{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Solution Notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Implement depth-first searches (in-order, pre-order, post-order traversals) on a binary tree.\n", "\n", "* [Constraints](#Constraints)\n", "* [Test Cases](#Test-Cases)\n", "* [Algorithm](#Algorithm)\n", "* [Code](#Code)\n", "* [Unit Test](#Unit-Test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constraints\n", "\n", "* Can we assume we already have a Node class with an insert method?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "### In-Order Traversal\n", "\n", "* 5, 2, 8, 1, 3 -> 1, 2, 3, 5, 8\n", "* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5\n", "\n", "### Pre-Order Traversal\n", "\n", "* 5, 2, 8, 1, 3 -> 5, 2, 1, 3, 8\n", "* 1, 2, 3, 4, 5 -> 1, 2, 3, 4, 5\n", "\n", "### Post-Order Traversal\n", "\n", "* 5, 2, 8, 1, 3 -> 1, 3, 2, 8, 5\n", "* 1, 2, 3, 4, 5 -> 5, 4, 3, 2, 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "## Test Cases\n", "\n", "### In-Order Traversal\n", "\n", "* Recursively call in-order traversal on the left child\n", "* Visit the current node\n", "* Recursively call in-order traversal on the right child\n", "\n", "Complexity:\n", "* Time: O(n)\n", "* Space: O(log n)\n", "\n", "Note:\n", "* This is a form of a depth-first traversal\n", "\n", "### Pre-Order Traversal\n", "\n", "* Visit the current node\n", "* Recursively call pre-order traversal on the left child\n", "* Recursively call pre-order traversal on the right child\n", "\n", "Complexity:\n", "* Time: O(n)\n", "* Space: O(log n)\n", "\n", "Note:\n", "* This is a form of a depth-first traversal\n", "\n", "### Post-Order Traversal\n", "\n", "* Recursively call post-order traversal on the left child\n", "* Recursively call post-order traversal on the right child\n", "* Visit the current node\n", "\n", "Complexity:\n", "* Time: O(n)\n", "* Space: O(log n)\n", "\n", "Note:\n", "* This is a form of a depth-first traversal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%run ../bst/bst.py" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def in_order_traversal(node, visit_func):\n", " if node is not None:\n", " in_order_traversal(node.left, visit_func)\n", " visit_func(node.data)\n", " in_order_traversal(node.right, visit_func)\n", "\n", "def pre_order_traversal(node, visit_func):\n", " if node is not None:\n", " visit_func(node.data)\n", " pre_order_traversal(node.left, visit_func)\n", " pre_order_traversal(node.right, visit_func)\n", "\n", "def post_order_traversal(node, visit_func):\n", " if node is not None:\n", " post_order_traversal(node.left, visit_func)\n", " post_order_traversal(node.right, visit_func)\n", " visit_func(node.data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unit Test" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%run ../utils/results.py" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting test_dfs.py\n" ] } ], "source": [ "%%writefile test_dfs.py\n", "from nose.tools import assert_equal\n", "\n", "\n", "class TestDfs(object):\n", "\n", " def __init__(self):\n", " self.results = Results()\n", "\n", " def test_dfs(self):\n", " node = Node(5)\n", " insert(node, 2)\n", " insert(node, 8)\n", " insert(node, 1)\n", " insert(node, 3)\n", "\n", " in_order_traversal(node, self.results.add_result)\n", " assert_equal(str(self.results), \"[1, 2, 3, 5, 8]\")\n", " self.results.clear_results()\n", "\n", " pre_order_traversal(node, self.results.add_result)\n", " assert_equal(str(self.results), \"[5, 2, 1, 3, 8]\")\n", " self.results.clear_results()\n", "\n", " post_order_traversal(node, self.results.add_result)\n", " assert_equal(str(self.results), \"[1, 3, 2, 8, 5]\")\n", " self.results.clear_results()\n", "\n", " node = Node(1)\n", " insert(node, 2)\n", " insert(node, 3)\n", " insert(node, 4)\n", " insert(node, 5)\n", "\n", " in_order_traversal(node, self.results.add_result)\n", " assert_equal(str(self.results), \"[1, 2, 3, 4, 5]\")\n", " self.results.clear_results()\n", "\n", " pre_order_traversal(node, self.results.add_result)\n", " assert_equal(str(self.results), \"[1, 2, 3, 4, 5]\")\n", " self.results.clear_results()\n", "\n", " post_order_traversal(node, self.results.add_result)\n", " assert_equal(str(self.results), \"[5, 4, 3, 2, 1]\")\n", "\n", " print('Success: test_dfs')\n", "\n", "\n", "def main():\n", " test = TestDfs()\n", " test.test_dfs()\n", "\n", "\n", "if __name__ == '__main__':\n", " main()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Success: test_dfs\n" ] } ], "source": [ "%run -i test_dfs.py" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }