binary search tree recursive Algorithm
The binary search tree (BST) recursive algorithm is a versatile technique used in computer science to perform various operations, such as searching, inserting, and deleting elements in a binary search tree data structure. A binary search tree is a binary tree where each node has at most two children, and the nodes are arranged such that the left child has a value less than the parent node, and the right child has a value greater than the parent node. The recursive algorithm takes advantage of this ordered structure to perform operations efficiently by breaking down the problem into smaller subproblems, with each subproblem being tackled by a subsequent recursive call.
In the context of searching for a particular value in the binary search tree, the recursive algorithm begins at the root node and compares the target value with the value of the current node. If the target value is equal to the current node's value, the search is successful, and the algorithm returns the node. If the target value is less than the current node's value, the algorithm makes a recursive call to search the left subtree; otherwise, it searches the right subtree. This process continues until the target value is found, or the algorithm reaches a leaf node without finding the target value, resulting in an unsuccessful search. Similarly, for insertion and deletion operations, the recursive algorithm navigates the tree structure to identify the appropriate node to be inserted or deleted, following the rules of the binary search tree.
"""
This is a python3 implementation of binary search tree using recursion
To run tests:
python -m unittest binary_search_tree_recursive.py
To run an example:
python binary_search_tree_recursive.py
"""
import unittest
class Node:
def __init__(self, label: int, parent):
self.label = label
self.parent = parent
self.left = None
self.right = None
class BinarySearchTree:
def __init__(self):
self.root = None
def empty(self):
"""
Empties the tree
>>> t = BinarySearchTree()
>>> assert t.root is None
>>> t.put(8)
>>> assert t.root is not None
"""
self.root = None
def is_empty(self) -> bool:
"""
Checks if the tree is empty
>>> t = BinarySearchTree()
>>> t.is_empty()
True
>>> t.put(8)
>>> t.is_empty()
False
"""
return self.root is None
def put(self, label: int):
"""
Put a new node in the tree
>>> t = BinarySearchTree()
>>> t.put(8)
>>> assert t.root.parent is None
>>> assert t.root.label == 8
>>> t.put(10)
>>> assert t.root.right.parent == t.root
>>> assert t.root.right.label == 10
>>> t.put(3)
>>> assert t.root.left.parent == t.root
>>> assert t.root.left.label == 3
"""
self.root = self._put(self.root, label)
def _put(self, node: Node, label: int, parent: Node = None) -> Node:
if node is None:
node = Node(label, parent)
else:
if label < node.label:
node.left = self._put(node.left, label, node)
elif label > node.label:
node.right = self._put(node.right, label, node)
else:
raise Exception(f"Node with label {label} already exists")
return node
def search(self, label: int) -> Node:
"""
Searches a node in the tree
>>> t = BinarySearchTree()
>>> t.put(8)
>>> t.put(10)
>>> node = t.search(8)
>>> assert node.label == 8
>>> node = t.search(3)
Traceback (most recent call last):
...
Exception: Node with label 3 does not exist
"""
return self._search(self.root, label)
def _search(self, node: Node, label: int) -> Node:
if node is None:
raise Exception(f"Node with label {label} does not exist")
else:
if label < node.label:
node = self._search(node.left, label)
elif label > node.label:
node = self._search(node.right, label)
return node
def remove(self, label: int):
"""
Removes a node in the tree
>>> t = BinarySearchTree()
>>> t.put(8)
>>> t.put(10)
>>> t.remove(8)
>>> assert t.root.label == 10
>>> t.remove(3)
Traceback (most recent call last):
...
Exception: Node with label 3 does not exist
"""
node = self.search(label)
if not node.right and not node.left:
self._reassign_nodes(node, None)
elif not node.right and node.left:
self._reassign_nodes(node, node.left)
elif node.right and not node.left:
self._reassign_nodes(node, node.right)
else:
lowest_node = self._get_lowest_node(node.right)
lowest_node.left = node.left
lowest_node.right = node.right
node.left.parent = lowest_node
if node.right:
node.right.parent = lowest_node
self._reassign_nodes(node, lowest_node)
def _reassign_nodes(self, node: Node, new_children: Node):
if new_children:
new_children.parent = node.parent
if node.parent:
if node.parent.right == node:
node.parent.right = new_children
else:
node.parent.left = new_children
else:
self.root = new_children
def _get_lowest_node(self, node: Node) -> Node:
if node.left:
lowest_node = self._get_lowest_node(node.left)
else:
lowest_node = node
self._reassign_nodes(node, node.right)
return lowest_node
def exists(self, label: int) -> bool:
"""
Checks if a node exists in the tree
>>> t = BinarySearchTree()
>>> t.put(8)
>>> t.put(10)
>>> t.exists(8)
True
>>> t.exists(3)
False
"""
try:
self.search(label)
return True
except Exception:
return False
def get_max_label(self) -> int:
"""
Gets the max label inserted in the tree
>>> t = BinarySearchTree()
>>> t.get_max_label()
Traceback (most recent call last):
...
