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[ADDED]: Red-black tree implementation

pull/911/head
Anirudh Makhana 2022-10-04 17:17:43 +07:00
parent 5d18a66cd8
commit 191c883abf
1 changed files with 364 additions and 0 deletions
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algorithms/Python/trees/red_black_tree.py 100644
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#Contributor: Anirudh Makhana (https://github.com/anirudhmakhana)
#source: https://a.co/d/7oRsCT2
#To learn more about R-B Tree: https://www.youtube.com/watch?v=qvZGUFHWChY
from collections import deque
BLACK = True
RED = False
class Node:
def __init__(self, key):
self.key = key
self.p = None # parent
self.color = RED
self.left = None
self.right = None
def print_color(self):
if self.color == BLACK:
return '(b)'
return '(r)'
class RedBlackTree:
def __init__(self):
self.NIL = Node(99999) # arbitrary value
self.NIL.color = BLACK
self.NIL.left = None
self.NIL.right = None
self.root = self.NIL
# O(1)
def left_rotate(self, x):
y = x.right
x.right = y.left
if y.left != self.NIL:
y.left.p = x
y.p = x.p
if x.p is None:
self.root = y
elif x == x.p.left:
x.p.left = y
else:
x.p.right = y
y.left = x
x.p = y
# O(1)
def right_rotate(self, x):
y = x.left
x.left = y.right
if y.right != self.NIL:
y.right.p = x
y.p = x.p
if x.p is None:
self.root = y
elif x == x.p.right:
x.p.right = y
else:
x.p.left = y
y.right = x
x.p = y
# O(logn) total
def insert(self, key):
z = Node(key)
z.left = self.NIL
z.right = self.NIL
y = None
x = self.root
while x != self.NIL:
y = x
if z.key < x.key:
x = x.left
else:
x = x.right
z.p = y
if y == None:
self.root = z
elif z.key < y.key:
y.left = z
else:
y.right = z
self.insert_fixup(z)
# O(logn)
def insert_fixup(self, z):
while z.p and z.p.color == RED:
if z.p == z.p.p.left:
y = z.p.p.right
if y.color == RED:
z.p.color = BLACK
y.color = BLACK
z.p.p.color = RED
z = z.p.p
else:
if z == z.p.right:
z = z.p
self.left_rotate(z)
z.p.color = BLACK
z.p.p.color = RED
self.right_rotate(z.p.p)
else:
y = z.p.p.left
if y.color == RED:
z.p.color = BLACK
y.color = BLACK
z.p.p.color = RED
z = z.p.p
else:
if z == z.p.left:
z = z.p
self.right_rotate(z)
z.p.color = BLACK
z.p.p.color = RED
self.left_rotate(z.p.p)
if z == self.root:
break
self.root.color = BLACK
# O(logn) total
def delete(self, k):
z = self.search(k)
if z == self.NIL:
return "Key not found!"
