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

Solution Notebook¶

Problem: Implement depth-first traversals (in-order, pre-order, post-order) on a binary tree.¶

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

Algorithm¶

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)

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

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

        bst.post_order_traversal(bst.root, self.results.add_result)
        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)

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

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

        bst.post_order_traversal(bst.root, self.results.add_result)
        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