Selection sort algorithm in Rust

You could use min_by_key to find the minimum's index and the method swap defined in slices:

fn selection_sort(array: &mut [i32]) {
    let len = array.len();
    for i in 0..len {
        let min = (i..len).min_by_key(|x| array[*x])
                          .unwrap();
        array.swap(min, i);
    }
}

1. No newlines after an opening brace but before the code starts
2. Use spaces around binary operators like +.
3. Use swap. This prevents you from needing to make a copy/clone of the variable.
4. Declare variables in as small a scope as possible. There's no reason to declare min outside of the array.
5. I'd use more iterator methods like enumerate to avoid array indexing, which incurs a small penalty for out-of-bounds checking.

fn selection_sort(array: &mut [i32]) {
    for i in 0..array.len() {
        let min_idx = array[i..].iter()
            .enumerate()
            .min_by_key(|&(_, v)| v)
            .map(|(i, _)| i)
            .unwrap_or(0);

        array.swap(i, min_idx + i);
    }
}

As a follow-up, I'd challenge you to make this algorithm work with more than just i32 types!

Why use selection sort? It has O(N^2) best, average AND worst case time complexity while Insertion Sort has O(N) best case, and O(N^2) worst and average case. Try Insertion Sort instead (or Quick Sort if your system can handle the recursion). Here's a good implementation of Insertion Sort done in Java. Basically, we go through the array and if we see that a value is out of place (not sorted correctly) then we move it towards the start of the array until it fits between two appropriate values.

    public static void insertionSort(int[] ar)
{       
    int index = 0;
    while (index < ar.length - 1) {
        if (ar[index] > ar[index + 1]) {
            swap(ar, index, index + 1);
            int oldIndex = index;
            while (index > 0 && ar[index] < ar[index - 1]) {
                swap(ar, index, index - 1);
                index--;
            }
            index = oldIndex + 1;
        }
        else
            index++;
    }
}

swap is just a helper method that switches two elements in an array.

Also check out:

http://bigocheatsheet.com/

https://en.wikipedia.org/wiki/Selection_sort