019f8fd211
git-subtree-dir: users/wpcarro git-subtree-mainline:464bbcb15cgit-subtree-split:24f5a642afChange-Id: I6105b3762b79126b3488359c95978cadb3efa789
145 lines
4.2 KiB
Python
145 lines
4.2 KiB
Python
import unittest
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from itertools import combinations
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def balanced(xs):
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"""Return True if `xs` contains no two values that differ by more than
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one."""
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if len(xs) == 0 or len(xs) == 1:
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return True
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if len(xs) == 2:
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return math.abs(xs[0] - xs[1]) <= 1
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else:
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pass
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def is_leaf(node):
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return node.left is None and node.right is None
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def is_balanced(tree_root):
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"""Returns True if the difference between the depths of any two leaf nodes
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does not exceed 1."""
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depths = set()
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populate_depths(tree_root, 0, depths)
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# cartesian product - only the top half
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for diff in set(abs(a - b) for a, b in combinations(depths, 2)):
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if diff > 1:
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return False
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return True
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def populate_depths(node, depth, depths):
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if is_leaf(node):
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depths.add(depth)
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else:
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if node.left is not None:
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populate_depths(node.left, depth + 1, depths)
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if node.right is not None:
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populate_depths(node.right, depth + 1, depths)
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################################################################################
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# Tests
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################################################################################
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class Test(unittest.TestCase):
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class BinaryTreeNode(object):
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def __init__(self, value):
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self.value = value
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self.left = None
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self.right = None
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def insert_left(self, value):
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self.left = Test.BinaryTreeNode(value)
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return self.left
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def insert_right(self, value):
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self.right = Test.BinaryTreeNode(value)
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return self.right
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def test_full_tree(self):
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tree = Test.BinaryTreeNode(5)
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left = tree.insert_left(8)
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right = tree.insert_right(6)
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left.insert_left(1)
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left.insert_right(2)
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right.insert_left(3)
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right.insert_right(4)
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result = is_balanced(tree)
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self.assertTrue(result)
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def test_both_leaves_at_the_same_depth(self):
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tree = Test.BinaryTreeNode(3)
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left = tree.insert_left(4)
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right = tree.insert_right(2)
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left.insert_left(1)
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right.insert_right(9)
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result = is_balanced(tree)
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self.assertTrue(result)
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def test_leaf_heights_differ_by_one(self):
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tree = Test.BinaryTreeNode(6)
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left = tree.insert_left(1)
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right = tree.insert_right(0)
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right.insert_right(7)
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result = is_balanced(tree)
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self.assertTrue(result)
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def test_leaf_heights_differ_by_two(self):
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tree = Test.BinaryTreeNode(6)
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left = tree.insert_left(1)
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right = tree.insert_right(0)
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right_right = right.insert_right(7)
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right_right.insert_right(8)
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result = is_balanced(tree)
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self.assertFalse(result)
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def test_three_leaves_total(self):
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tree = Test.BinaryTreeNode(1)
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left = tree.insert_left(5)
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right = tree.insert_right(9)
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right.insert_left(8)
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right.insert_right(5)
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result = is_balanced(tree)
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self.assertTrue(result)
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def test_both_subtrees_superbalanced(self):
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tree = Test.BinaryTreeNode(1)
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left = tree.insert_left(5)
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right = tree.insert_right(9)
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right_left = right.insert_left(8)
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right.insert_right(5)
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right_left.insert_left(7)
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result = is_balanced(tree)
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self.assertFalse(result)
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def test_both_subtrees_superbalanced_two(self):
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tree = Test.BinaryTreeNode(1)
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left = tree.insert_left(2)
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right = tree.insert_right(4)
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left.insert_left(3)
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left_right = left.insert_right(7)
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left_right.insert_right(8)
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right_right = right.insert_right(5)
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right_right_right = right_right.insert_right(6)
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right_right_right.insert_right(9)
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result = is_balanced(tree)
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self.assertFalse(result)
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def test_only_one_node(self):
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tree = Test.BinaryTreeNode(1)
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result = is_balanced(tree)
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self.assertTrue(result)
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def test_linked_list_tree(self):
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tree = Test.BinaryTreeNode(1)
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right = tree.insert_right(2)
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right_right = right.insert_right(3)
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right_right.insert_right(4)
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result = is_balanced(tree)
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self.assertTrue(result)
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unittest.main(verbosity=2)
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