A straightforward red-black tree implementation based on the algorithms in the "Introduction to Algorithms" book by Cormen, Leiserson, Rivest, Stein. Unfortunately I have not needed delete functionality so this is not implemented yet.
Python, 300 lines
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"""
A node in a red black tree. See Cormen, Leiserson, Rivest, Stein 2nd edition pg 273.
"""
def __init__(self, key):
"Construct."
self._key = key
self._red = False
self._left = None
self._right = None
self._p = None
key = property(fget=lambda self: self._key, doc="The node's key")
red = property(fget=lambda self: self._red, doc="Is the node red?")
left = property(fget=lambda self: self._left, doc="The node's left child")
right = property(fget=lambda self: self._right, doc="The node's right child")
p = property(fget=lambda self: self._p, doc="The node's parent")
def __str__(self):
"String representation."
return str(self.key)
def __repr__(self):
"String representation."
return str(self.key)
class rbtree(object):
"""
A red black tree. See Cormen, Leiserson, Rivest, Stein 2nd edition pg 273.
"""
def __init__(self, create_node=rbnode):
"Construct."
self._nil = create_node(key=None)
"Our nil node, used for all leaves."
self._root = self.nil
"The root of the tree."
self._create_node = create_node
"A callable that creates a node."
root = property(fget=lambda self: self._root, doc="The tree's root node")
nil = property(fget=lambda self: self._nil, doc="The tree's nil node")
def search(self, key, x=None):
"""
Search the subtree rooted at x (or the root if not given) iteratively for the key.
@return: self.nil if it cannot find it.
"""
if None == x:
x = self.root
while x != self.nil and key != x.key:
if key < x.key:
x = x.left
else:
x = x.right
return x
def minimum(self, x=None):
"""
@return: The minimum value in the subtree rooted at x.
"""
if None == x:
x = self.root
while x.left != self.nil:
x = x.left
return x
def maximum(self, x=None):
"""
@return: The maximum value in the subtree rooted at x.
"""
if None == x:
x = self.root
while x.right != self.nil:
x = x.right
return x
def insert_key(self, key):
"Insert the key into the tree."
self.insert_node(self._create_node(key=key))
def insert_node(self, z):
"Insert node z into the tree."
y = self.nil
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 == self.nil:
self._root = z
elif z.key < y.key:
y._left = z
else:
y._right = z
z._left = self.nil
z._right = self.nil
z._red = True
self._insert_fixup(z)
def _insert_fixup(self, z):
"Restore red-black properties after insert."
while z.p.red:
if z.p == z.p.p.left:
y = z.p.p.right
if y.red:
z.p._red = False
y._red = False
z.p.p._red = True
z = z.p.p
else:
if z == z.p.right:
z = z.p
self._left_rotate(z)
z.p._red = False
z.p.p._red = True
self._right_rotate(z.p.p)
else:
y = z.p.p.left
if y.red:
z.p._red = False
y._red = False
z.p.p._red = True
z = z.p.p
else:
if z == z.p.left:
z = z.p
self._right_rotate(z)
z.p._red = False
z.p.p._red = True
self._left_rotate(z.p.p)
self.root._red = False
def _left_rotate(self, x):
"Left rotate x."
y = x.right
x._right = y.left
if y.left != self.nil:
y.left._p = x
y._p = x.p
if x.p == self.nil:
self._root = y
elif x == x.p.left:
x.p._left = y
else:
x.p._right = y
y._left = x
x._p = y
def _right_rotate(self, y):
"Left rotate y."
x = y.left
y._left = x.right
if x.right != self.nil:
x.right._p = y
x._p = y.p
if y.p == self.nil:
self._root = x
elif y == y.p.right:
y.p._right = x
else:
y.p._left = x
x._right = y
y._p = x
def check_invariants(self):
"@return: True iff satisfies all criteria to be red-black tree."
