def build_min_height_bst_from_sorted_subarray(start, end):
if start >= end:
return None
mid = (start + end) // 2
return BstNode(A[mid],
build_min_height_bst_from_sorted_subarray(start, mid),
build_min_height_bst_from_sorted_subarray(mid + 1, end))
def build_min_height_bst_from_sorted_array(A: List[int]) -> Optional[BstNode]:
if not A:
return None
return BstNode(
A[len(A) // 2],
left=build_min_height_bst_from_sorted_array(A[:len(A) // 2]),
right=build_min_height_bst_from_sorted_array(A[len(A) // 2 + 1:]))
def build_tree(l: int, r: int) -> Optional[BstNode]:
if r < l: return None
m = (l + r) // 2
root: BstNode = BstNode(A[m])
root.left = build_tree(l, m - 1)
root.right = build_tree(m + 1, r)
return root
def build_tree(start, end):
if start > end:
return None
root_val = preorder_sequence[start]
right_index = start + 1
while right_index <= end:
if preorder_sequence[right_index] > root_val:
break
right_index += 1
tree = BstNode(root_val)
tree.left = build_tree(start + 1, right_index - 1)
tree.right = build_tree(right_index, end)
return tree
def build_min_height_bst_from_sorted_array(A):
if len(A) == 0:
return None
n = len(A)
return BstNode(A[n // 2],
build_min_height_bst_from_sorted_array(A[:n // 2]),
build_min_height_bst_from_sorted_array(A[n // 2 + 1:]))
def build_bst(start=0, end=len(A)-1):
if start > end:
return None
m = (start + end) // 2
left = build_bst(start, m - 1)
right = build_bst(m + 1, end)
return BstNode(A[m], left, right)
def build_min_height_bst_from_sorted_array(A):
# SOS!!! check exactly the limits of the subarrays!
if not A:
return None
head_idx = len(A) // 2
return BstNode(A[head_idx],
build_min_height_bst_from_sorted_array(A[:head_idx]),
build_min_height_bst_from_sorted_array(A[head_idx + 1:]))
def make(lower_bound, upper_bound):
if index[0] == len(preorder_sequence):
return None
root = preorder_sequence[index[0]]
if not lower_bound <= root <= upper_bound:
return None
index[0] += 1
L = make(lower_bound, root)
R = make(root, upper_bound)
return BstNode(root, L, R)
def rebuild_bst_from_preorder(preorder_sequence):
if not preorder_sequence:
return None
point = next((i for i, val in enumerate(preorder_sequence)
if val > preorder_sequence[0]),
len(preorder_sequence))
return BstNode(preorder_sequence[0],
rebuild_bst_from_preorder(preorder_sequence[1:point]),
rebuild_bst_from_preorder(preorder_sequence[point:]))
def rebuild_bst_from_preorder(preorder_sequence):
if not preorder_sequence:
return None
transition_point = next((i for i, a in enumerate(preorder_sequence)
if a > preorder_sequence[0]),
len(preorder_sequence))
return BstNode(
preorder_sequence[0],
rebuild_bst_from_preorder(preorder_sequence[1:transition_point]),
rebuild_bst_from_preorder(preorder_sequence[transition_point:]))
def build_min_height_bst_from_sorted_array(A: List[int]) -> Optional[BstNode]:
if len(A) == 0:
return None
root_idx = len(A) // 2
root = A[root_idx]
left_list = A[:root_idx]
right_list = A[root_idx + 1:]
left_subtree = build_min_height_bst_from_sorted_array(left_list)
right_subtree = build_min_height_bst_from_sorted_array(right_list)
return BstNode(root, left_subtree, right_subtree)
def helper(root_idx, lower_bound, upper_bound):
if root_idx >= len(preorder_sequence):
return None
elif not lower_bound <= preorder_sequence[root_idx] <= upper_bound:
return None
root = preorder_sequence[root_idx]
root_idx += 1
return BstNode(
root,
helper(root_idx, lower_bound, root),
helper(root_idx, root, upper_bound),
)
def rebuild_bst_from_preorder(
preorder_sequence: List[int]) -> Optional[BstNode]:
if len(preorder_sequence) == 0: return None
