feat: add quicksort and binary tree model

The binary tree is used to bookkeep simulated recursion on subarray
bounds during quicksort. It may be removed later if I can successfully
rewrite the levels using coroutines, which I will hold off until Godot
4.0 for now because of improvements to yield/await.

Author: danielzting

levels/quick_sort.gd

@@ -0,0 +1,79 @@
+class_name QuickSort
+extends ComparisonSort
+
+const NAME = "QUICKSORT"
+const ABOUT = """
+Quicksort designates the last element as the pivot and puts everything
+less than the pivot before it and everything greater after it. This
+partitioning is done by iterating through the array while keeping track
+of a pointer initially set to the first element. Every time an element
+less than the pivot is encountered, it is swapped with the pointed
+element and the pointer moves forward. At the end, the pointer and pivot
+are swapped, and the process is repeated on the left and right halves.
+"""
+const CONTROLS = """
+If the highlighted element is less than the pivot or the pivot has been
+reached, press LEFT ARROW to swap it with the pointer. Otherwise, press
+RIGHT ARROW to move on.
+"""
+
+const ACTIONS = {
+    "SWAP": "Left",
+    "CONTINUE": "Right",
+}
+var _index = 0
+var _pointer = 0
+# Bookkeep simulated recursion with a binary tree of subarray bounds
+var _stack = BinaryTreeModel.new(Vector2(0, array.size - 1))
+
+func _init(array).(array):
+    pass
+
+func next(action):
+    if _index == _pivot():
+        if action != null and action != ACTIONS.SWAP:
+            return emit_signal("mistake")
+        array.swap(_index, _pointer)
+        if _pointer - _begin() > 1:
+            _stack.left = BinaryTreeModel.new(Vector2(_begin(), _pointer - 1))
+            _stack = _stack.left
+        elif _pivot() - _pointer > 1:
+            _stack.right = BinaryTreeModel.new(Vector2(_pointer + 1, _pivot()))
+            _stack = _stack.right
+        else:
+            while (_stack.parent.right != null
+                or _stack.parent.left.value.y + 2 >= _stack.parent.value.y):
+                _stack = _stack.parent
+                if _stack.parent == null:
+                    return emit_signal("done")
+            _stack.parent.right = BinaryTreeModel.new(Vector2(
+                _stack.parent.left.value.y + 2, _stack.parent.value.y))
+            _stack = _stack.parent.right
+        _index = _begin()
+        _pointer = _index
+    elif array.at(_index) < array.at(_pivot()):
+        if action != null and action != ACTIONS.SWAP:
+            return emit_signal("mistake")
+        array.swap(_index, _pointer)
+        _index += 1
+        _pointer += 1
+    else:
+        if action != null and action != ACTIONS.CONTINUE:
+            return emit_signal("mistake")
+        _index += 1
+
+func _begin():
+    return _stack.value.x
+
+func _pivot():
+    return _stack.value.y
+
+func get_effect(i):
+    if i < _begin() or i > _pivot():
+        return EFFECTS.DIMMED
+    if i == _index or i == _pivot():
+        return EFFECTS.HIGHLIGHTED
+    return EFFECTS.NONE
+
+func get_pointer():
+    return _pointer

models/binary_tree_model.gd

@@ -0,0 +1,18 @@
+class_name BinaryTreeModel
+extends Reference
+
+var left: BinaryTreeModel setget set_left
+var right: BinaryTreeModel setget set_right
+var parent: BinaryTreeModel
+var value = null
+
+func _init(value):
+    self.value = value
+
+func set_left(child: BinaryTreeModel):
+    child.parent = self
+    left = child
+
+func set_right(child: BinaryTreeModel):
+    child.parent = self
+    right = child

project.godot

@@ -19,6 +19,11 @@ _global_script_classes=[ {
 "language": "GDScript",
 "path": "res://views/array_view.gd"
 }, {
+"base": "Reference",
+"class": "BinaryTreeModel",
+"language": "GDScript",
+"path": "res://models/binary_tree_model.gd"
+}, {
 "base": "ComparisonSort",
 "class": "BogoSort",
 "language": "GDScript",
@@ -45,18 +50,25 @@ _global_script_classes=[ {
 "path": "res://levels/merge_sort.gd"
 }, {
 "base": "ComparisonSort",
+"class": "QuickSort",
+"language": "GDScript",
+"path": "res://levels/quick_sort.gd"
+}, {
+"base": "ComparisonSort",
 "class": "SelectionSort",
 "language": "GDScript",
 "path": "res://levels/selection_sort.gd"
 } ]
 _global_script_class_icons={
 "ArrayModel": "",
 "ArrayView": "",
+"BinaryTreeModel": "",
 "BogoSort": "",
 "BubbleSort": "",
 "ComparisonSort": "",
 "InsertionSort": "",
 "MergeSort": "",
+"QuickSort": "",
 "SelectionSort": ""
 }
 

scripts/levels.gd

@@ -5,6 +5,7 @@ const LEVELS = [
     InsertionSort,
     SelectionSort,
     MergeSort,
+    QuickSort,
 ]
 const MIN_WAIT = 1.0 / 32 # Should be greater than maximum frame time
 const MAX_WAIT = 4