added BST, but remove not working

recursion/recursive_datastructure/solution/search_trees.py

@@ -1,45 +1,49 @@
-from typing import Iterator, Optional
-from trees import Node, traverse
-from dataclasses import InitVar, dataclass
+from typing import Optional
+from trees import Node
 
-@dataclass
-class BinarySearchTree[T]:
-    
-    def __post_init__(self):
-        self.__root: Optional[Node[T]] = None
-        
-        
-    def insert(self, value: T):
-        prev = None
-        curr = self.__root
-        while curr:
-            prev = curr
-            if curr.value > value:
-                curr = curr.left
-            else:
-                curr = curr.right
-        if prev is None:
-            self.__root = Node(value, None, None)
-        elif value < prev.value:
-            prev.left = Node(value, None, None)
+type BinarySearchTree[T] = Optional[Node[T]]
+
+
+def insert[T](node: BinarySearchTree[T], value: T) -> BinarySearchTree[T]:
+    prev = None
+    curr = node
+    while curr:
+        prev = curr
+        if curr.value > value:
+            curr = curr.left
         else:
-            prev.right = Node(value, None, None)
-            
-    def __delete(prev: Node[T], to_delete: Node[T]) -> Node[T]:
-        # TODO: implement
-        pass
-    
-    def remove(self, value: T):
-        prev = None
-        curr = self.__root
-        while curr:
-            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)
+            curr = curr.right
+    if prev is 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 exists[T](node: Optional[Node[T]],  value: T) -> bool:
+    return node and (exists(node.left, value)
+                     if value < node.value
+                     else (value == node.value or exists(node.right, value)))
+
+
+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