Exception: Binary search tree is empty
>>> t.put(8)
>>> t.put(10)
>>> t.get_max_label()
10
"""
if self.is_empty():
raise Exception("Binary search tree is empty")
node = self.root
while node.right is not None:
node = node.right
return node.label
def get_min_label(self) -> int:
"""
Gets the min label inserted in the tree
>>> t = BinarySearchTree()
>>> t.get_min_label()
Traceback (most recent call last):
...
Exception: Binary search tree is empty
>>> t.put(8)
>>> t.put(10)
>>> t.get_min_label()
8
"""
if self.is_empty():
raise Exception("Binary search tree is empty")
node = self.root
while node.left is not None:
node = node.left
return node.label
def inorder_traversal(self) -> list:
"""
Return the inorder traversal of the tree
>>> t = BinarySearchTree()
>>> [i.label for i in t.inorder_traversal()]
[]
>>> t.put(8)
>>> t.put(10)
>>> t.put(9)
>>> [i.label for i in t.inorder_traversal()]
[8, 9, 10]
"""
return self._inorder_traversal(self.root)
def _inorder_traversal(self, node: Node) -> list:
if node is not None:
yield from self._inorder_traversal(node.left)
yield node
yield from self._inorder_traversal(node.right)
def preorder_traversal(self) -> list:
"""
Return the preorder traversal of the tree
>>> t = BinarySearchTree()
>>> [i.label for i in t.preorder_traversal()]
[]
>>> t.put(8)
>>> t.put(10)
>>> t.put(9)
>>> [i.label for i in t.preorder_traversal()]
[8, 10, 9]
"""
return self._preorder_traversal(self.root)
def _preorder_traversal(self, node: Node) -> list:
if node is not None:
yield node
yield from self._preorder_traversal(node.left)
yield from self._preorder_traversal(node.right)
class BinarySearchTreeTest(unittest.TestCase):
@staticmethod
def _get_binary_search_tree():
r"""
8
/ \
3 10
/ \ \
1 6 14
/ \ /
4 7 13
\
5
"""
t = BinarySearchTree()
t.put(8)
t.put(3)
t.put(6)
t.put(1)
t.put(10)
t.put(14)
t.put(13)
t.put(4)
t.put(7)
t.put(5)
return t
def test_put(self):
t = BinarySearchTree()
assert t.is_empty()
t.put(8)
r"""
8
"""
assert t.root.parent is None
assert t.root.label == 8
t.put(10)
r"""
8
\
10
"""
assert t.root.right.parent == t.root
assert t.root.right.label == 10
t.put(3)
r"""
8
/ \
3 10
"""
assert t.root.left.parent == t.root
assert t.root.left.label == 3
t.put(6)
r"""
8
/ \
3 10
\
6
"""
assert t.root.left.right.parent == t.root.left
assert t.root.left.right.label == 6
t.put(1)
r"""
8
/ \
3 10
/ \
1 6
"""
assert t.root.left.left.parent == t.root.left
assert t.root.left.left.label == 1
with self.assertRaises(Exception):
t.put(1)
def test_search(self):
t = self._get_binary_search_tree()
node = t.search(6)
assert node.label == 6
node = t.search(13)
assert node.label == 13
with self.assertRaises(Exception):
t.search(2)
def test_remove(self):
t = self._get_binary_search_tree()
t.remove(13)
r"""
8
/ \
3 10
/ \ \
1 6 14
/ \
4 7
\
5
"""
assert t.root.right.right.right is None
assert t.root.right.right.left is None
t.remove(7)
r"""
8
/ \
3 10
/ \ \
1 6 14
/
4
\
5
"""
assert t.root.left.right.right is None
assert t.root.left.right.left.label == 4
t.remove(6)
r"""
8
/ \
3 10
/ \ \
1 4 14
\
5
"""
assert t.root.left.left.label == 1
assert t.root.left.right.label == 4
assert t.root.left.right.right.label == 5
assert t.root.left.right.left is None
assert t.root.left.left.parent == t.root.left
assert t.root.left.right.parent == t.root.left
t.remove(3)
r"""
8
/ \
4 10
/ \ \
1 5 14
"""
assert t.root.left.label == 4
assert t.root.left.right.label == 5
assert t.root.left.left.label == 1
assert t.root.left.parent == t.root
