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1. Run Rustfmt, a tool for automatically formatting Rust code to the community-accepted style.

2. Run Clippy, a tool for finding common mistakes that may not be compilation errors but are unlikely to be what the programmer intended.

3. Don't accept a &String — Why is it discouraged to accept a reference to a String (&String) or Vec (&Vec) as a function argument?

4. Don't use explicit return keywords at the end of blocks.

5. Instead of

   if let Some(_) = max {
    max.unwrap()
   

   bind the variable:

   if let Some(x) = max {
    x
   

6. Your whole last conditional can be simplified to max.unwrap_or_default().

7. Add some automated tests.

   #[test]
   fn example_1() {
    assert_eq!(longest_con_seq("ABAZDC", "BACBAD"), "ABAD");
   }
   #[test]
   fn example_2() {
    assert_eq!(longest_con_seq("AGGTAB", "GXTKAYB"), "GTAB");
   }
   #[test]
   fn example_3() {
    assert_eq!(longest_con_seq("aaaa", "aa"), "aa");
   }
   #[test]
   fn example_4() {
    assert_eq!(longest_con_seq("ABBA", "ABJABA"), "ABBA");
   }
   

8. As before, don't match on Some and then unwrap, bind the variable. We can also avoid the clone by matching on a reference:

   match max {
    Some(_) => {
    let max_str = max.clone();
    let max_str = max_str.unwrap();
   

   match &max {
    Some(max_str) => {
   

End result

#[macro_use]
extern crate criterion;
use criterion::Criterion;
fn longest_con_seq(s1: &str, s2: &str) -> String {
 let mut max: Option<String> = None; // Holds value of string with maximum length
 let mut current = String::new(); // String container to hold current longest value
 let mut s1_iter = s1.chars().peekable(); // Peekable iterator for string s1
 let mut s2_iter = s2.chars(); //Iterator for string s2
 let mut s2_prev_pos = s2_iter.clone(); // Iterator that holds position of previous location of first iterator
 let mut s1_prev_pos = s1_iter.clone(); // Peekable iterator used to make sure all possible combinations are located.
 loop {
 let s1_char = s1_iter.next(); // Get character in s1
 if current.is_empty() {
 // If no consecutive string found yet store location of iterator
 s1_prev_pos = s1_iter.clone()
 }
 match s1_char {
 Some(s1_char) => loop {
 match s2_iter.next() {
 Some(s2_char) if s1_char == s2_char => {
 current.push(s1_char);
 s2_prev_pos = s2_iter.clone();
 break;
 }
 Some(_) => continue,
 None => {
 s2_iter = s2_prev_pos.clone();
 break;
 }
 }
 },
 None => match s1_prev_pos.peek() {
 Some(_) => {
 match &max {
 Some(max_str) => {
 if max_str.len() < current.len() {
 max = Some(current.clone());
 }
 current.clear();
 }
 None => {
 max = Some(current.clone());
 current.clear();
 }
 }
 s1_iter = s1_prev_pos.clone();
 s2_iter = s2.chars();
 }
 None => break,
 },
 }
 }
 max.unwrap_or_default()
}
fn criterion_benchmark(c: &mut Criterion) {
 let s1 = "GXTKAYB";
 let s2 = "AGGTAB";
 c.bench_function("Benchmark", move |b| b.iter(|| longest_con_seq(s1, s2)));
}
criterion_group!(benches, criterion_benchmark);
criterion_main!(benches);
#[test]
fn example_1() {
 assert_eq!(longest_con_seq("ABAZDC", "BACBAD"), "ABAD");
}
#[test]
fn example_2() {
 assert_eq!(longest_con_seq("AGGTAB", "GXTKAYB"), "GTAB");
}
#[test]
fn example_3() {
 assert_eq!(longest_con_seq("aaaa", "aa"), "aa");
}
#[test]
fn example_4() {
 assert_eq!(longest_con_seq("ABBA", "ABJABA"), "ABBA");
}