From 3774bc2e02310857b8b6b8dd7bfcd999f21cc579 Mon Sep 17 00:00:00 2001 From: Donne Martin Date: Thu, 14 May 2015 06:59:38 -0400 Subject: [PATCH] Added notebook solving the following: Add two numbers whose digits are stored in a linked list in reverse order. --- README.md | 1 + linked-lists/add-reverse.ipynb | 186 +++++++++++++++++++++++++++++++++ 2 files changed, 187 insertions(+) create mode 100644 linked-lists/add-reverse.ipynb diff --git a/README.md b/README.md index 114d98c..8f54824 100644 --- a/README.md +++ b/README.md @@ -19,6 +19,7 @@ Continually updated IPython Notebooks containing algorithms and data structures. * [Find the kth to last element of a linked list](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/kth-to-last-elem.ipynb) * [Delete a node in the middle of a linked list, given access to only that node](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/delete-mid.ipynb) * [Partition a linked list around a given value](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/partition.ipynb) +* [Add two numbers whose digits are stored in a linked list in reverse order](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/add-reverse.ipynb) ## License diff --git a/linked-lists/add-reverse.ipynb b/linked-lists/add-reverse.ipynb new file mode 100644 index 0000000..ae769f8 --- /dev/null +++ b/linked-lists/add-reverse.ipynb @@ -0,0 +1,186 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Add two numbers whose digits are stored in a linked list in reverse order.\n", + "\n", + "* [Clarifying Questions](#Clarifying-Questions)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Clarifying Questions\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" + ] + }, + { + "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 recursive. Note this takes an extra space of O(m) where m is the recursion depth.\n", + "\n", + "* Test for error cases\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\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" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%run linked_list.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "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", + " #import pdb; pdb.set_trace()\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": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print('Add values of different lengths')\n", + "# Input 1: 6->5->None\n", + "# Input 2: 9->8->7\n", + "# Result: 5->4->8\n", + "first_head = Node(6)\n", + "first_list = MyLinkedList(first_head)\n", + "first_list.append(5)\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", + "result.print_list()\n", + "print('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", + "result.print_list()\n", + "print('Empty list(s)')\n", + "result = MyLinkedList().add(None, None)\n", + "result = MyLinkedList().add(first_head, None)\n", + "result = MyLinkedList().add(None, second_head)" + ] + } + ], + "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": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}