Question

(Please help me with Coding in Python3)

AVLTree

complete the following implementation of the balanced (AVL) binary search tree. Note that you should not be implementing the map-based API described in the plain (unbalanced) BSTree notebook — i.e., nodes in the AVLTree will only contain a single value.

class AVLTree:
class Node:
def __init__(self, val, left=None, right=None):
self.val = val
self.left = left
self.right = right

def rotate_right(self):
n = self.left
self.val, n.val = n.val, self.val
self.left, n.left, self.right, n.right = n.left, n.right, n, self.right
  
def rotate_left(self):
# YOUR CODE HERE
raise NotImplementedError()
  
@staticmethod
def height(n):
if not n:
return 0
else:
return max(1+AVLTree.Node.height(n.left), 1+AVLTree.Node.height(n.right))

def __init__(self):
self.size = 0
self.root = None
  
@staticmethod
def rebalance(t):
# YOUR CODE HERE
raise NotImplementedError()
  
def add(self, val):
assert(val not in self)
# YOUR CODE HERE
raise NotImplementedError()
  
def __delitem__(self, val):
assert(val in self)
# YOUR CODE HERE
raise NotImplementedError()
  
def __contains__(self, val):
def contains_rec(node):
if not node:
return False
elif val < node.val:
return contains_rec(node.left)
elif val > node.val:
return contains_rec(node.right)
else:
return True
return contains_rec(self.root)
  
def __len__(self):
return self.size
  
def __iter__(self):
def iter_rec(node):
if node:
yield from iter_rec(node.left)
yield node.val
yield from iter_rec(node.right)
yield from iter_rec(self.root)
  
def pprint(self, width=64):
"""Attempts to pretty-print this tree's contents."""
height = self.height()
nodes = [(self.root, 0)]
prev_level = 0
repr_str = ''
while nodes:
n,level = nodes.pop(0)
if prev_level != level:
prev_level = level
repr_str += '\n'
if not n:
if level < height-1:
nodes.extend([(None, level+1), (None, level+1)])
repr_str += '{val:^{width}}'.format(val='-', width=width//2**level)
elif n:
if n.left or level < height-1:
nodes.append((n.left, level+1))
if n.right or level < height-1:
nodes.append((n.right, level+1))
repr_str += '{val:^{width}}'.format(val=n.val, width=width//2**level)
print(repr_str)
  
def height(self):
"""Returns the height of the longest branch of the tree."""
def height_rec(t):
if not t:
return 0
else:
return max(1+height_rec(t.left), 1+height_rec(t.right))
return height_rec(self.root)

LL-fix (simple) test
# 3 points

from unittest import TestCase

def height(t):
if not t:
return 0
else:
return max(1+height(t.left), 1+height(t.right))

tc = TestCase()
t = AVLTree()

for x in [3, 2, 1]:
t.add(x)
  
tc.assertEqual(height(t.root), 2)
tc.assertEqual([t.root.left.val, t.root.val, t.root.right.val], [1, 2, 3])

# RR-fix (simple) test
# 3 points

from unittest import TestCase

def height(t):
if not t:
return 0
else:
return max(1+height(t.left), 1+height(t.right))

tc = TestCase()
t = AVLTree()

for x in [1, 2, 3]:
t.add(x)
  
tc.assertEqual(height(t.root), 2)
tc.assertEqual([t.root.left.val, t.root.val, t.root.right.val], [1, 2, 3])

# LR-fix (simple) test
# 3 points

from unittest import TestCase

def height(t):
if not t:
return 0
else:
return max(1+height(t.left), 1+height(t.right))

tc = TestCase()
t = AVLTree()

for x in [3, 1, 2]:
t.add(x)
  
tc.assertEqual(height(t.root), 2)
tc.assertEqual([t.root.left.val, t.root.val, t.root.right.val], [1, 2, 3])

# RL-fix (simple) test
# 3 points

from unittest import TestCase

def height(t):
if not t:
return 0
else:
return max(1+height(t.left), 1+height(t.right))

tc = TestCase()
t = AVLTree()

for x in [1, 3, 2]:
t.add(x)
  
tc.assertEqual(height(t.root), 2)
tc.assertEqual([t.root.left.val, t.root.val, t.root.right.val], [1, 2, 3])

# ensure key order is maintained after insertions and removals
# 15 points

from unittest import TestCase
import random

tc = TestCase()
vals = list(range(0, 100000000, 333333))
random.shuffle(vals)

t = AVLTree()
for x in vals:
t.add(x)

for _ in range(len(vals) // 3):
to_rem = vals.pop(random.randrange(len(vals)))
del t[to_rem]

vals.sort()

for i,val in enumerate(t):
tc.assertEqual(val, vals[i])

