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Code Issues Releases Wiki Activity

Optimise exactness criterion

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1. Cache some results between calls to next()
2. Compute the combinations of exact words more efficiently
This commit is contained in:
Loïc Lecrenier 2022-11-03 15:22:38 +01:00
parent a8defb585b
commit 32c6062e65
1 changed files with 478 additions and 60 deletions
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538
milli/src/search/criteria/exactness.rs
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@ -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<dyn Criterion + 't>,
query: Vec<ExactQueryPart>,
cache: Option<ExactWordsCombinationCache>,
}
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<ExactWordsCombinationCache>,
) -> Result<(RoaringBitmap, Option<State>)> {
use State::*;
match state {
@ -186,6 +190,7 @@ 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());
}
}
@ -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);
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.
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 = owned_cache.combinations.clone();
for candidates in candidates_array.iter_mut() {
*candidates &= &allowed_candidates;
}
*cache = Some(owned_cache);
let mut candidates_array = Vec::new();
let best_candidates = candidates_array.pop().unwrap();
// 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);
}
// 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();
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) => {
@ -317,13 +289,10 @@ fn attribute_start_with_docids(
Ok(attribute_candidates_array)
}
#[inline(never)]
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(),
}
roaring::MultiOps::intersection(rbs.into_iter())
}
#[derive(Debug, Clone)]
@ -363,3 +332,452 @@ impl ExactQueryPart {
Ok(part)
}
}
struct ExactWordsCombinationCache {
// index 0 is only 1 word
combinations: Vec<RoaringBitmap>,
}
fn compute_combinations(
ctx: &dyn Context,
query: &[ExactQueryPart],
) -> Result<ExactWordsCombinationCache> {
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<RoaringBitmap>) -> Vec<RoaringBitmap> {
let nbr_parts = bitmaps.len();
if nbr_parts == 1 {
let flattened_base_level = MultiOps::union(bitmaps.into_iter());
return vec![flattened_base_level];
}
let mut flattened_levels = vec![];
let mut last_level: BTreeMap<usize, RoaringBitmap> =
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.values());
flattened_levels.push(flattened_last_level);
last_level = new_level;
}
// Flatten the last level
let flattened_last_level = MultiOps::union(last_level.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]`.
///
/// ## Implementation
/// 1. We first create `Y0,Y1,...Yn` such that `Yi` contains all the elements that are contained in
/// **at least** `i+1` bitmaps among `b0,b1,...,bn`. This is done using `create_non_disjoint_combinations`.
///
/// 2. We create a set of "forbidden" elements, `Fn`, which is initialised to the empty set.
///
/// 3. We compute:
/// - `Xn = Yn - Fn`
/// - `Fn-1 = Fn | Xn`
fn create_disjoint_combinations(parts_candidates_array: Vec<RoaringBitmap>) -> Vec<RoaringBitmap> {
let non_disjoint_combinations = create_non_disjoint_combinations(parts_candidates_array);
let mut disjoint_combinations = vec![];
let mut forbidden = RoaringBitmap::new();
for mut combination in non_disjoint_combinations.into_iter().rev() {
combination -= &forbidden;
forbidden |= &combination;
disjoint_combinations.push(combination)
}
disjoint_combinations.reverse();
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::<usize>();
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<RoaringBitmap> = dividers
.iter()
.map(|&divider| {
(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, &dividers);
}
#[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<RoaringBitmap> = 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, &dividers);
}
}