Binary search in Rust
Style

Spaces and punctuation

if array.is_empty(){


should be

if array.is_empty() {


(likewise match key.cmp(&amp;middle_element){ → match key.cmp(&amp;middle_element) {, etc.)

Ordering::Equal =&gt; {return Some(start+middle as usize);} ,


should be

Ordering::Equal =&gt; return Some(start + middle as usize),


although really, the comma at the end isn't necessary; you can remove that too.

And there should only be one new line below use std::cmp::Ordering and none above.

Scope

middle isn't used outside the loop, so you can replace:

let mut middle;

loop {
    middle = (end - start) / 2;


with:

loop {
    let middle = (end - start) / 2;


Note how the mut can go away, because the value of middle is only set once (per loop).

Unnecessary cast (as)

Ordering::Equal =&gt; {
    return Some(start + middle as usize);
},


The as usize is unnecessary; Rust already knows that you're returning Option&lt;usize&gt;. In fact, both start and middle are already usize, as is start + middle, so Rust isn't even doing anything fancy to get this to work. However, writing as usize makes it seem like those aren't usize, which could end up confusing your reader quite a lot.

(Same with start as usize → start and end as usize → end.)

Misleading comments

This comment:

//The slicing syntax produces an unborrowed slice
//(type: [i32]) which we must then borrow (to give a &amp;[i32]),
//even if we are slicing a borrowed slice.//More can be read at
//https://github.com/nrc/r4cppp/blob/master/arrays.md
if end - start &lt;= 1 {


is misleading, for two reasons:


It's right above (hence attached to) the wrong piece of code.
You don't use the slicing syntax (array[4..6]) anywhere in your code; you use the indexing syntax.


Just remove it; perhaps replace it with

let middle_element = array[start + middle];
// cmp requires a reference
match key.cmp(&amp;middle_element) {


or something if you think it would be helpful. Though be aware that let middle_element = array[start + middle] makes a copy of middle_element, so the reference is to middle_element on the stack, not array[start + middle] wherever array is stored.

loop with if and break

if end - start &lt;= 1 {
    break;
};


You're trying to make a do while loop here. However, if end - start &lt;= 1 already, you don't need to enter this loop in the first place. This means you can just use a regular while:

while end - start &gt; 1 {
    let middle = (end - start) / 2;
    let middle_element = array[start + middle];
    // cmp requires a reference
    match key.cmp(&amp;middle_element) {
        Ordering::Less =&gt; end -= middle,
        Ordering::Greater =&gt; start += middle,
        Ordering::Equal =&gt; return Some(start + middle),
    }
}


And now cargo fmt doesn't change the code, and cargo clippy doesn't give any suggestions. Hooray!

Implementation

middle

In my mind, middle should be the index of the middle element – not the difference between start and the middle element. You might want to calculate this as (start + end) / 2 but that risks overflow; fortunately, start + (end - start) / 2 works fine.

So this:

let middle = (end - start) / 2;
let middle_element = array[start + middle];
// cmp requires a reference
match key.cmp(&amp;middle_element) {
    Ordering::Less =&gt; end -= middle,
    Ordering::Greater =&gt; start += middle,
    Ordering::Equal =&gt; return Some(start + middle)
}


becomes:

while end - start &gt; 1 {
    let middle = start + (end - start) / 2;
    let middle_element = array[middle];
    // cmp requires a reference
    match key.cmp(&amp;middle_element) {
        Ordering::Less =&gt; end = middle,
        Ordering::Greater =&gt; start = middle,
        Ordering::Equal =&gt; return Some(middle)
    }
}


Unnecessary variable

Now we've made that change, I think array[middle] is obviously the middle element; so much so that we can remove middle_element entirely and get clearer code:

let middle = start + (end - start) / 2;
// cmp requires a reference
match key.cmp(&amp;array[middle]) {


Ordering ordering

I actually think it'd be clearer if these were in Less, Equal, Greater order:

match key.cmp(&amp;array[middle]) {
    Ordering::Less =&gt; end = middle,
    Ordering::Equal =&gt; return Some(middle),
    Ordering::Greater =&gt; start = middle
}


Implicit return

At the end, it might be clearer to use the implicit return form:

if array[start] == key {
    Some(start)
} else if array[end] == key {
    Some(end)
} else {
    None
}


Addendum: Tests

To make sure I didn't break your code while making these changes, I wrote a test. Tests are good to have (not that this is a particularly good test).

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_find() {
        assert_eq!(find(&amp;[2, 4, 5, 7, 11, 12, 17], 5), Some(2));
        assert_eq!(find(&amp;[], 5), None);
        assert_eq!(find(&amp;[2, 4, 5, 7, 11, 12, 17], 6), None);
        assert_eq!(find(&amp;[-63, -42, 1, 2, 4, 5, 7, 11, 12, 17, 17, 18], 12), Some(8));

        call_find(&amp;[-10, -7, 0, 2, 4, 4, 5, 16, 27, 37, 38, 40, 40, 40, 40, 63, 628, 844, 10000000, 41230456]);
    }

    fn call_find(array: &amp;[i32]) {
        for i in 0..array.len() {
            assert_eq!(array[find(array, array[i]).unwrap()], array[i]);
        }
    }
}