# stress testing
# 15 points

from unittest import TestCase
import random

tc = TestCase()

def traverse(t, fn):
if t:
fn(t)
traverse(t.left, fn)
traverse(t.right, fn)

def height(t):
if not t:
return 0
else:
return max(1+height(t.left), 1+height(t.right))
  
def check_balance(t):
tc.assertLess(abs(height(t.left) - height(t.right)), 2, 'Tree is out of balance')

t = AVLTree()
vals = list(range(1000))
random.shuffle(vals)
for i in range(len(vals)):
t.add(vals[i])
for x in vals[:i+1]:
tc.assertIn(x, t, 'Element added not in tree')
traverse(t.root, check_balance)

random.shuffle(vals)
for i in range(len(vals)):
del t[vals[i]]
for x in vals[i+1:]:
tc.assertIn(x, t, 'Incorrect element removed from tree')
for x in vals[:i+1]:
tc.assertNotIn(x, t, 'Element removed still in tree')
traverse(t.root, check_balance)

Answer 1

class AVLTree:
    class Node:
        def __init__(self, val, left=None, right=None):
            self.val = val
            self.left = left
            self.right = right

        def rotate_right(self):
            n = self.left
            self.val, n.val = n.val, self.val
            self.left, n.left, self.right, n.right = n.left, n.right, n, self.right

        def rotate_left(self):
            n = self.right
            self.val, n.val = n.val, self.val
            self.right, n.right, self.left, n.left = n.right, n.left, n, self.left

        @staticmethod
        def height(n):
            if not n:
                return 0
            else:
                return max(1 + AVLTree.Node.height(n.left), 1 + AVLTree.Node.height(n.right))

    def __init__(self):
        self.size = 0
        self.root = None

    @staticmethod
    def rebalance(t):
        if AVLTree.Node.height(t.left) > AVLTree.Node.height(t.right):
            if AVLTree.Node.height(t.left.left) >= AVLTree.Node.height(t.left.right): # LL
                t.rotate_right()
            else:
                t.left.rotate_left()
                t.rotate_right()
        else:
            if AVLTree.Node.height(t.right.right) >= AVLTree.Node.height(t.right.left): # RR
                t.rotate_left()
            else:
                t.right.rotate_right()
                t.rotate_left()

    def add(self, val):
        assert (val not in self)

        def add_rec(node):
            if not node:
                return AVLTree.Node(val)
            elif val < node.val:
                node.left = add_rec(node.left)
            elif val > node.val:
                node.right = add_rec(node.right)
            if abs(AVLTree.Node.height(node.left) - AVLTree.Node.height(node.right)) >= 2:
                AVLTree.rebalance(node)
            return node

        self.root = add_rec(self.root)
        self.size += 1

    def __delitem__(self, val):
        assert (val in self)
        rebal = []

        def delitem_rec(node):
            if val < node.val:
                node.left = delitem_rec(node.left)
            elif val > node.val:
                node.right = delitem_rec(node.right)
            else:
                if not node.left and not node.right:
                    return None
                elif node.left and not node.right:
                    return node.left
                elif node.right and not node.left:
                    return node.right
                else:
                    # remove the largest value from the left subtree (t) as a replacement
                    # for the root value of this tree
                    t = node.left
                    rebal.append(t)

                    if not t.right:
                        node.val = t.val
                        node.left = t.left
                    else:
                        n = t
                        while n.right.right:
                            n = n.right
                            rebal.append(n)
                        rebal.append(n)
                        t = n.right
                        n.right = t.left
                        node.val = t.val

                while rebal:
                    s = rebal.pop()
                    if abs(AVLTree.Node.height(s.left) - AVLTree.Node.height(s.right)) >= 2:
                        AVLTree.rebalance(s)

            if abs(AVLTree.Node.height(node.left) - AVLTree.Node.height(node.right)) >= 2:
                AVLTree.rebalance(node)
            return node

        self.root = delitem_rec(self.root)
        self.size -= 1

    def __contains__(self, val):
        def contains_rec(node):
            if not node:
                return False
            elif val < node.val:
                return contains_rec(node.left)
            elif val > node.val:
                return contains_rec(node.right)
            else:
                return True

        return contains_rec(self.root)

    def __len__(self):
        return self.size

    def __iter__(self):
        def iter_rec(node):
            if node:
                yield from iter_rec(node.left)
                yield node.val
                yield from iter_rec(node.right)

        yield from iter_rec(self.root)

    def pprint(self, width=64):
        """Attempts to pretty-print this tree's contents."""
        height = self.height()
        nodes = [(self.root, 0)]
        prev_level = 0
        repr_str = ''
        while nodes:
            n, level = nodes.pop(0)
            if prev_level != level:
                prev_level = level
                repr_str += '\n'
            if not n:
                if level < height - 1:
                    nodes.extend([(None, level + 1), (None, level + 1)])
                repr_str += '{val:^{width}}'.format(val='-', width=width // 2 ** level)
            elif n:
                if n.left or level < height - 1:
                    nodes.append((n.left, level + 1))
                if n.right or level < height - 1:
                    nodes.append((n.right, level + 1))
                repr_str += '{val:^{width}}'.format(val=n.val, width=width // 2 ** level)
        print(repr_str)

    def height(self):
        """Returns the height of the longest branch of the tree."""

        def height_rec(t):
            if not t:
                return 0
            else:
                return max(1 + height_rec(t.left), 1 + height_rec(t.right))

        return height_rec(self.root)