root = BstNode(preorder_sequence[0])
searchPath = deque([root], maxlen=len(preorder_sequence))
i = 1
while i < len(preorder_sequence):
if preorder_sequence[i] < preorder_sequence[i - 1]:
node = BstNode(preorder_sequence[i])
searchPath[-1].left = node
searchPath.append(node)
else:
node = searchPath.pop()
while len(
searchPath) and searchPath[-1].data < preorder_sequence[i]:
node = searchPath.pop()
right = BstNode(preorder_sequence[i])
node.right = right
searchPath.append(right)
i += 1
return root
def binary_tree_from_preorder_inorder(preorder, inorder):
# for a preorder traversal, the first element is the root,
# followed by a set of elements for the left subtree then the right
# the set of left subtree elements in the preorder traversal can be determined by
# using the root element to divide the inorder traversal elements into
# left and right subtree elements,
# the left subtree elements in the inorder traversal is the elements that
# preceeds the root element in the inorder traversal
if not preorder:
return None
root_val = preorder[0]
root = BstNode(root_val)
inorder_root_index = inorder.index(root_val)
inorder_left_tree = inorder[:inorder_root_index]
inorder_right_tree = inorder[inorder_root_index + 1:]
preorder_left_tree = preorder[1:(len(inorder_left_tree) + 1)] #skip root
preorder_right_tree = preorder[(len(inorder_left_tree) + 1):]
root.left = binary_tree_from_preorder_inorder(preorder_left_tree,
inorder_left_tree)
root.right = binary_tree_from_preorder_inorder(preorder_right_tree,
inorder_right_tree)
return root
def rebuild_bst_from_preorder_on_value_range(lower_bound, upper_bound):
if root_idx[0] == len(preorder_sequence):
return None
root = preorder_sequence[root_idx[0]]
if not lower_bound <= root <= upper_bound:
return None
root_idx[0] += 1
left_subtree = rebuild_bst_from_preorder_on_value_range(
lower_bound, root)
right_subtree = rebuild_bst_from_preorder_on_value_range(
root, upper_bound)
return BstNode(root, left_subtree, right_subtree)
def rebuild_bst_from_preorder_on_value_range(lower_bound, upper_bound):
if root_idx[0] == len(preorder_sequence):
return None
root = preorder_sequence[root_idx[0]]
if not lower_bound <= root <= upper_bound:
return None
root_idx[0] += 1
# Note that rebuild_bst_from_preorder_on_value_range updates root_idx[0]
# So the order of following two calls are critical
left_subtree = rebuild_bst_from_preorder_on_value_range(
lower_bound, root)
right_subtree = rebuild_bst_from_preorder_on_value_range(
root, upper_bound)
return BstNode(root, left_subtree, right_subtree)
def reconstruct(lower_bound, upper_bound):
if root_idx[0] == len(preorder_sequence):
return None
root = preorder_sequence[root_idx[0]]
if not (lower_bound < root < upper_bound):
return None
root_idx[0] += 1
left_subtree = reconstruct(lower_bound, root)
right_subtree = reconstruct(root, upper_bound)
return BstNode(root, left_subtree, right_subtree)
def reconstruct(preorder_start, preorder_end):
if preorder_start > preorder_end:
return None
root = preorder_sequence[preorder_start]
# Find idx where val > root
partition_idx = preorder_start
for i in range(preorder_start + 1, preorder_end + 1):
if preorder_sequence[i] < root:
partition_idx = i
else:
break
return BstNode(root, reconstruct(preorder_start + 1, partition_idx),
reconstruct(partition_idx + 1, preorder_end))
def merge_two_sorted_lists(A, B):
sorted_head = BstNode()
tail = sorted_head
AB = [A, B]
while all(AB):
A_or_B = 0 if AB[0].data < AB[1].data else 1
tail.right = AB[A_or_B]
tail = tail.right # Resets tail to the last node.
