This notebook was prepared by Donne Martin. Source and license info is on GitHub.

# Solution Notebook¶

## Constraints¶

• Is this a binary search tree?
• Yes
• Should each level be a list of nodes?
• Yes
• Can we assume we already have a Node class with an insert method?
• Yes
• Can we assume this fits memory?
• Yes

## Test Cases¶

• 5, 3, 8, 2, 4, 1, 7, 6, 9, 10, 11 -> [[5], [3, 8], [2, 4, 7, 9], [1, 6, 10], [11]]

Note: Each number in the result is actually a node containing the number

## Algorithm¶

We can use either a depth-first or a breadth-first search. Intuitively, it seems like a breadth-first search might be a better fit as we are creating a linked list for each level.

We can use a modified breadth-first search that keeps track of parents as we build the linked list for the current level.

• Append the root to the current level's linked list current
• While the current is not empty:
• Add current to results
• Set parents to current to prepare to go one level deeper
• Clear current so it can hold the next level
• For each parent in parents, add the children to current
• Return the results

Complexity:

• Time: O(n)
• Space: O(n)

## Code¶

In [1]:
%run ../bst/bst.py

In [2]:
class BstLevelLists(Bst):

def create_level_lists(self):
if self.root is None:
return
results = []
current = []
parents = []
current.append(self.root)
while current:
results.append(current)
parents = list(current)
current = []
for parent in parents:
if parent.left is not None:
current.append(parent.left)
if parent.right is not None:
current.append(parent.right)
return results


## Unit Test¶

In [3]:
%run ../utils/results.py

In [4]:
%%writefile test_tree_level_lists.py
import unittest

class TestTreeLevelLists(unittest.TestCase):

def test_tree_level_lists(self):
bst = BstLevelLists(Node(5))
bst.insert(3)
bst.insert(8)
bst.insert(2)
bst.insert(4)
bst.insert(1)
bst.insert(7)
bst.insert(6)
bst.insert(9)
bst.insert(10)
bst.insert(11)

levels = bst.create_level_lists()
results_list = []
for level in levels:
results = Results()
for node in level:
results_list.append(results)

self.assertEqual(str(results_list[0]), '[5]')
self.assertEqual(str(results_list[1]), '[3, 8]')
self.assertEqual(str(results_list[2]), '[2, 4, 7, 9]')
self.assertEqual(str(results_list[3]), '[1, 6, 10]')
self.assertEqual(str(results_list[4]), '[11]')

print('Success: test_tree_level_lists')

def main():
test = TestTreeLevelLists()
test.test_tree_level_lists()

if __name__ == '__main__':
main()

Overwriting test_tree_level_lists.py

In [5]:
%run -i test_tree_level_lists.py

Success: test_tree_level_lists