typos on first letter counts as 2

Cargo.toml

@@ -18,3 +18,6 @@ opt-level = 3
 opt-level = 3
 [profile.test.build-override]
 opt-level = 3
+
+[patch.crates-io]
+fst = { path = "/Users/mpostma/Documents/code/rust/fst/" }

milli/src/search/mod.rs

@@ -7,7 +7,8 @@ use std::str::Utf8Error;
 use std::time::Instant;
 
 use distinct::{Distinct, DocIter, FacetDistinct, NoopDistinct};
-use fst::{IntoStreamer, Streamer};
+use fst::automaton::Str;
+use fst::{Automaton, IntoStreamer, Streamer};
 use levenshtein_automata::{LevenshteinAutomatonBuilder as LevBuilder, DFA};
 use log::debug;
 use meilisearch_tokenizer::{Analyzer, AnalyzerConfig};
@@ -285,6 +286,18 @@ pub fn word_derivations<'c>(
         Entry::Vacant(entry) => {
             let mut derived_words = Vec::new();
             let dfa = build_dfa(word, max_typo, is_prefix);
+            if max_typo == 1 {
+                let starts = Str::new(get_first(word));
+                let mut stream = fst.search_with_state(starts.intersection(&dfa)).into_stream();
+
+                while let Some((word, state)) = stream.next() {
+                    let word = std::str::from_utf8(word)?;
+                    let distance = dfa.distance(state.1);
+                    derived_words.push((word.to_string(), distance.to_u8()));
+                }
+
+                Ok(entry.insert(derived_words))
+            } else {
                 let mut stream = fst.search_with_state(&dfa).into_stream();
 
                 while let Some((word, state)) = stream.next() {
@@ -297,6 +310,14 @@ pub fn word_derivations<'c>(
             }
         }
     }
+}
+
+fn get_first(s: &str) -> &str {
+    match s.chars().next() {
+        Some(c) => &s[..c.len_utf8()],
+        None => s,
+    }
+}
 
 pub fn build_dfa(word: &str, typos: u8, is_prefix: bool) -> DFA {
     let lev = match typos {