Merge #2601

2601: Ease search result pagination r=Kerollmops a=ManyTheFish

# Summary
This PR is a prototype enhancing search results pagination (#2577)

# Todo

- [x] Update the API to return the number of pages and allow users to directly choose a page instead of computing an offset
- [x] Change computation of `total_pages` in order to have an exact count
  - [x] compute query tree exhaustively
  - [x] compute distinct exhaustively

# Small Documentation

## Default search query

**request**:
```sh
curl \
  -X POST 'http://localhost:7700/indexes/movies/search' \
  -H 'Content-Type: application/json' \
  --data-binary '{ "q": "botman" }'
```

**result**:
```json
{
  "hits":[...],
  "query":"botman",
  "processingTimeMs":5,
  "hitsPerPage":20,
  "page":1,
  "totalPages":4,
  "totalHits":66
}
```

## Search query with offset parameter

**request**:
```sh
curl \
  -X POST 'http://localhost:7700/indexes/movies/search' \
  -H 'Content-Type: application/json' \
  --data-binary '{ "q": "botman", "offset": 0 }'
```

**result**:
```json
{
  "hits":[...],
  "query":"botman",
  "processingTimeMs":3,
  "limit":20,
  "offset":0,
  "estimatedTotalHits":66
}
```

## Search query selecting page with page parameter

**request**:
```sh
curl \
  -X POST 'http://localhost:7700/indexes/movies/search' \
  -H 'Content-Type: application/json' \
  --data-binary '{ "q": "botman", "page": 2 }'
```

**result**:
```json
{
  "hits":[...],
  "query":"botman",
  "processingTimeMs":5,
  "hitsPerPage":20,
  "page":2,
  "totalPages":4,
  "totalHits":66
}
```

# Related

fixes #2577

## In charge of the feature

Core: `@ManyTheFish` 
Docs: `@guimachiavelli` 
Integration: `@bidoubiwa` 


Co-authored-by: ManyTheFish <many@meilisearch.com>

meilisearch-http/src/analytics/segment_analytics.rs

@@ -10,7 +10,7 @@ use http::header::CONTENT_TYPE;
 use meilisearch_auth::SearchRules;
 use meilisearch_lib::index::{
     SearchQuery, SearchResult, DEFAULT_CROP_LENGTH, DEFAULT_CROP_MARKER,
-    DEFAULT_HIGHLIGHT_POST_TAG, DEFAULT_HIGHLIGHT_PRE_TAG,
+    DEFAULT_HIGHLIGHT_POST_TAG, DEFAULT_HIGHLIGHT_PRE_TAG, DEFAULT_SEARCH_LIMIT,
 };
 use meilisearch_lib::index_controller::Stats;
 use meilisearch_lib::MeiliSearch;
@@ -373,6 +373,7 @@ pub struct SearchAggregator {
     // pagination
     max_limit: usize,
     max_offset: usize,
+    finite_pagination: usize,
 
     // formatting
     highlight_pre_tag: bool,
@@ -427,12 +428,20 @@ impl SearchAggregator {
             ret.max_terms_number = q.split_whitespace().count();
         }
 
+        if query.is_finite_pagination() {
+            let limit = query.hits_per_page.unwrap_or_else(DEFAULT_SEARCH_LIMIT);
+            ret.max_limit = limit;
+            ret.max_offset = query.page.unwrap_or(1).saturating_sub(1) * limit;
+            ret.finite_pagination = 1;
+        } else {
+            ret.max_limit = query.limit;
+            ret.max_offset = query.offset;
+            ret.finite_pagination = 0;
+        }
+
         ret.matching_strategy
             .insert(format!("{:?}", query.matching_strategy), 1);
 
-        ret.max_limit = query.limit;
-        ret.max_offset = query.offset.unwrap_or_default();
-
         ret.highlight_pre_tag = query.highlight_pre_tag != DEFAULT_HIGHLIGHT_PRE_TAG();
         ret.highlight_post_tag = query.highlight_post_tag != DEFAULT_HIGHLIGHT_POST_TAG();
         ret.crop_marker = query.crop_marker != DEFAULT_CROP_MARKER();
@@ -491,6 +500,7 @@ impl SearchAggregator {
         // pagination
         self.max_limit = self.max_limit.max(other.max_limit);
         self.max_offset = self.max_offset.max(other.max_offset);
+        self.finite_pagination += other.finite_pagination;
 
         self.highlight_pre_tag |= other.highlight_pre_tag;
         self.highlight_post_tag |= other.highlight_post_tag;
@@ -534,6 +544,7 @@ impl SearchAggregator {
                 "pagination": {
                    "max_limit": self.max_limit,
                    "max_offset": self.max_offset,
+                   "finite_pagination": self.finite_pagination > self.total_received / 2,
                 },
                 "formatting": {
                     "highlight_pre_tag": self.highlight_pre_tag,

meilisearch-http/src/routes/indexes/search.rs

@@ -4,6 +4,7 @@ use meilisearch_auth::IndexSearchRules;
 use meilisearch_lib::index::{
     MatchingStrategy, SearchQuery, DEFAULT_CROP_LENGTH, DEFAULT_CROP_MARKER,
     DEFAULT_HIGHLIGHT_POST_TAG, DEFAULT_HIGHLIGHT_PRE_TAG, DEFAULT_SEARCH_LIMIT,
+    DEFAULT_SEARCH_OFFSET,
 };
 use meilisearch_lib::MeiliSearch;
 use meilisearch_types::error::ResponseError;
@@ -27,8 +28,12 @@ pub fn configure(cfg: &mut web::ServiceConfig) {
 #[serde(rename_all = "camelCase", deny_unknown_fields)]
 pub struct SearchQueryGet {
     q: Option<String>,
-    offset: Option<usize>,
-    limit: Option<usize>,
+    #[serde(default = "DEFAULT_SEARCH_OFFSET")]
+    offset: usize,
+    #[serde(default = "DEFAULT_SEARCH_LIMIT")]
+    limit: usize,
+    page: Option<usize>,
+    hits_per_page: Option<usize>,
     attributes_to_retrieve: Option<CS<String>>,
     attributes_to_crop: Option<CS<String>>,
     #[serde(default = "DEFAULT_CROP_LENGTH")]
@@ -62,7 +67,9 @@ impl From<SearchQueryGet> for SearchQuery {
         Self {
             q: other.q,
             offset: other.offset,
-            limit: other.limit.unwrap_or_else(DEFAULT_SEARCH_LIMIT),
+            limit: other.limit,
+            page: other.page,
+            hits_per_page: other.hits_per_page,
             attributes_to_retrieve: other
                 .attributes_to_retrieve
                 .map(|o| o.into_iter().collect()),