{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://bit.ly/code-notes)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Add two numbers whose digits are stored in a linked list in reverse order.\n", "\n", "* [Constraints and Assumptions](#Constraints-and-Assumptions)\n", "* [Test Cases](#Test-Cases)\n", "* [Algorithm](#Algorithm)\n", "* [Code](#Code)\n", "* [Unit Test](#Unit-Test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constraints\n", "\n", "*Problem statements are often intentionally ambiguous. Identifying constraints and stating assumptions can help to ensure you code the intended solution.*\n", "\n", "* Do you expect the return to be in reverse order too?\n", " * Yes\n", "* What if one of the inputs is NULL?\n", " * Return NULL for an invalid operation\n", "* How large are these numbers--can they fit in memory?\n", " * Yes\n", "* Can we assume we already have a linked list class that can be used for this problem?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "* Empty list(s)\n", "* Add values of different lengths\n", " * Input 1: 6->5->None\n", " * Input 2: 9->8->7\n", " * Result: 5->4->8\n", "* Add values of same lengths\n", " * Exercised from values of different lengths\n", " * Done here for completeness" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "We could solve this with an iterative or a recursive algorithm, both are well suited for this exercise. We'll use a recursive algorithm for practice with recursion. Note this takes an extra space of O(m) where m is the recursion depth.\n", "\n", "* Base case:\n", " * if first and second lists are NULL AND carry is zero\n", " * Return NULL\n", "* Recursive case:\n", " * value = carry\n", " * value += first.data + second.data\n", " * remainder = value % 10\n", " * new_carry = 1 if value >= 10, else 0\n", " * Create a node with the remainder\n", " * node.next = self.add(first.next, second.next, new_carry)\n", " * Return node\n", "\n", "Complexity:\n", "* Time: O(n)\n", "* Space: O(n), extra space for result and recursion depth\n", "\n", "Notes:\n", "* Careful with adding if the lists differ\n", " * Only add if a node is not NULL\n", " * Alternatively, we could add trailing zeroes to the smaller list" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%run linked_list.py" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "class MyLinkedList(LinkedList):\n", " def __add__(self, first_node, second_node, carry):\n", " if type(carry) != int and carry < 0:\n", " raise ValueError('Invalid int argument: carry')\n", " if first_node is None and second_node is None and carry == 0:\n", " return None\n", " value = carry\n", " value += first_node.data if first_node is not None else 0\n", " value += second_node.data if second_node is not None else 0\n", " remainder = value % 10\n", " new_carry = 1 if value >= 10 else 0\n", " node = Node(remainder)\n", " node.next = self.__add__(first_node.next if first_node is not None else None, \n", " second_node.next if first_node is not None else None, \n", " new_carry)\n", " return node\n", "\n", " def add(self, first_list, second_list):\n", " if first_list is None or second_list is None:\n", " return None\n", " head = self.__add__(first_list.head, second_list.head, 0)\n", " return MyLinkedList(head)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unit Test" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*It is important to identify and run through general and edge cases from the [Test Cases](#Test-Cases) section by hand. You generally will not be asked to write a unit test like what is shown below.*" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test: Empty list(s)\n", "Test: Add values of different lengths\n", "Test: Add values of same lengths\n", "Success: test_add\n" ] } ], "source": [ "from nose.tools import assert_equal\n", "\n", "class Test(object):\n", " def test_add(self):\n", " print('Test: Empty list(s)')\n", " assert_equal(MyLinkedList().add(None, None), None)\n", " assert_equal(MyLinkedList().add(Node(5), None), None)\n", " assert_equal(MyLinkedList().add(None, Node(10)), None)\n", "\n", " print('Test: Add values of different lengths')\n", " # Input 1: 6->5->None\n", " # Input 2: 9->8->7\n", " # Result: 5->4->8\n", " first_list = MyLinkedList(Node(6))\n", " first_list.append(5)\n", " second_list = MyLinkedList(Node(9))\n", " second_list.append(8)\n", " second_list.append(7)\n", " result = MyLinkedList().add(first_list, second_list)\n", " assert_equal(result.get_all_data(), [5, 4, 8])\n", "\n", " print('Test: Add values of same lengths')\n", " # Input 1: 6->5->4\n", " # Input 2: 9->8->7\n", " # Result: 5->4->2->1\n", " first_head = Node(6)\n", " first_list = MyLinkedList(first_head)\n", " first_list.append(5)\n", " first_list.append(4)\n", " second_head = Node(9)\n", " second_list = MyLinkedList(second_head)\n", " second_list.append(8)\n", " second_list.append(7)\n", " result = MyLinkedList().add(first_list, second_list)\n", " assert_equal(result.get_all_data(), [5, 4, 2, 1])\n", " \n", " print('Success: test_add')\n", "\n", "if __name__ == '__main__':\n", " test = Test()\n", " test.test_add()" ] } ], "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 }