AB[A_or_B] = tail.right
if AB[0]: # Appends the remaining of A.
tail.right = AB[0]
elif AB[1]: # Appends the remaining of B.
tail.right = AB[1]
return sorted_head.right
def build_bst(lower_bound=-float('inf'), upper_bound=+float('inf')):
nonlocal root_idx
if root_idx >= len(preorder_sequence):
return None
root = preorder_sequence[root_idx]
if not lower_bound < root < upper_bound:
return None
root_idx += 1
left = build_bst(lower_bound, root)
right = build_bst(root, upper_bound)
return BstNode(root, left, right)
def find_k_largest_in_bst(tree: BstNode, k: int) -> List[int]:
#Reverse inorder traversal (sorta)
path = []
stack = [tree]
while k != 0 and stack:
tree = stack.pop()
if tree:
if tree.left:
stack.append(tree.left)
if not tree.right:
#Current node is the right most value
path.append(tree.data)
k -= 1
else:
#Keeping going right, but save the current node too
right = tree.right
tree.left, tree.right = None, None #Prune the tree
stack.append(tree)
stack.append(right)
return path
from test_framework import generic_test
from bst_node import BstNode
left_left = BstNode(4)
left_right = BstNode(5)
left = BstNode(1, left_left, left_right)
right = BstNode(3)
root = BstNode(2, left, right)
print('root={}, left={}, right={}'.format(root, left, right))
root_parent_l = BstNode(6, root)
root_parent_l_parent_l = BstNode(7, root_parent_l)
result = []
def tree_traversal(tree, result, order):
# TODO - you fill in here.
if tree:
if order == -1:
print('Preorder: {}'.format(tree.data))
result.append(tree.data)
tree_traversal(tree.left, result, order)
if order == 0:
print('Inorder: {}'.format(tree.data))
result.append(tree.data)
tree_traversal(tree.right, result, order)
if order == 1:
print('Postorder: {}'.format(tree.data))
result.append(tree.data)
print('tree={}, result={}'.format(tree, result))
return result
from test_framework import generic_test
from bst_node import BstNode
# preorder = [1,2,3], inorder=[2,1,3], ["1", "2", "3"]
# preorder = [1, 2, 3, 4] inorder = [4, 3, 2, 1] ["1", "2", "null", "3", "null", "4"]
# preorder = ['H','B','F','E','A','C','D','G','I']
# inorder = ['F','B','A','E','H','C','D','I','G']
pl = ['B', 'F', 'E', 'A']
il = ['F', 'B', 'A', 'E']
pr = ['C', 'D', 'G', 'I']
ir = ['C', 'D', 'I', 'G']
# left subtree
a = BstNode('A')
e = BstNode('E', a)
f = BstNode('F')
b = BstNode('B', f, e)
# right subtree
i = BstNode('I')
g = BstNode('G', i)
d = BstNode('D', None, g)
c = BstNode('C', None, d)
h = BstNode('H', b, c)
def x_binary_tree_from_preorder_inorder(preorder, inorder):
def reconstruct_tree(preorder, inorder):
# TODO - you fill in here.
# 1. root is first node in preorder traversal
# 2. use root to divide inorder traversal into left and right subtrees (inorder)
# 3. use (left,right) inorder traversal set to partition preorder traversal
def getRoot(A, low, high):
if low > high:
return None
mid = low + ((high - low) // 2)
return BstNode(A[mid], getRoot(A, low, mid - 1), getRoot(A, mid + 1, high))
from test_framework import generic_test
from bst_node import BstNode
left_left = BstNode(2)
left_right = BstNode(4)
left = BstNode(3, left_left, left_right)
right = BstNode(6)
root = BstNode(5, left, right)
print('root={}, left={}, right={}'.format(root, left, right))
def tree_traversal(tree, order, result):
# TODO - you fill in here.
# print('tree_traversal,tree={},result={},order={}'.format(tree, result, order))
if tree:
if order == -1:
# print('Preorder: {}'.format(tree.data))
result.append(tree.data)
tree_traversal(tree.left, order, result)
if order == 0:
# print('Inorder: {}'.format(tree.data))
result.append(tree.data)
tree_traversal(tree.right, order, result)
if order == 1:
# print('Postorder: {}'.format(tree.data))
result.append(tree.data)
# print('result={}'.format(result))
return result
def preorder_traversal(tree):
def helper(i, j):
if i < j:
m = (j + i) // 2
return BstNode(A[m], helper(i, m), helper(m + 1, j))
