Function natural_sort 

pub fn natural_sort(a: &str, b: &str) -> Ordering

Performs natural sorting comparison between two strings.

Natural sorting is an ordering that handles numeric sequences in a way that matches human expectations. For example, “file2” comes before “file10” (unlike standard lexicographic sorting).

Characteristics

• Case-sensitive with lowercase priority: When comparing same letters, lowercase comes before uppercase
• Numbers are compared by numeric value, not character by character
• Leading zeros affect ordering when numeric values are equal
• Can handle numbers larger than u128::MAX (falls back to string comparison)
• When strings are equal case-insensitively, lowercase is prioritized (lowercase < uppercase)

Algorithm

The function works by:

1. Processing strings character by character in a case-insensitive manner
2. When encountering digits, treating consecutive digits as a single number
3. Comparing numbers by their numeric value rather than lexicographically
4. For non-numeric characters, using case-insensitive comparison
5. If everything is equal case-insensitively, using case-sensitive comparison as final tie-breaker