assert t.root.left.left.parent == t.root.left
assert t.root.left.right.parent == t.root.left
t.remove(4)
r"""
8
/ \
5 10
/ \
1 14
"""
assert t.root.left.label == 5
assert t.root.left.right is None
assert t.root.left.left.label == 1
assert t.root.left.parent == t.root
assert t.root.left.left.parent == t.root.left
def test_remove_2(self):
t = self._get_binary_search_tree()
t.remove(3)
r"""
8
/ \
4 10
/ \ \
1 6 14
/ \ /
5 7 13
"""
assert t.root.left.label == 4
assert t.root.left.right.label == 6
assert t.root.left.left.label == 1
assert t.root.left.right.right.label == 7
assert t.root.left.right.left.label == 5
assert t.root.left.parent == t.root
assert t.root.left.right.parent == t.root.left
assert t.root.left.left.parent == t.root.left
assert t.root.left.right.left.parent == t.root.left.right
def test_empty(self):
t = self._get_binary_search_tree()
t.empty()
assert t.root is None
def test_is_empty(self):
t = self._get_binary_search_tree()
assert not t.is_empty()
t.empty()
assert t.is_empty()
def test_exists(self):
t = self._get_binary_search_tree()
assert t.exists(6)
assert not t.exists(-1)
def test_get_max_label(self):
t = self._get_binary_search_tree()
assert t.get_max_label() == 14
t.empty()
with self.assertRaises(Exception):
t.get_max_label()
def test_get_min_label(self):
t = self._get_binary_search_tree()
assert t.get_min_label() == 1
t.empty()
with self.assertRaises(Exception):
t.get_min_label()
def test_inorder_traversal(self):
t = self._get_binary_search_tree()
inorder_traversal_nodes = [i.label for i in t.inorder_traversal()]
assert inorder_traversal_nodes == [1, 3, 4, 5, 6, 7, 8, 10, 13, 14]
def test_preorder_traversal(self):
t = self._get_binary_search_tree()
preorder_traversal_nodes = [i.label for i in t.preorder_traversal()]
assert preorder_traversal_nodes == [8, 3, 1, 6, 4, 5, 7, 10, 14, 13]
def binary_search_tree_example():
r"""
Example
8
/ \
3 10
/ \ \
1 6 14
/ \ /
4 7 13
\
5
Example After Deletion
4
/ \
1 7
\
5
"""
t = BinarySearchTree()
t.put(8)
t.put(3)
t.put(6)
t.put(1)
t.put(10)
t.put(14)
t.put(13)
t.put(4)
t.put(7)
t.put(5)
print(
"""
8
/ \\
3 10
/ \\ \\
1 6 14
/ \\ /
4 7 13
\\
5
"""
)
print("Label 6 exists:", t.exists(6))
print("Label 13 exists:", t.exists(13))
print("Label -1 exists:", t.exists(-1))
print("Label 12 exists:", t.exists(12))
# Prints all the elements of the list in inorder traversal
inorder_traversal_nodes = [i.label for i in t.inorder_traversal()]
print("Inorder traversal:", inorder_traversal_nodes)
# Prints all the elements of the list in preorder traversal
preorder_traversal_nodes = [i.label for i in t.preorder_traversal()]
print("Preorder traversal:", preorder_traversal_nodes)
print("Max. label:", t.get_max_label())
print("Min. label:", t.get_min_label())
# Delete elements
print("\nDeleting elements 13, 10, 8, 3, 6, 14")
print(
"""
4
/ \\
1 7
\\
5
"""
)
t.remove(13)
t.remove(10)
t.remove(8)
t.remove(3)
t.remove(6)
t.remove(14)
# Prints all the elements of the list in inorder traversal after delete
inorder_traversal_nodes = [i.label for i in t.inorder_traversal()]
print("Inorder traversal after delete:", inorder_traversal_nodes)
# Prints all the elements of the list in preorder traversal after delete
preorder_traversal_nodes = [i.label for i in t.preorder_traversal()]
print("Preorder traversal after delete:", preorder_traversal_nodes)
print("Max. label:", t.get_max_label())
print("Min. label:", t.get_min_label())
if __name__ == "__main__":
binary_search_tree_example()