def is_red_black_node(node):
"@return: num_black"
# check has _left and _right or neither
if (node.left and not node.right) or (node.right and not node.left):
return 0, False
# check leaves are black
if not node.left and not node.right and node.red:
return 0, False
# if node is red, check children are black
if node.red and node.left and node.right:
if node.left.red or node.right.red:
return 0, False
# descend tree and check black counts are balanced
if node.left and node.right:
# check children's parents are correct
if self.nil != node.left and node != node.left.p:
return 0, False
if self.nil != node.right and node != node.right.p:
return 0, False
# check children are ok
left_counts, left_ok = is_red_black_node(node.left)
if not left_ok:
return 0, False
right_counts, right_ok = is_red_black_node(node.right)
if not right_ok:
return 0, False
# check children's counts are ok
if left_counts != right_counts:
return 0, False
return left_counts, True
else:
return 0, True
num_black, is_ok = is_red_black_node(self.root)
return is_ok and not self.root._red
def write_tree_as_dot(t, f, show_nil=False):
"Write the tree in the dot language format to f."
def node_id(node):
return 'N%d' % id(node)
def node_color(node):
if node.red:
return "red"
else:
return "black"
def visit_node(node):
"Visit a node."
print >> f, " %s [label=\"%s\", color=\"%s\"];" % (node_id(node), node, node_color(node))
if node.left:
if node.left != t.nil or show_nil:
visit_node(node.left)
print >> f, " %s -> %s ;" % (node_id(node), node_id(node.left))
if node.right:
if node.right != t.nil or show_nil:
visit_node(node.right)
print >> f, " %s -> %s ;" % (node_id(node), node_id(node.right))
print >> f, "// Created by rbtree.write_dot()"
print >> f, "digraph red_black_tree {"
visit_node(t.root)
print >> f, "}"
def test_tree(t, keys):
"Insert keys one by one checking invariants and membership as we go."
assert t.check_invariants()
for i, key in enumerate(keys):
for key2 in keys[:i]:
assert t.nil != t.search(key2)
for key2 in keys[i:]:
assert (t.nil == t.search(key2)) ^ (key2 in keys[:i])
t.insert_key(key)
assert t.check_invariants()
if '__main__' == __name__:
import os, sys, numpy.random as R
def write_tree(t, filename):
"Write the tree as an SVG file."
f = open('%s.dot' % filename, 'w')
write_tree_as_dot(t, f)
f.close()
os.system('dot %s.dot -Tsvg -o %s.svg' % (filename, filename))
# test the rbtree
R.seed(2)
size=50
keys = R.randint(-50, 50, size=size)
t = rbtree()
test_tree(t, keys)
write_tree(t, 'tree')
|
Thanks. Any benchmarks?
I'm afraid I didn't benchmark it. What would you have liked to have seen it benchmarked against? set? The tree as it stands is more like a multiset.
I implemented it to solve a problem that was way too slow when I coded it using the built-in data types. This tree was easily quick enough. For the record what I needed was an augmented red-black tree that worked on intervals (see Cormen, Leiserson, Rivest, Stein 2nd edition pg 311). Augmenting the tree was relatively straightforward.
Your test does not count the number of black nodes.
Hi John,
I have used your code and commented it a bit: https://github.com/MartinThoma/algorithms/blob/master/datastructures/redBlackTree.py
I've changed your check_invariants and added a check if the red-black-tree is still a search tree.
I've also added a method for deletion which does NOT work by now. I'm still working on it.
(See http://www.d.umn.edu/~ddunham/cs4521f10/notes/ch13.txt for notes on the code)
I got it work :-)
Currently I only have 93% branch coverage. 18 statements are missing and 14 are only partially executed. See http://www.martin-thoma.de/redblacktree/htmlcov/redBlackTree.html for the report.
Does anybody know some testcases to get 100%?
Great! Thanks for taking the time to improve it so much.
A word of caution: this implementation is likely very, very slow.
If you need to maintain a sorted list, dict, or set, check out the Python sortedcontainers module. It's pure-Python and fast-as-C implementations. There's a performance comparison page with benchmark results and a discussion of alternative implementations.