def minimal_tree(lst):
"""time: O(n) space: O(n)"""
if not lst: return None
middle = len(lst) // 2
root = BinaryNode(lst[middle])
root.left = minimal_tree(lst[:middle])
root.right = minimal_tree(lst[middle+1:])
return root
def test_invalid_bst(fn):
# 8
# / \
# 4 10
# / \ \
# 2 12 20
n2 = BinaryNode(2)
n12 = BinaryNode(12)
n4 = BinaryNode(4, left=n2, right=n12)
n20 = BinaryNode(20)
n10 = BinaryNode(10, right=n20)
n8 = BinaryNode(8, left=n4, right=n10)
assert fn(n8) == False
def test_valid_bst(fn):
# 8
# / \
# 4 10
# / \ \
# 2 6 20
n2 = BinaryNode(2)
n6 = BinaryNode(6)
n4 = BinaryNode(4, left=n2, right=n6)
n20 = BinaryNode(20)
n10 = BinaryNode(10, right=n20)
n8 = BinaryNode(8, left=n4, right=n10)
assert fn(n8) == True
def test_list_of_depth(fn):
# 8
# / \
# 4 10
# / \ \
# 2 6 20
n2 = BinaryNode(2)
n6 = BinaryNode(6)
n4 = BinaryNode(4, left=n2, right=n6)
n20 = BinaryNode(20)
n10 = BinaryNode(10, right=n20)
n8 = BinaryNode(8, left=n4, right=n10)
levels = list_of_depths(n8)
levels = [map(lambda node: node.value, level) for level in levels]
assert levels == [[8], [4, 10], [2, 6, 20]]
def test_complex(fn):
# 3
# / \
# 2 5
# / / \
# 1 4 6
n1 = BinaryNode(1)
n2 = BinaryNode(2, left=n1)
n4 = BinaryNode(4)
n6 = BinaryNode(6)
n5 = BinaryNode(5, left=n4, right=n6)
root = BinaryNode(3, left=n2, right=n5)
assert fn(root) == True
# 3
# / \
# 2 5
# / / \
# 1 4 6
# \
# 7
n7 = BinaryNode(7)
n6.right = n7
assert fn(root) == True
# 3
# / \
# 2 5
# / / \
# 1 4 6
# \
# 7
# \
# 8
n8 = BinaryNode(8)
n7.right = n8
assert fn(root) == False
def test_degenerate(fn):
root = BinaryNode(1, right=BinaryNode(2, right=BinaryNode(3)))
assert fn(root) == False
def test_only_right_child(fn):
root = BinaryNode(1, right=BinaryNode(2))
assert fn(root) == True
def test_only_left_child(fn):
root = BinaryNode(1, left=BinaryNode(2))
assert fn(root) == True
def test_only_root(fn):
root = BinaryNode(1)
assert fn(root) == True