Insert and search for numbers in a binary tree.
When we need to represent sorted data, an array does not make a good data structure.
Say we have the array [1, 3, 4, 5], and we add 2 to it so it becomes
[1, 3, 4, 5, 2] now we must sort the entire array again! We can
improve on this by realizing that we only need to make space for the new
item [1, nil, 3, 4, 5], and then adding the item in the space we
added. But this still requires us to shift many elements down by one.
Binary Search Trees, however, can operate on sorted data much more efficiently.
A binary search tree consists of a series of connected nodes. Each node
contains a piece of data (e.g. the number 3), a variable named left,
and a variable named right. The left and right variables point at
nil, or other nodes. Since these other nodes in turn have other nodes
beneath them, we say that the left and right variables are pointing at
subtrees. All data in the left subtree is less than or equal to the
current node's data, and all data in the right subtree is greater than
the current node's data.
For example, if we had a node containing the data 4, and we added the data 2, our tree would look like this:
4
/
2
If we then added 6, it would look like this:
4
/ \
2 6
If we then added 3, it would look like this
4
/ \
2 6
\
3
And if we then added 1, 5, and 7, it would look like this
4
/ \
/ \
2 6
/ \ / \
1 3 5 7
Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.
To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
raise Exception, you should write:
raise Exception("Meaningful message indicating the source of the error")
To run the tests, run the appropriate command below (why they are different):
py.test binary_search_tree_test.py
pytest binary_search_tree_test.py
Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
python -m pytest binary_search_tree_test.py
pytest options-v : enable verbose output-x : stop running tests on first failure--ff : run failures from previous test before running other test casesFor other options, see python -m pytest -h
Note that, when trying to submit an exercise, make sure the solution is in the $EXERCISM_WORKSPACE/python/binary-search-tree directory.
You can find your Exercism workspace by running exercism debug and looking for the line that starts with Workspace.
For more detailed information about running tests, code style and linting, please see Running the Tests.
Josh Cheek https://twitter.com/josh_cheek
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
import unittest
from binary_search_tree import BinarySearchTree, TreeNode
# Tests adapted from `problem-specifications//canonical-data.json` @ v1.0.0
class BinarySearchTreeTest(unittest.TestCase):
def test_data_is_retained(self):
expected = TreeNode('4', None, None)
self.assertTreeEqual(BinarySearchTree(['4']).data(), expected)
# Test inserting data at proper node
def test_smaller_data_at_left_node(self):
expected = TreeNode('4', TreeNode('2', None, None), None)
self.assertTreeEqual(BinarySearchTree(['4', '2']).data(), expected)
def test_same_number_at_left_node(self):
expected = TreeNode('4', TreeNode('4', None, None), None)
self.assertTreeEqual(BinarySearchTree(['4', '4']).data(), expected)
def test_greater_number_at_right_node(self):
expected = TreeNode('4', None, TreeNode('5', None, None))
self.assertTreeEqual(BinarySearchTree(['4', '5']).data(), expected)
def test_can_create_complex_tree(self):
expected = TreeNode(
'4',
TreeNode(
'2',
TreeNode('1', None, None),
TreeNode('3', None, None)
),
TreeNode(
'6',
TreeNode('5', None, None),
TreeNode('7', None, None)
)
)
self.assertTreeEqual(
BinarySearchTree(['4', '2', '6', '1', '3', '5', '7']).data(),
expected
)
# Test can sort data
def test_can_sort_single_number(self):
self.assertEqual(BinarySearchTree(['2']).sorted_data(), ['2'])
def test_can_sort_if_second_number_is_smaller_than_first(self):
self.assertEqual(
BinarySearchTree(['2', '1']).sorted_data(), ['1', '2']
)
def test_can_sort_if_second_number_is_same_as_first(self):
self.assertEqual(
BinarySearchTree(['2', '2']).sorted_data(), ['2', '2']
)
def test_can_sort_if_second_number_is_greater_than_first(self):
self.assertEqual(
BinarySearchTree(['2', '3']).sorted_data(), ['2', '3']
)
def test_can_sort_complex_tree(self):
self.assertEqual(
BinarySearchTree(['2', '1', '3', '6', '7', '5']).sorted_data(),
['1', '2', '3', '5', '6', '7']
)
# Utilities
def assertTreeEqual(self, tree_one, tree_two):
try:
self.compare_tree(tree_one, tree_two)
except AssertionError:
raise AssertionError("{} != {}".format(tree_one, tree_two))
def compare_tree(self, tree_one, tree_two):
self.assertEqual(tree_one.data, tree_two.data)
# Compare left tree nodes
if tree_one.left and tree_two.left:
self.compare_tree(tree_one.left, tree_two.left)
elif tree_one.left is None and tree_two.left is None:
pass
else:
raise AssertionError
# Compare right tree nodes
if tree_one.right and tree_two.right:
self.compare_tree(tree_one.right, tree_two.right)
elif tree_one.right is None and tree_two.right is None:
pass
else:
raise AssertionError
if __name__ == '__main__':
unittest.main()class TreeNode(object):
def __init__(self, data, left, right):
self.data = data
self.left = left
self.right = right
def __str__(self):
fmt = 'TreeNode(data={}, left={}, right={})'
return fmt.format(self.data, self.left, self.right)
class BinarySearchTree(object):
def __init__(self, tree_data):
self.root = TreeNode(tree_data.pop(0), None, None)
while len(tree_data) > 0:
ptr = self.root
node = TreeNode(tree_data.pop(0), None, None)
while (ptr != None):
if ptr.data >= node.data:
next_ptr = ptr.left
if next_ptr is None:
ptr.left = node
if ptr.data < node.data:
next_ptr = ptr.right
if next_ptr is None:
ptr.right = node
ptr = next_ptr
def data(self):
return self.root
def sorted_data(self): # infix traversal
return self._inorder_traversal(self.root)
def _inorder_traversal(self, root):
if root:
left_subtree = self._inorder_traversal(root.left)
right_subtree = self._inorder_traversal(root.right)
else:
return []
return left_subtree + [root.data] + right_subtreeA huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.
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