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A binary search tree, or BST for short, is a tree whose nodes each store a key greater than all their left child nodes and less than all of their right child nodes. Binary trees are useful for storing data in an organized way, which allows for it to be fetched, inserted, updated, and deleted quickly. The greater-than and less-than ordering of nodes mean that each comparison skips about half of the remaining tree, so the whole lookup takes time proportional to the number of nodes in the tree.
To be precise, binary search trees provide an average Big-O complexity of O(log(n)) for retrieval, insertion, update, and delete operations. Log(n) is much faster than the linear O(n) time required to find items in an unsorted array. Many popular production databases such as PostgreSQL and MySQL use binary trees under the hood to speed up CRUD operations.
Step 1 – BSTNode Class
Our implementation won’t use a Tree class, but instead just a Node class. Binary trees are really just a pointer to a root node that in turn connects to each child node, so we’ll run with that idea.
First, we create a constructor:
class BSTNode:
def __init__ (self, val=None):
self.left = None
self.right = None
self.val = val
We’ll allow a value (key) to be provided, but if one isn’t provided we’ll just set it to None. We’ll also initialize both children of the new node to None.
Step 2 – Insert
We need a way to insert new data. The insert method is as follows:
def insert(self, val):
if not self.val:
self.val = val
return
if self.val == val:
return
if val < self.val:
if self.left:
self.left.insert(val)
return
self.left = BSTNode(val)
return
if self.right:
self.right.insert(val)
return
self.right = BSTNode(val)
If the node doesn’t yet have a value, we can just set the given value and return. If we ever try to insert a value that also exists, we can also simply return as this can be considered a noop. If the given value is less than our node’s value and we already have a left child then we recursively call insert on our left child. If we don’t have a left child yet then we just make the given value our new left child. We can do the same (but inverted) for our right side.
Step 3 – Get Min and Get Max
def get_min(self):
current = self
while current.left is not None:
current = current.left
return current.val
def get_max(self):
current = self
while current.right is not None:
current = current.right
return current.val
getMin and getMax are useful helper functions, and they’re easy to write! They are simple recursive functions that traverse the edges of the tree to find the smallest or largest values stored therein.
Step 4 – Delete
def delete(self, val):
if self == None:
return self
if val < self.val:
self.left = self.left.delete(val)
return self
if val > self.val:
self.right = self.right.delete(val)
return self
if self.right == None:
return self.left
if self.left == None:
return self.right
min_larger_node = self.right
while min_larger_node.left:
min_larger_node = min_larger_node.left
self.val = min_larger_node.val
self.right = self.right.delete(min_larger_node.val)
return selfdef delete(self, val):
if self == None:
return self
if val < self.val:
if self.left:
self.left = self.left.delete(val)
return self
if val > self.val:
if self.right:
self.right = self.right.delete(val)
return self
if self.right == None:
return self.left
if self.left == None:
return self.right
min_larger_node = self.right
while min_larger_node.left:
min_larger_node = min_larger_node.left
self.val = min_larger_node.val
self.right = self.right.delete(min_larger_node.val)
return selfdef delete(self, val):
if self == None:
return self
if val < self.val:
self.left = self.left.delete(val)
return self
if val > self.val:
self.right = self.right.delete(val)
return self
if self.right == None:
return self.left
if self.left == None:
return self.right
min_larger_node = self.right
while min_larger_node.left:
min_larger_node = min_larger_node.left
self.val = min_larger_node.val
self.right = self.right.delete(min_larger_node.val)
return self
The delete operation is one of the more complex ones. It is a recursive function as well, but it also returns the new state of the given node after performing the delete operation. This allows a parent whose child has been deleted to properly set it’s left or right data member to None.
Step 5 – Exists
The exists function is another simple recursive function that returns True or False depending on whether a given value already exists in the tree.
def exists(self, val):
if val == self.val:
return True
if val < self.val:
if self.left == None:
return False
return self.left.exists(val)
if self.right == None:
return False
return self.right.exists(val)
Step 6 – Inorder
It’s useful to be able to print out the tree in a readable format. The inorder method print’s the values in the tree in the order of their keys.
def inorder(self, vals):
if self.left is not None:
self.left.inorder(vals)
if self.val is not None:
vals.append(self.val)
if self.right is not None:
self.right.inorder(vals)
return vals
Step 7 – Preorder
def preorder(self, vals):
if self.val is not None:
vals.append(self.val)
if self.left is not None:
self.left.preorder(vals)
if self.right is not None:
self.right.preorder(vals)
return vals
Step 8 – Postorder
def postorder(self, vals):
if self.left is not None:
self.left.postorder(vals)
if self.right is not None:
self.right.postorder(vals)
if self.val is not None:
vals.append(self.val)
return vals
Usage
def main():
nums = [12, 6, 18, 19, 21, 11, 3, 5, 4, 24, 18]
bst = BSTNode()
for num in nums:
bst.insert(num)
print("preorder:")
print(bst.preorder([]))
print("#")
print("postorder:")
print(bst.postorder([]))
print("#")
print("inorder:")
print(bst.inorder([]))
print("#")
nums = [2, 6, 20]
print("deleting " + str(nums))
for num in nums:
bst.delete(num)
print("#")
print("4 exists:")
print(bst.exists(4))
print("2 exists:")
print(bst.exists(2))
print("12 exists:")
print(bst.exists(12))
print("18 exists:")
print(bst.exists(18))
Full Binary Search Tree in Python
class BSTNode:
def __init__ (self, val=None):
self.left = None
self.right = None
self.val = val
def insert(self, val):
if not self.val:
self.val = val
return
if self.val == val:
return
if val < self.val:
if self.left:
self.left.insert(val)
return
self.left = BSTNode(val)
return
if self.right:
self.right.insert(val)
return
self.right = BSTNode(val)
def get_min(self):
current = self
while current.left is not None:
current = current.left
return current.val
def get_max(self):
current = self
while current.right is not None:
current = current.right
return current.val
def delete(self, val):
if self == None:
return self
if val < self.val:
if self.left:
self.left = self.left.delete(val)
return self
if val > self.val:
if self.right:
self.right = self.right.delete(val)
return self
if self.right == None:
return self.left
if self.left == None:
return self.right
min_larger_node = self.right
while min_larger_node.left:
min_larger_node = min_larger_node.left
self.val = min_larger_node.val
self.right = self.right.delete(min_larger_node.val)
return self
def exists(self, val):
if val == self.val:
return True
if val < self.val:
if self.left == None:
return False
return self.left.exists(val)
if self.right == None:
return False
return self.right.exists(val)
def preorder(self, vals):
if self.val is not None:
vals.append(self.val)
if self.left is not None:
self.left.preorder(vals)
if self.right is not None:
self.right.preorder(vals)
return vals
def inorder(self, vals):
if self.left is not None:
self.left.inorder(vals)
if self.val is not None:
vals.append(self.val)
if self.right is not None:
self.right.inorder(vals)
return vals
def postorder(self, vals):
if self.left is not None:
self.left.postorder(vals)
if self.right is not None:
self.right.postorder(vals)
if self.val is not None:
vals.append(self.val)
return vals
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