take_while(|x| *x < 150).collect(); + let b3: RoaringBitmap = (1..).into_iter().map(|x| 7 * x).take_while(|x| *x < 150).collect(); + + let parts_candidates = vec![b0, b1, b2, b3]; + + let combinations = create_disjoint_combinations(parts_candidates); + + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [2, 3, 4, 5, 7, 8, 9, 16, 22, 25, 26, 27, 32, 33, 34, 38, 39, 44, 46, 49, 51, 52, 55, 57, 58, 62, 64, 65, 68, 69, 74, 76, 77, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99, 104, 106, 111, 115, 116, 117, 118, 119, 122, 123, 124, 125, 128, 129, 133, 134, 136, 141, 142, 145, 146, 148, ] + [6, 10, 12, 14, 15, 18, 20, 21, 24, 28, 35, 36, 40, 45, 48, 50, 54, 56, 63, 66, 72, 75, 78, 80, 96, 98, 100, 102, 108, 110, 112, 114, 130, 132, 135, 138, 144, 147, ] + [30, 42, 60, 70, 84, 90, 105, 120, 126, 140, ] + [] + "###); + + // But we also check it programmatically + assert_correct_combinations(&combinations, &[2, 3, 5, 7]); + } + + #[test] + fn compute_combinations_4_with_some_equal_bitmaps() { + let b0: RoaringBitmap = (0..).into_iter().map(|x| 2 * x).take_while(|x| *x < 150).collect(); + let b1: RoaringBitmap = (0..).into_iter().map(|x| 3 * x).take_while(|x| *x < 150).collect(); + let b2: RoaringBitmap = (0..).into_iter().map(|x| 5 * x).take_while(|x| *x < 150).collect(); + // b3 == b1 + let b3: RoaringBitmap = (0..).into_iter().map(|x| 3 * x).take_while(|x| *x < 150).collect(); + + let parts_candidates = vec![b0, b1, b2, b3]; + + let combinations = create_disjoint_combinations(parts_candidates); + + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [2, 4, 5, 8, 14, 16, 22, 25, 26, 28, 32, 34, 35, 38, 44, 46, 52, 55, 56, 58, 62, 64, 65, 68, 74, 76, 82, 85, 86, 88, 92, 94, 95, 98, 104, 106, 112, 115, 116, 118, 122, 124, 125, 128, 134, 136, 142, 145, 146, 148, ] + [3, 9, 10, 20, 21, 27, 33, 39, 40, 50, 51, 57, 63, 69, 70, 80, 81, 87, 93, 99, 100, 110, 111, 117, 123, 129, 130, 140, 141, 147, ] + [6, 12, 15, 18, 24, 36, 42, 45, 48, 54, 66, 72, 75, 78, 84, 96, 102, 105, 108, 114, 126, 132, 135, 138, 144, ] + [0, 30, 60, 90, 120, ] + "###); + + // But we also check it programmatically + assert_correct_combinations(&combinations, &[2, 3, 5, 3]); + } + + #[test] + fn compute_combinations_10() { + let dividers = [2, 3, 5, 7, 11, 6, 15, 35, 18, 14]; + let parts_candidates: Vec = dividers + .iter() + .map(|÷r| { + (0..).into_iter().map(|x| divider * x).take_while(|x| *x <= 210).collect() + }) + .collect(); + + let combinations = create_disjoint_combinations(parts_candidates); + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [2, 3, 4, 5, 7, 8, 9, 11, 16, 25, 26, 27, 32, 34, 38, 39, 46, 49, 51, 52, 57, 58, 62, 64, 65, 68, 69, 74, 76, 81, 82, 85, 86, 87, 91, 92, 93, 94, 95, 104, 106, 111, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 128, 129, 133, 134, 136, 141, 142, 143, 145, 146, 148, 152, 153, 155, 158, 159, 161, 164, 166, 171, 172, 177, 178, 183, 184, 185, 187, 188, 194, 201, 202, 203, 205, 206, 207, 208, 209, ] + [10, 20, 21, 22, 33, 40, 44, 50, 55, 63, 77, 80, 88, 99, 100, 130, 147, 160, 170, 176, 189, 190, 200, ] + [6, 12, 14, 15, 24, 28, 35, 45, 48, 56, 75, 78, 96, 98, 102, 110, 112, 114, 135, 138, 156, 174, 175, 182, 186, 192, 195, 196, 204, ] + [18, 36, 54, 66, 72, 108, 132, 144, 154, 162, 165, ] + [30, 42, 60, 70, 84, 105, 120, 140, 150, 168, 198, ] + [90, 126, 180, ] + [] + [210, ] + [] + [0, ] + "###); + + assert_correct_combinations(&combinations, ÷rs); + } + + #[test] + fn compute_combinations_30() { + let dividers: [u32; 30] = [ + 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, + 5, + ]; + let parts_candidates: Vec = dividers + .iter() + .map(|divider| { + (0..).into_iter().map(|x| divider * x).take_while(|x| *x <= 100).collect() + }) + .collect(); + + let combinations = create_non_disjoint_combinations(parts_candidates.clone()); + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, ] + [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, ] + [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, ] + [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, ] + [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, ] + [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, ] + [0, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, ] + [0, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, ] + [0, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, ] + [0, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, ] + [0, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, ] + [0, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100, ] + [0, 4, 6, 8, 10, 12, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 100, ] + [0, 4, 6, 8, 10, 12, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 100, ] + [0, 4, 6, 8, 10, 12, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 100, ] + [0, 4, 6, 8, 10, 12, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 100, ] + [0, 4, 6, 8, 10, 12, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 100, ] + [0, 4, 6, 8, 10, 12, 15, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 100, ] + [0, 12, 20, 24, 30, 36, 40, 48, 60, 72, 80, 84, 90, 96, 100, ] + [0, 12, 20, 24, 30, 36, 40, 48, 60, 72, 80, 84, 90, 96, 100, ] + [0, 12, 20, 24, 30, 36, 40, 48, 60, 72, 80, 84, 90, 96, 100, ] + [0, 12, 20, 24, 30, 36, 40, 48, 60, 72, 80, 84, 90, 96, 100, ] + [0, 12, 20, 24, 30, 36, 40, 48, 60, 72, 80, 84, 90, 96, 100, ] + [0, 12, 20, 24, 30, 36, 40, 48, 60, 72, 80, 84, 90, 96, 100, ] + [0, 60, ] + [0, 60, ] + [0, 60, ] + [0, 60, ] + [0, 60, ] + [0, 60, ] + "###); + + let combinations = create_disjoint_combinations(parts_candidates); + insta::assert_snapshot!(print_combinations(&combinations), @r###" + [] + [] + [] + [] + [] + [1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, ] + [] + [] + [] + [] + [] + [2, 3, 5, 9, 14, 21, 22, 25, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 63, 65, 69, 74, 81, 82, 85, 86, 87, 93, 94, 95, 98, 99, ] + [] + [] + [] + [] + [] + [4, 6, 8, 10, 15, 16, 18, 28, 32, 42, 44, 45, 50, 52, 54, 56, 64, 66, 68, 70, 75, 76, 78, 88, 92, ] + [] + [] + [] + [] + [] + [12, 20, 24, 30, 36, 40, 48, 72, 80, 84, 90, 96, 100, ] + [] + [] + [] + [] + [] + [0, 60, ] + "###); + + assert_correct_combinations(&combinations, ÷rs); + } +}