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/tests/search/mod.rs

@@ -3,6 +3,7 @@
 
 mod errors;
 mod formatted;
+mod pagination;
 
 use crate::common::Server;
 use once_cell::sync::Lazy;

meilisearch-http/tests/search/pagination.rs

@@ -0,0 +1,112 @@
+use crate::common::Server;
+use crate::search::DOCUMENTS;
+use serde_json::json;
+
+#[actix_rt::test]
+async fn default_search_should_return_estimated_total_hit() {
+    let server = Server::new().await;
+    let index = server.index("basic");
+
+    let documents = DOCUMENTS.clone();
+    index.add_documents(documents, None).await;
+    index.wait_task(0).await;
+
+    index
+        .search(json!({}), |response, code| {
+            assert_eq!(code, 200, "{}", response);
+            assert!(response.get("estimatedTotalHits").is_some());
+            assert!(response.get("limit").is_some());
+            assert!(response.get("offset").is_some());
+
+            // these fields shouldn't be present
+            assert!(response.get("totalHits").is_none());
+            assert!(response.get("page").is_none());
+            assert!(response.get("totalPages").is_none());
+        })
+        .await;
+}
+
+#[actix_rt::test]
+async fn simple_search() {
+    let server = Server::new().await;
+    let index = server.index("basic");
+
+    let documents = DOCUMENTS.clone();
+    index.add_documents(documents, None).await;
+    index.wait_task(0).await;
+
+    index
+        .search(json!({"page": 1}), |response, code| {
+            assert_eq!(code, 200, "{}", response);
+            assert_eq!(response["hits"].as_array().unwrap().len(), 5);
+            assert!(response.get("totalHits").is_some());
+            assert_eq!(response["page"], 1);
+            assert_eq!(response["totalPages"], 1);
+
+            // these fields shouldn't be present
+            assert!(response.get("estimatedTotalHits").is_none());
+            assert!(response.get("limit").is_none());
+            assert!(response.get("offset").is_none());
+        })
+        .await;
+}
+
+#[actix_rt::test]
+async fn page_zero_should_not_return_any_result() {
+    let server = Server::new().await;
+    let index = server.index("basic");
+
+    let documents = DOCUMENTS.clone();
+    index.add_documents(documents, None).await;
+    index.wait_task(0).await;
+
+    index
+        .search(json!({"page": 0}), |response, code| {
+            assert_eq!(code, 200, "{}", response);
+            assert_eq!(response["hits"].as_array().unwrap().len(), 0);
+            assert!(response.get("totalHits").is_some());
+            assert_eq!(response["page"], 0);
+            assert_eq!(response["totalPages"], 1);
+        })
+        .await;
+}
+
+#[actix_rt::test]
+async fn hits_per_page_1() {
+    let server = Server::new().await;
+    let index = server.index("basic");
+
+    let documents = DOCUMENTS.clone();
+    index.add_documents(documents, None).await;
+    index.wait_task(0).await;
+
+    index
+        .search(json!({"hitsPerPage": 1}), |response, code| {
+            assert_eq!(code, 200, "{}", response);
+            assert_eq!(response["hits"].as_array().unwrap().len(), 1);
+            assert_eq!(response["totalHits"], 5);
+            assert_eq!(response["page"], 1);
+            assert_eq!(response["totalPages"], 5);
+        })
+        .await;
+}
+
+#[actix_rt::test]
+async fn hits_per_page_0_should_not_return_any_result() {
+    let server = Server::new().await;
+    let index = server.index("basic");
+
+    let documents = DOCUMENTS.clone();
+    index.add_documents(documents, None).await;
+    index.wait_task(0).await;
+
+    index
+        .search(json!({"hitsPerPage": 0}), |response, code| {
+            assert_eq!(code, 200, "{}", response);
+            assert_eq!(response["hits"].as_array().unwrap().len(), 0);
+            assert_eq!(response["totalHits"], 5);
+            assert_eq!(response["page"], 1);
+            assert_eq!(response["totalPages"], 0);
+        })
+        .await;
+}