Quicksort in rust by GPT4

md

Sure, here's a markdown document with an example of a functional implementation of quicksort in Rust, along with a Mermaid diagram and some documentation.

```markdown
# QuickSort in Rust

Quicksort is a divide and conquer algorithm. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then recursively sorted.

## Mermaid Diagram

```mermaid
graph TD
    A[Unsorted Array] --> B{Choose Pivot}
    B --> C[Partition Array]
    C --> D[Sub-Array Less Than Pivot]
    C --> E[Sub-Array Greater Than Pivot]
    D --> F[Recursively Sort]
    E --> G[Recursively Sort]
    F --> H[Concatenate]
    G --> H
    H --> I[Sorted Array]
```

## Rust Implementation

```rust
fn quicksort<T: Ord>(arr: &[T]) -> Vec<T> {
    if arr.len() <= 1 {
        return arr.to_vec();
    }

    let pivot = &arr[arr.len() / 2];
    let less: Vec<T> = arr.iter().filter(|x| *x < pivot).cloned().collect();
    let equal: Vec<T> = arr.iter().filter(|x| *x == pivot).cloned().collect();
    let greater: Vec<T> = arr.iter().filter(|x| *x > pivot).cloned().collect();

    let mut result: Vec<T> = Vec::new();
    result.extend(quicksort(&less));
    result.extend(equal);
    result.extend(quicksort(&greater));

    result
}
```

This implementation of quicksort in Rust is functional in style. It first checks if the array is small enough to return immediately. If not, it selects a pivot (the middle element of the array), then partitions the array into elements less than, equal to, and greater than the pivot. It then recursively sorts the less than and greater than partitions, and concatenates the results together to form the final sorted array.
```