added BST, but remove not working

recursion/recursive_datastructure/README.md

@@ -85,3 +85,11 @@ Mit `yield from ...` kann man einen ganzen Iterator *yield*en.
 def my_range(start: int, end: int) -> Iterator[int]:
     yield from range(start, end)
 ```
+
+## [BinarySearchTree](./search_trees.py) (*Schwer*)
+
+Was wäre wenn wir nun einen Binary Tree haben, dieser aber eine Sortierung hat. Wenn wir ein Element hinzufügen packen wir alle Elemente kleiner nach Links und alle anderen nach Rechts.
+
+[Hier eine kleine Visualisierung](https://www.cs.usfca.edu/~galles/visualization/BST.html)
+
+Probiert einfach mal rum damit ihr euch die Funktion eines BST vorstellen könnt. Wirklich komplex wird `delete`.

recursion/recursive_datastructure/search_trees.py

@@ -0,0 +1,13 @@
+from typing import Optional
+from trees import Node
+
+type BinarySearchTree[T] = Optional[Node[T]]
+
+def insert[T](node: BinarySearchTree[T], value: T) -> BinarySearchTree[T]:
+    pass
+
+def exists[T](node: Optional[Node[T]],  value: T) -> bool:
+    pass
+
+def remove[T](node: BinarySearchTree[T], value: T) -> BinarySearchTree[T]:
+    pass

recursion/recursive_datastructure/solution/search_trees.py

@@ -1,17 +1,12 @@
-from typing import Iterator, Optional
+from typing import Optional
-from trees import Node, traverse
+from trees import Node
-from dataclasses import InitVar, dataclass
 
-@dataclass
+type BinarySearchTree[T] = Optional[Node[T]]
-class BinarySearchTree[T]:
-    
-    def __post_init__(self):
-        self.__root: Optional[Node[T]] = None
 
 
-    def insert(self, value: T):
+def insert[T](node: BinarySearchTree[T], value: T) -> BinarySearchTree[T]:
     prev = None
-        curr = self.__root
+    curr = node
     while curr:
         prev = curr
         if curr.value > value:
@@ -19,27 +14,36 @@ class BinarySearchTree[T]:
         else:
             curr = curr.right
     if prev is None:
-            self.__root = Node(value, None, None)
+        return Node(value, None, None)
     elif value < prev.value:
         prev.left = Node(value, None, None)
     else:
         prev.right = Node(value, None, None)
+    return node
 
-    def __delete(prev: Node[T], to_delete: Node[T]) -> Node[T]:
-        # TODO: implement
-        pass
 
-    def remove(self, value: T):
+def exists[T](node: Optional[Node[T]],  value: T) -> bool:
-        prev = None
+    return node and (exists(node.left, value)
-        curr = self.__root
+                     if value < node.value
-        while curr:
+                     else (value == node.value or exists(node.right, value)))
-            prev = curr
-            if curr.value > value:
-                curr = curr.left 
-            elif curr.value < value:
-                curr = curr.right
-            else:
-                curr = self.__delete(prev, curr)
 
-    def __iter__(self) -> Iterator[T]:
+
-        yield from traverse(self.__root)
+def remove[T](node: BinarySearchTree[T], value: T) -> BinarySearchTree[T]:
+    if node is None:
+        return node
+    if value < node.value:
+        node.left = remove(node.left, value)
+        return node
+    if value > node.value:
+        node.right = remove(node.right, value)
+        return node
+    if node.right is None:
+        return node.left
+    if node.left is None:
+        return node.right
+    min_node = node.right
+    while min_node.left:
+        min_node = min_node.left
+    node.value = min_node.value
+    node.right = remove(node.right, min_node.value)
+    return node

recursion/recursive_datastructure/solution/test_search_trees.py

@@ -1,24 +1,51 @@
-from search_trees import BinarySearchTree
+from typing import Iterator, Optional
+from search_trees import BinarySearchTree, insert, remove, exists
+from trees import Node
 from random import randint as random
 
-MAX= 1000
+
+def traverse[T](tree: Optional[Node[T]]) -> Iterator[T]:
+    match tree:
+        case Node(value, left, right):
+            yield from traverse(left)
+            yield value
+            yield from traverse(right)
+        case _:
+            return
+
+
+MAX = 100
 MIN = 0
 LENGTH = 100
 
+NUMS = {random(MIN, MAX) for _ in range(0, LENGTH)}
+NUMS_FILTER = {random(MIN, MAX) for _ in range(0, LENGTH // 4)}
+
 def test_insert():
-    nums = [random(MIN, MAX) for _ in range(0, LENGTH)]
+    bst: BinarySearchTree = None
-    bst = BinarySearchTree()
+    for num in NUMS:
-    for num in nums:
+        bst = insert(bst, num)
-        bst.insert(num)
+    assert list(traverse(bst)) == sorted(NUMS)
-    assert list(iter(bst)) == sorted(nums)
+
 
 def test_remove():
-    nums = {random(MIN, MAX) for _ in range(0, LENGTH)}
+    bst: BinarySearchTree = None
-    fil = {random(MIN, MAX) for _ in range(0, LENGTH // 4)}
+    for num in NUMS:
-    bst = BinarySearchTree()
+        bst = insert(bst, num)
-    for num in nums:
+    assert list(traverse(bst)) == sorted(NUMS)
-        bst.insert(num)
+    for num in NUMS_FILTER:
-    for num in fil:
+        remove(bst, num)
-        bst.remove(num)
 
-    assert list(iter(bst)) == sorted(filter(lambda x: x not in fil, nums))
+    assert list(traverse(bst)) == sorted(filter(lambda x: x not in NUMS_FILTER, NUMS))
+
+
+def test_exists():
+    bst: BinarySearchTree = None
+    for num in NUMS:
+        bst = insert(bst, num)
+    for num in NUMS_FILTER:
+        remove(bst, num)
+
+    assert all(map(lambda x: exists(bst, x),
+               filter(lambda x: x not in NUMS_FILTER, NUMS)))
+    assert all(map(lambda x: not exists(bst, x), NUMS_FILTER))