y = z
y_orig_color = y.color
# case 1
if z.left == self.NIL:
x = z.right
self.transplant(z, z.right)
# case 2
elif z.right == self.NIL:
x = z.left
self.transplant(z, z.left)
# case 3
else:
y = self.minimum(z.right)
y_orig_color = y.color
x = y.right
if y.p == z:
x.p = y
else:
self.transplant(y, y.right)
y.right = z.right
y.right.p = y
self.transplant(z, y)
y.left = z.left
y.left.p = y
y.color = z.color
if y_orig_color == BLACK:
self.delete_fixup(x)
# O(logn)
def delete_fixup(self, x):
while x != self.root and x.color == BLACK:
if x == x.p.left:
w = x.p.right
# type 1
if w.color == RED:
w.color = BLACK
x.p.color = RED
self.left_rotate(x.p)
w = x.p.right
# type 2
if w.left.color == BLACK and w.right.color == BLACK:
w.color = RED
x = x.p
else:
# type 3
if w.right.color == BLACK:
w.left.color = BLACK
w.color = RED
self.right_rotate(w)
w = x.p.right
# type 4
w.color = x.p.color
x.p.color = BLACK
w.right.color = BLACK
self.left_rotate(x.p)
x = self.root
else:
w = x.p.left
# type 1
if w.color == RED:
w.color = BLACK
x.p.color = RED
self.right_rotate(x.p)
w = x.p.left
# type 2
if w.right.color == BLACK and w.left.color == BLACK:
w.color = RED
x = x.p
else:
# type 3
if w.left.color == BLACK:
w.right.color = BLACK
w.color = RED
self.left_rotate(w)
w = x.p.left
# type 4
w.color = x.p.color
x.p.color = BLACK
w.left.color = BLACK
self.right_rotate(x.p)
x = self.root
x.color = BLACK
# O(1)
def transplant(self, u, v):
if u.p == None:
self.root = v
elif u == u.p.left:
u.p.left = v
else:
u.p.right = v
v.p = u.p
# O(h) = O(logn) for RB trees
def minimum(self, x):
while x.left != self.NIL:
x = x.left
return x
# O(h) = O(logn) for RB trees
def search(self, k):
x = self.root
while x != self.NIL and k != x.key:
if k < x.key:
x = x.left
else:
x = x.right
return x
# simple level-order tree traversal
def print_tree(self, print_color=False):
queue = deque()
queue.append(self.root)
while(queue):
node = queue.popleft()
if print_color:
print(f'{node.key}{node.print_color()}', end=' ')
else:
print(node.key, end=' ')
# don't add NIL nodes
if node.left != self.NIL:
queue.append(node.left)
if node.right != self.NIL:
queue.append(node.right)
def make_larger_tree():
RB = RedBlackTree()
RB.insert(8)
RB.insert(5)
RB.insert(15)
RB.insert(12)
RB.insert(19)
RB.insert(9)
RB.insert(13)
RB.insert(23)
return RB
# ignoring color, just demonstrating rotation
def rotations():
print('\n-- ROTATIONS --')
RB = RedBlackTree()
RB.insert(5)
RB.insert(2)
RB.insert(10)
RB.insert(8)
RB.insert(12)
RB.insert(6)
RB.insert(9)
RB.print_tree()
print('\n\n-- After left rotation --')
five = RB.search(5)
RB.left_rotate(five)
RB.print_tree()
print('\n\n-- After right rotation --')
ten = RB.search(10)
RB.right_rotate(ten)
RB.print_tree()
def insertions():
RB = RedBlackTree()
print('\n\n-- INSERTIONS, after case 0 --')
RB.insert(15)
RB.print_tree(True)
print('\n\n-- Insert 5 --')
RB.insert(5)
RB.print_tree(True)
print('\n\n-- Insert 1 (case 3) --')
RB.insert(1)
RB.print_tree(True)
print('\n\n-- Move to larger tree --')
RB = make_larger_tree()
RB.print_tree(True)
print('\n\n-- Insert 10 (case 1, 2, and 3) --')
RB.insert(10)
RB.print_tree(True)
def deletions():
print('\n\n-- DELETIONS --')
RB = make_larger_tree()
RB.insert(10)
RB.print_tree(True)
print('\n\n-- Delete 19 (case 1) --')
RB.delete(19)
RB.print_tree(True)
print('\n\n-- Insert 1 --')
RB.insert(1)
RB.print_tree(True)
print('\n\n-- Delete 5 (case 2) --')
RB.delete(5)
RB.print_tree(True)
print('\n\n-- Delete 12 (case 3) --')
RB.delete(12)
RB.print_tree(True)
if __name__ == '__main__':
# https://youtu.be/95s3ndZRGbk
rotations()
# https://youtu.be/A3JZinzkMpk
insertions()
#https://www.youtube.com/watch?v=lU99loSvD8s
deletions()