{ "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: Find the second largest node in a binary search 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", "* If this is called on a None input or a single node, should we raise an exception?\n", " * Yes\n", " * None -> TypeError\n", " * Single node -> ValueError\n", "* Can we assume we already have a Node class with an insert method?\n", " * Yes\n", "* Can we assume this fits memory?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "* None or single node -> Exception\n", "\n", "
\n", "Input:\n", " _10_\n", " _/ \\_ \n", " 5 15\n", " / \\ / \\\n", " 3 8 12 20\n", " / \\ \\\n", " 2 4 30\n", "\n", "Output: 20\n", "\n", "Input:\n", " 10\n", " / \n", " 5\n", " / \\\n", " 3 7\n", "Output: 7\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "
\n", "\n", "If there is no right node, the second largest is the right most left subtree:\n", "\n", " 10\n", " / \n", " 5\n", " / \\\n", " 3 7\n", "\n", "If there is a right node and the right node has children, recurse to that right child:\n", "\n", " _10_\n", " _/ \\_ \n", " 5 15\n", " / \\ / \\\n", " 3 8 12 20\n", " / \\ \\\n", " 2 4 30\n", "\n", "Eventually we'll get to the following scenario:\n", "\n", " 20\n", " \\\n", " 30\n", "\n", "If the right node has no children, the second largest is the current node.\n", "\n", "\n", "\n", "Complexity:\n", "* Time: O(h)\n", "* Space: O(h), where h is the height of the tree" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%run ../bst/bst.py" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "class Solution(Bst):\n", "\n", " def _find_second_largest(self, node):\n", " if node.right is not None:\n", " if node.right.left is not None or node.right.right is not None:\n", " return self._find_second_largest(node.right)\n", " else:\n", " return node\n", " else:\n", " return self._find_right_most_node(node.left)\n", "\n", " def _find_right_most_node(self, node):\n", " if node.right is not None:\n", " return self._find_right_most_node(node.right)\n", " else:\n", " return node\n", "\n", " def find_second_largest(self):\n", " if self.root is None:\n", " raise TypeError('root cannot be None')\n", " if self.root.right is None and self.root.left is None:\n", " raise ValueError('root must have at least one child')\n", " return self._find_second_largest(self.root)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unit Test" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting test_bst_second_largest.py\n" ] } ], "source": [ "%%writefile test_bst_second_largest.py\n", "import unittest\n", "\n", "\n", "class TestBstSecondLargest(unittest.TestCase):\n", "\n", " def test_bst_second_largest(self):\n", " bst = Solution(None)\n", " self.assertRaises(TypeError, bst.find_second_largest)\n", " root = Node(10)\n", " bst = Solution(root)\n", " node5 = bst.insert(5)\n", " node15 = bst.insert(15)\n", " node3 = bst.insert(3)\n", " node8 = bst.insert(8)\n", " node12 = bst.insert(12)\n", " node20 = bst.insert(20)\n", " node2 = bst.insert(2)\n", " node4 = bst.insert(4)\n", " node30 = bst.insert(30)\n", " self.assertEqual(bst.find_second_largest(), node20)\n", " root = Node(10)\n", " bst = Solution(root)\n", " node5 = bst.insert(5)\n", " node3 = bst.insert(3)\n", " node7 = bst.insert(7)\n", " self.assertEqual(bst.find_second_largest(), node7)\n", " print('Success: test_bst_second_largest')\n", "\n", "\n", "def main():\n", " test = TestBstSecondLargest()\n", " test.test_bst_second_largest()\n", "\n", "\n", "if __name__ == '__main__':\n", " main()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Success: test_bst_second_largest\n" ] } ], "source": [ "%run -i test_bst_second_largest.py" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 1 }