binary search tree Algorithm
The binary search tree algorithm is a fundamental data structure and searching technique used in computer science and programming. It is an efficient and effective way of storing, retrieving, and organizing data in a hierarchical manner. A binary search tree (BST) is a binary tree data structure where each node has at most two child nodes, arranged in a way that the value of the node to the left is less than or equal to the parent node, and the value of the node to the right is greater than or equal to the parent node. This ordering property ensures that a search can be run in logarithmic time, making it a highly efficient method for searching and sorting large datasets.
To search for a specific value in a binary search tree, the algorithm starts at the root node and compares the desired value with the value of the current node. If the desired value is equal to the current node's value, the search is successful. If the desired value is less than the current node's value, the algorithm continues the search on the left subtree. Conversely, if the desired value is greater than the current node's value, the search continues on the right subtree. This process is repeated recursively until either the desired value is found or the subtree being searched is empty, indicating that the value is not in the tree. This efficient search process, which eliminates half of the remaining nodes with each comparison, is the key advantage of using a binary search tree algorithm in data management and search operations.
"""
A binary search Tree
"""
class Node:
def __init__(self, value, parent):
self.value = value
self.parent = parent # Added in order to delete a node easier
self.left = None
self.right = None
def __repr__(self):
from pprint import pformat
if self.left is None and self.right is None:
return str(self.value)
return pformat({"%s" % (self.value): (self.left, self.right)}, indent=1)
class BinarySearchTree:
def __init__(self, root=None):
self.root = root
def __str__(self):
"""
Return a string of all the Nodes using in order traversal
"""
return str(self.root)
def __reassign_nodes(self, node, new_children):
if new_children is not None: # reset its kids
new_children.parent = node.parent
if node.parent is not None: # reset its parent
if self.is_right(node): # If it is the right children
node.parent.right = new_children
else:
node.parent.left = new_children
else:
self.root = new_children
def is_right(self, node):
return node == node.parent.right
def empty(self):
return self.root is None
def __insert(self, value):
"""
Insert a new node in Binary Search Tree with value label
"""
new_node = Node(value, None) # create a new Node
if self.empty(): # if Tree is empty
self.root = new_node # set its root
else: # Tree is not empty
parent_node = self.root # from root
while True: # While we don't get to a leaf
if value < parent_node.value: # We go left
if parent_node.left is None:
parent_node.left = new_node # We insert the new node in a leaf
break
else:
parent_node = parent_node.left
else:
if parent_node.right is None:
parent_node.right = new_node
break
else:
parent_node = parent_node.right
new_node.parent = parent_node
def insert(self, *values):
for value in values:
self.__insert(value)
return self
def search(self, value):
if self.empty():
raise IndexError("Warning: Tree is empty! please use another.")
else:
node = self.root
# use lazy evaluation here to avoid NoneType Attribute error
while node is not None and node.value is not value:
node = node.left if value < node.value else node.right
return node
def get_max(self, node=None):
"""
We go deep on the right branch
"""
if node is None:
node = self.root
if not self.empty():
while node.right is not None:
node = node.right
return node
def get_min(self, node=None):
"""
We go deep on the left branch
"""
if node is None:
node = self.root
if not self.empty():
node = self.root
while node.left is not None:
node = node.left
return node
def remove(self, value):
node = self.search(value) # Look for the node with that label
if node is not None:
if node.left is None and node.right is None: # If it has no children
self.__reassign_nodes(node, None)
elif node.left is None: # Has only right children
self.__reassign_nodes(node, node.right)
elif node.right is None: # Has only left children
self.__reassign_nodes(node, node.left)
else:
tmp_node = self.get_max(
node.left
) # Gets the max value of the left branch
self.remove(tmp_node.value)
node.value = (
tmp_node.value
) # Assigns the value to the node to delete and keep tree structure
def preorder_traverse(self, node):
if node is not None:
yield node # Preorder Traversal
yield from self.preorder_traverse(node.left)
yield from self.preorder_traverse(node.right)
def traversal_tree(self, traversal_function=None):
"""
This function traversal the tree.
You can pass a function to traversal the tree as needed by client code
"""
if traversal_function is None:
return self.preorder_traverse(self.root)
else:
return traversal_function(self.root)
def postorder(curr_node):
"""
postOrder (left, right, self)
"""
node_list = list()
if curr_node is not None:
node_list = postorder(curr_node.left) + postorder(curr_node.right) + [curr_node]
return node_list
def binary_search_tree():
r"""
Example
8
/ \
3 10
/ \ \
1 6 14
/ \ /
4 7 13
>>> t = BinarySearchTree().insert(8, 3, 6, 1, 10, 14, 13, 4, 7)
>>> print(" ".join(repr(i.value) for i in t.traversal_tree()))
8 3 1 6 4 7 10 14 13
>>> print(" ".join(repr(i.value) for i in t.traversal_tree(postorder)))
1 4 7 6 3 13 14 10 8
>>> BinarySearchTree().search(6)
Traceback (most recent call last):
...
IndexError: Warning: Tree is empty! please use another.
"""
testlist = (8, 3, 6, 1, 10, 14, 13, 4, 7)
t = BinarySearchTree()
for i in testlist:
t.insert(i)
# Prints all the elements of the list in order traversal
print(t)
if t.search(6) is not None:
print("The value 6 exists")
else:
print("The value 6 doesn't exist")
if t.search(-1) is not None:
print("The value -1 exists")
else:
print("The value -1 doesn't exist")
if not t.empty():
print("Max Value: ", t.get_max().value)
print("Min Value: ", t.get_min().value)
for i in testlist:
t.remove(i)
print(t)
if __name__ == "__main__":
import doctest
doctest.testmod()
# binary_search_tree()
