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

# Solution Notebook¶

## Constraints¶

• Can we assume we already have a Node class with an insert method?
• Yes
• What should we do with each node when we process it?
• Call an input method visit_func on the node
• Can we assume this fits in memory?
• Yes

## Test Cases¶

### In-Order Traversal¶

• 5, 2, 8, 1, 3 -> 1, 2, 3, 5, 8
• 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5

### Pre-Order Traversal¶

• 5, 2, 8, 1, 3 -> 5, 2, 1, 3, 8
• 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5

### Post-Order Traversal¶

• 5, 2, 8, 1, 3 -> 1, 3, 2, 8, 5
• 1, 2, 3, 4, 5 -> 5, 4, 3, 2, 1

## Test Cases¶

Note:

• This following are all forms of depth-first traversals

### In-Order Traversal¶

• Recursively call in-order traversal on the left child
• Visit the current node
• Recursively call in-order traversal on the right child

Complexity:

• Time: O(n)
• Space: O(m), where m is the recursion depth, or O(1) if using an iterative approach

### Pre-Order Traversal¶

• Visit the current node
• Recursively call pre-order traversal on the left child
• Recursively call pre-order traversal on the right child

Complexity:

• Time: O(n)
• Space: O(m), where m is the recursion depth, or O(1) if using an iterative approach

### Post-Order Traversal¶

• Recursively call post-order traversal on the left child
• Recursively call post-order traversal on the right child
• Visit the current node

Complexity:

• Time: O(n)
• Space: O(m), where m is the recursion depth, or O(1) if using an iterative approach

## Code¶

In [1]:
%run ../bst/bst.py

In [2]:
class BstDfs(Bst):

def in_order_traversal(self, node, visit_func):
if node is not None:
self.in_order_traversal(node.left, visit_func)
visit_func(node)
self.in_order_traversal(node.right, visit_func)

def pre_order_traversal(self, node, visit_func):
if node is not None:
visit_func(node)
self.pre_order_traversal(node.left, visit_func)
self.pre_order_traversal(node.right, visit_func)

def post_order_traversal(self, node, visit_func):
if node is not None:
self.post_order_traversal(node.left, visit_func)
self.post_order_traversal(node.right, visit_func)
visit_func(node)


## Unit Test¶

In [3]:
%run ../utils/results.py

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

class TestDfs(unittest.TestCase):

def __init__(self, *args, **kwargs):
super(TestDfs, self).__init__()
self.results = Results()

def test_dfs(self):
bst = BstDfs(Node(5))
bst.insert(2)
bst.insert(8)
bst.insert(1)
bst.insert(3)

self.assertEqual(str(self.results), "[1, 2, 3, 5, 8]")
self.results.clear_results()

self.assertEqual(str(self.results), "[5, 2, 1, 3, 8]")
self.results.clear_results()

self.assertEqual(str(self.results), "[1, 3, 2, 8, 5]")
self.results.clear_results()

bst = BstDfs(Node(1))
bst.insert(2)
bst.insert(3)
bst.insert(4)
bst.insert(5)

self.assertEqual(str(self.results), "[1, 2, 3, 4, 5]")
self.results.clear_results()

self.assertEqual(str(self.results), "[1, 2, 3, 4, 5]")
self.results.clear_results()

self.assertEqual(str(self.results), "[5, 4, 3, 2, 1]")

print('Success: test_dfs')

def main():
test = TestDfs()
test.test_dfs()

if __name__ == '__main__':
main()

Overwriting test_dfs.py

In [5]:
%run -i test_dfs.py

Success: test_dfs