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Added notebook solving the following: Add two numbers whose digits are stored in a linked list in reverse order.
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Donne Martin
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@ -19,6 +19,7 @@ Continually updated IPython Notebooks containing algorithms and data structures.
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* [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)
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* [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)
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* [Partition a linked list around a given value](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/partition.ipynb)
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* [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)
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## License
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186
linked-lists/add-reverse.ipynb
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186
linked-lists/add-reverse.ipynb
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@ -0,0 +1,186 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Add two numbers whose digits are stored in a linked list in reverse order.\n",
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"\n",
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"* [Clarifying Questions](#Clarifying-Questions)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Clarifying Questions\n",
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"\n",
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"* Do you expect the return to be in reverse order too?\n",
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" * Yes\n",
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"* What if one of the inputs is NULL?\n",
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" * Return NULL for an invalid operation"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* Empty list(s)\n",
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"* Add values of different lengths\n",
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" * Input 1: 6->5->None\n",
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" * Input 2: 9->8->7\n",
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" * Result: 5->4->8\n",
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"* Add values of same lengths\n",
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" * Exercised from values of different lengths\n",
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" * Done here for completeness"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"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",
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"\n",
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"* Test for error cases\n",
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"* Careful with adding if the lists differ\n",
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" * Only add if a node is not NULL\n",
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" * Alternatively, we could add trailing zeroes to the smaller list\n",
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"* Base case:\n",
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" * if first and second lists are NULL AND carry is zero\n",
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" * Return NULL\n",
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"* Recursive case:\n",
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" * value = carry\n",
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" * value += first.data + second.data\n",
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" * remainder = value % 10\n",
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" * new_carry = 1 if value >= 10, else 0\n",
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" * Create a node with the remainder\n",
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" * node.next = self.add(first.next, second.next, new_carry)\n",
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" * Return node\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n)\n",
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"* Space: O(n), extra space for result and recursion depth"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"%run linked_list.py"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class MyLinkedList(LinkedList):\n",
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" def __add__(self, first_node, second_node, carry):\n",
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" if type(carry) != int and carry < 0:\n",
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" raise ValueError('Invalid int argument: carry')\n",
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" if first_node is None and second_node is None and carry == 0:\n",
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" return None\n",
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" value = carry\n",
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" value += first_node.data if first_node is not None else 0\n",
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" value += second_node.data if second_node is not None else 0\n",
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" remainder = value % 10\n",
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" new_carry = 1 if value >= 10 else 0\n",
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" node = Node(remainder)\n",
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" #import pdb; pdb.set_trace()\n",
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" node.next = self.__add__(first_node.next if first_node is not None else None, \n",
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" second_node.next if first_node is not None else None, \n",
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" new_carry)\n",
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" return node\n",
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"\n",
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" def add(self, first_list, second_list):\n",
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" if first_list is None or second_list is None:\n",
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" return None\n",
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" head = self.__add__(first_list.head, second_list.head, 0)\n",
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" return MyLinkedList(head)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"print('Add values of different lengths')\n",
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"# Input 1: 6->5->None\n",
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"# Input 2: 9->8->7\n",
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"# Result: 5->4->8\n",
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"first_head = Node(6)\n",
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"first_list = MyLinkedList(first_head)\n",
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"first_list.append(5)\n",
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"second_head = Node(9)\n",
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"second_list = MyLinkedList(second_head)\n",
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"second_list.append(8)\n",
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"second_list.append(7)\n",
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"result = MyLinkedList().add(first_list, second_list)\n",
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"result.print_list()\n",
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"print('Add values of same lengths')\n",
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"# Input 1: 6->5->4\n",
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"# Input 2: 9->8->7\n",
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"# Result: 5->4->2->1\n",
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"first_head = Node(6)\n",
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"first_list = MyLinkedList(first_head)\n",
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"first_list.append(5)\n",
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"first_list.append(4)\n",
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"second_head = Node(9)\n",
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"second_list = MyLinkedList(second_head)\n",
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"second_list.append(8)\n",
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"second_list.append(7)\n",
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"result = MyLinkedList().add(first_list, second_list)\n",
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"result.print_list()\n",
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"print('Empty list(s)')\n",
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"result = MyLinkedList().add(None, None)\n",
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"result = MyLinkedList().add(first_head, None)\n",
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"result = MyLinkedList().add(None, second_head)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 2",
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"language": "python",
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"name": "python2"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"version": "2.7.9"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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