p3l/examples/quicksort.p3l

type List<T> = Option<Rc<(T, List<T>)>>;
type Partition<T> = (List<T>, T, List<T>);

// Return a random number between 0 (inclusive) and
// max (exclusive).
fn random(max: int) -> int {
	while true {
		let value: int = 0;
		let max_value: int = 0;
		while max_value < max {
			max_value = max_value * 2 + 1;
			value = value * 2;
			{ value = value + 1; } [0.5] {}
		}
		if value < max {
			return value;
		}
	}
}

// Return true if the option is `None`.
fn is_none<O>(opt: O) -> bool {
	if let Some(_value) = opt {
		return false;
	} else {
		return true;
	}
}

// Unwrap an option.
fn unwrap<T>(opt: Option<T>) -> T {
	if let Some(value) = opt {
		return value;
	}
}

// Create a new, empty list.
// Complexity: O(1)
fn list_new<T>() -> List<T> {
	return None;
}

// Push a new value to the front of the list.
// Complexity: O(1)
fn list_push_front<T>(list: List<T>, elem: T) -> List<T> {
	return Some(Rc((elem, list)));
}

// Pop the value from the front of the list.
// Complexity: O(1)
fn list_pop_front<T>(list: List<T>) -> (T, List<T>) {
	if let Some(front) = list {
		return *front;
	}
}

// Append a list to the end of this one.
// Complexity: O(n)
fn list_append<T>(list: List<T>, list2: List<T>) -> List<T> {
	if is_none::<List<T>>(list) {
		return list2;
	}
	
	let back: List<T> = list;
	while let Some(front) = back {
		let tail: List<T> = (*front).1;
		if is_none::<List<T>>(tail) {
			break;
		}
		back = tail;
	}
	
	if let Some(back) = back {
		back.1 = list2;
		return list;
	}
	// else unreachable - back is always a non-empty list
}

// Return the length of a list.
// Complexity: O(n)
fn list_len<T>(list: List<T>) -> int {
	let len: int = 0;
	while let Some(inner) = list {
		len = len + 1;
		list = (*inner).1;
	}
	return len;
}

// Swap the value of the two list elements.
fn list_swap<T>(list: List<T>, list2: List<T>) {
	let list: Rc<(T, List<T>)> = unwrap::<Rc<(T, List<T>)>>(list);
	let list2: Rc<(T, List<T>)> = unwrap::<Rc<(T, List<T>)>>(list2);
	let tmp: T = (*list).0;
	list.0 = (*list2).0;
	list2.0 = tmp;
}

// Swap the n-th and last elements, and return its value.
fn list_swap_nth_last<T>(list: List<T>, n: int) -> T {
	let i: int = 0;
	let nth: List<T> = None;
	while let Some(front) = list {
		if i == n {
			nth = list;
		}
		let tail: List<T> = (*front).1;
		if is_none::<List<T>>(tail) {
			let _unit: () = list_swap::<T>(nth, list);
			return (*front).0;
		}
		list = tail;
		i = i + 1;
	}
}

// Return the next list element.
fn list_next<T>(list: List<T>) -> List<T> {
	return (*unwrap::<Rc<(T, List<T>)>>(list)).1;
}

// Split the list at index n.
fn list_split<T>(list: List<T>, n: int) -> (List<T>, List<T>) {
	if n == 0 {
		return (None, list);
	}
	
	let list2: List<T> = list;
	let i: int = 0;
	while i < n - 1 {
		list2 = list_next::<T>(list2);
		i = i + 1;
	}
	
	if let Some(front) = list2 {
		list2 = (*front).1;
		front.1 = None;
	}
	return (list, list2);
}

// Increase swap count
fn inc_swaps(swaps_and_comps: Rc<(int, int)>) {
	swaps_and_comps.0 = (*swaps_and_comps).0 + 1;
}

// Increase comparison count
fn inc_comps(swaps_and_comps: Rc<(int, int)>) {
	swaps_and_comps.1 = (*swaps_and_comps).1 + 1;
}

// Randomised quicksort.
// Expected complexity: O(n log n)
fn quicksort(list: List<int>, swaps_and_comps: Rc<(int, int)>) -> List<int> {
	if list_len::<int>(list) < 2 {
		return list;
	}
	
	let partition: Partition<int> = partition(list, swaps_and_comps);
	let list: List<int> = quicksort(partition.0, swaps_and_comps);
	let pivot: int = partition.1;
	let list2: List<int> = quicksort(partition.2, swaps_and_comps);
	
	list2 = list_push_front::<int>(list2, pivot);
	return list_append::<int>(list, list2);
}

// Partition a list into smaller, pivot, and larger elements
fn partition(list: List<int>, swaps_and_comps: Rc<(int, int)>) -> Partition<int> {
	// choose some random element as pivot and move it to the last position
	let list_len: int = list_len::<int>(list);
	let pivot: int = list_swap_nth_last::<int>(list, random(list_len));
	let _unit: () = inc_swaps(swaps_and_comps);
	
	// this is our pivot position
	let iter: List<int> = list;
	let iter_idx: int = -1;
	
	// move all elements smaller than our pivot to its left
	let i: int = 0;
	let iter2: List<int> = list;
	while let Some(front) = iter2 {
		// don't swap out the pivot already
		if i != list_len - 1 {
			
			let _unit: () = inc_comps(swaps_and_comps);
			if (*front).0 <= pivot {
				// move pivot index forward
				if iter_idx >= 0 {
					iter = list_next::<int>(iter);
				}
				iter_idx = iter_idx + 1;
				
				// swap current element with pivot position
				if iter_idx != i {
					let _unit: () = list_swap::<int>(iter, iter2);
					let _unit: () = inc_swaps(swaps_and_comps);
				}
			}
			
		}
		
		iter2 = (*front).1;
		i = i + 1;
	}
	
	// move pivot to the correct pivot position
	iter_idx = iter_idx + 1;
	let _pivot: int = list_swap_nth_last::<int>(list, iter_idx);
	let _unit: () = inc_swaps(swaps_and_comps);
	
	// split the list into two
	let lists: (List<int>, List<int>) = list_split::<int>(list, iter_idx);
	let pop: (int, List<int>) = list_pop_front::<int>(lists.1);
	return (lists.0, pop.0, pop.1);
}

// Assert that the list is sorted.
fn assert_sorted(list: List<int>) -> () {
	if let Some(first) = list {
		if assert_sorted_impl((*first).1, (*first).0) {
			return ();
		}
		// else there's no path to a return statement - assert failed
	} else {
		return ();
	}
}
fn assert_sorted_impl(list: List<int>, prev: int) -> bool {
	while let Some(front) = list {
		let curr: int = (*front).0;
		if curr < prev {
			return false;
		}
		prev = curr;
		list = (*front).1;
	}
	return true;
}

input!(len);

// Create a random list.
let list: List<int> = list_new::<int>();
let i: int = 0;
while i < len {
	list = list_push_front::<int>(list, random(len*2));
	i = i + 1;
}

// Run quicksort.
let swaps_and_comps: Rc<(int, int)> = Rc((0, 0));
list = quicksort(list, swaps_and_comps);
let swaps: int = (*swaps_and_comps).0;
let comps: int = (*swaps_and_comps).1;

// Ensure the list is now sorted.
let _unit: () = assert_sorted(list);

output!(swaps);
output!(comps);