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"""
Binary Search Tree data structure implemented:
--------------------------------
The Binary Search Tree represents an ordered symbol table of generic
key-value pairs. Keys must be comparable. Does not permit duplicate keys.
When assocating a value with a key already present in the BST, the previous
value is replaced by the new one. This implementation is for an unbalanced
BST.
It supports the following primary operations:
Method Description
-----------------------------------------
size Return size of BST
get Retrieve value for key in BST
put Add key-value pair to BST
contains Check if key is in BST
is_empty Check if BST is empty
min_key Get the minimum key in BST
max_key Get the maximum key in BST
floor_key Get the biggest key that is less than or equal to key
ceiling_key Get the smallest key that is greater than or equal to key
rank Get get the number of keys less than key
select_key Get the key with a given rank
delete_min Delete the key-value pair with minimum key from BST
delete_max Delete the key-value pair with maximum key from BST
delete Delete key-value pair with given key from BST
keys Get all keys in BST in ascending order
Method Worst Case Balanced Tree
-----------------------------------------
size O(1) O(1)
get O(N) O(lg N)
put O(N) O(lg N)
contains O(N) O(lg N)
is_empty O(1) O(1)
min_key O(N) O(lg N)
max_key O(N) O(lg N)
floor_key O(N) O(lg N)
ceiling_key O(N) O(lg N)
rank O(N) O(lg N)
select_key O(N) O(lg N)
delete_min O(N) O(lg N)
delete_max O(N) O(lg N)
delete O(N) O(lg N)
keys O(N) O(N)
Adapted from: http://algs4.cs.princeton.edu/32bst
"""
class Node:
def __init__(self, key=None, val=None, size_of_subtree=1):
self.key = key
self.val = val
self.size_of_subtree = size_of_subtree
self.left = None
self.right = None
class BinarySearchTree:
def __init__(self):
self.root = None
def _size(self, node):
if node == None:
return 0
else:
return node.size_of_subtree
def size(self):
'''
Return the number of nodes in the BST
'''
return self._size(self.root)
def is_empty(self):
'''
Returns True if the BST is empty, False otherwise
'''
return self.size() == 0
def _get(self, key, node):
if node == None:
return None
if key < node.key:
return self._get(key, node.left)
elif key > node.key:
return self._get(key, node.right)
else:
return node.val
def get(self, key):
'''
Return the value paired with 'key'
'''
return self._get(key, self.root)
def contains(self, key):
'''
Returns True if the BST contains 'key', False otherwise
'''
return self.get(key) != None
def _put(self, key, val, node):
# If we hit the end of a branch, create a new node
if node == None:
return Node(key, val)
# Follow left branch
if key < node.key:
node.left = self._put(key, val, node.left)
# Follow right branch
elif key > node.key:
node.right = self._put(key, val, node.right)
# Overwrite value
else:
node.val = val
node.size_of_subtree = self._size(node.left) + self._size(node.right)+1
return node
def put(self, key, val):
'''
Add a new key-value pair.
'''
self.root = self._put(key, val, self.root)
def _min_node(self):
'''
Return the node with the minimum key in the BST
'''
min_node = self.root
# Return none if empty BST
if min_node == None: return None
while min_node.left != None:
min_node = min_node.left
return min_node
def min_key(self):
'''
Return the minimum key in the BST
'''
min_node = self._min_node()
if min_node == None:
return None
else:
return min_node.key
def _max_node(self):
'''
Return the node with the maximum key in the BST
'''
max_node = self.root
# Return none if empty BST
if max_node == None: return None
while max_node.right != None:
max_node = max_node.right
return max_node
def max_key(self):
'''
Return the maximum key in the BST
'''
max_node = self._max_node()
if max_node == None:
return None
else:
return max_node.key
def _floor_node(self, key, node):
'''
Returns the node with the biggest key that is less than or equal to the
given value 'key'
'''
if node == None: return None
if key < node.key:
# Floor must be in left subtree
return self._floor_node(key, node.left)
elif key > node.key:
# Floor is either in right subtree or is this node
attempt_in_right = self._floor_node(key, node.right)
if attempt_in_right == None:
return node
else:
return attempt_in_right
else:
# Keys are equal so floor is node with this key
return node
def floor_key(self, key):
'''
Returns the biggest key that is less than or equal to the given value
'key'
'''
floor_node = self._floor_node(key, self.root)
if floor_node == None:
return None
else:
return floor_node.key
def _ceiling_node(self, key, node):
'''
Returns the node with the smallest key that is greater than or equal to
the given value 'key'
'''
if node == None:
return None
if key < node.key:
# Ceiling is either in left subtree or is this node
attempt_in_left = self._ceiling_node(key, node.left)
if attempt_in_left == None:
return node
else:
return attempt_in_left
elif key > node.key:
# Ceiling must be in right subtree
return self._ceiling_node(key, node.right)
else:
# Keys are equal so ceiling is node with this key
return node
def ceiling_key(self, key):
'''
Returns the smallest key that is greater than or equal to the given
value 'key'
'''
ceiling_node = self._ceiling_node(key, self.root)
if ceiling_node == None:
return None
else:
return ceiling_node.key
def _select_node(self, rank, node):
'''
Return the node with rank equal to 'rank'
'''
if node == None:
return None
left_size = self._size(node.left)
if left_size < rank:
return self._select_node(rank - left_size - 1, node.right)
elif left_size > rank:
return self._select_node(rank, node.left)
else:
return node
def select_key(self, rank):
'''
Return the key with rank equal to 'rank'
'''
select_node = self._select_node(rank, self.root)
if select_node == None:
return None
else:
return select_node.key
def _rank(self, key, node):
if node == None: return None
if key < node.key:
return self._rank(key, node.left)
elif key > node.key:
return self._size(node.left) + self._rank(key, node.right) + 1
else:
return self._size(node.left)
def rank(self, key):
'''
Return the number of keys less than a given 'key'.
'''
return self._rank(key, self.root)
def _delete(self, key, node):
if node == None:
return None
if key < node.key:
node.left = self._delete(key, node.left)
elif key > node.key:
node.right = self._delete(key, node.right)
else:
if node.right == None:
return node.left
elif node.left == None:
return node.right
else:
old_node = node
node = self._ceiling_node(key, node.right)
node.right = self._delete_min(old_node.right)
node.left = old_node.left
node.size_of_subtree = self._size(node.left) + self._size(node.right)+1
return node
def delete(self, key):
'''
Remove the node with key equal to 'key'
'''
self.root = self._delete(key, self.root)
def _delete_min(self, node):
if node.left == None:
return node.right
node.left = self._delete_min(node.left)
node.size_of_subtree = self._size(node.left) + self._size(node.right)+1
return node
def delete_min(self):
'''
Remove the key-value pair with the smallest key.
'''
self.root = self._delete_min(self.root)
def _delete_max(self, node):
if node.right == None:
return node.left
node.right = self._delete_max(node.right)
node.size_of_subtree = self._size(node.left) + self._size(node.right)+1
return node
def delete_max(self):
'''
Remove the key-value pair with the largest key.
'''
self.root = self._delete_max(self.root)
def _keys(self, node, keys):
if node == None:
return keys
if node.left != None:
keys = self._keys(node.left, keys)
keys.append(node.key)
if node.right != None:
keys = self._keys(node.right, keys)
return keys
def keys(self):
'''
Return all of the keys in the BST in aschending order
'''
keys = []
return self._keys(self.root, keys)