Added notebook solving the following: Implement the Towers of Hanoi with 3 towers and N disks.

README.md

@@ -38,6 +38,7 @@ Continually updated IPython Notebooks containing coding problems and solutions (
 * [Implement n stacks using a single array](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/n-stacks.ipynb)
 * [Implement a stack that keeps track of its minimum element](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/stack-min.ipynb)
 * [Implement a set of stacks class that wraps a list of stacks, each bound by a capacity](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/set-of-stacks.ipynb)
+* [Implement the Towers of Hanoi with 3 towers and N disks](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/hanoi.ipynb)
 
 ## License
 

stacks-queues/hanoi.ipynb

@@ -0,0 +1,140 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Implement the [Towers of Hanoi](http://en.wikipedia.org/wiki/Tower_of_Hanoi) with 3 towers and N disks.\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",
+    "* None"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Cases\n",
+    "\n",
+    "* NULL towers\n",
+    "* 0 disks\n",
+    "* 1 disk\n",
+    "* 2 or more disks"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm\n",
+    "\n",
+    "* Create three stacks to represent each tower\n",
+    "* def hanoi(n, src, dest, buffer):\n",
+    "    * If 0 disks return\n",
+    "    * hanoi(n-1, src, buffer)\n",
+    "    * Move remaining element from src to dest\n",
+    "    * hanoi(n-1, buffer, dest)    \n",
+    "\n",
+    "Complexity:\n",
+    "* Time: O(2^n - 1)\n",
+    "* Space: O(m) where m is the number of recursion levels"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%run stack.py"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def hanoi(num_disks, src, dest, buff):\n",
+    "    if src is None or dest is None or buff is None:\n",
+    "        return\n",
+    "    if num_disks > 0:\n",
+    "        hanoi(num_disks-1, src, buff, dest)\n",
+    "        data = src.pop()\n",
+    "        dest.push(data)\n",
+    "        hanoi(num_disks-1, buff, dest, src)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "print('NULL towers')\n",
+    "hanoi(num_disks, None, None, None)\n",
+    "first = Stack()\n",
+    "second = Stack()\n",
+    "third = Stack()\n",
+    "print('0 disks')\n",
+    "hanoi(num_disks, first, third, second)\n",
+    "print('1 disk')\n",
+    "first.push(5)\n",
+    "hanoi(num_disks, first, third, second)\n",
+    "print(third.pop())\n",
+    "print('2 or more disks')\n",
+    "num_disks = 3\n",
+    "for i in xrange(num_disks, -1, -1):\n",
+    "    first.push(i)\n",
+    "hanoi(num_disks, first, third, second)\n",
+    "for i in xrange(0, num_disks):\n",
+    "    print(third.pop())"
+   ]
+  }
+ ],
+ "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
+}