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Reworked notebook: Added more detail to constraints and test cases. Reworked algorithm discussion and unit test.
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@ -13,19 +13,23 @@
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"source": [
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"## Problem: Implement the [Towers of Hanoi](http://en.wikipedia.org/wiki/Tower_of_Hanoi) with 3 towers and N disks.\n",
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"\n",
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"* [Clarifying Questions](#Clarifying-Questions)\n",
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"* [Constraints and Assumptions](#Constraints-and-Assumptions)\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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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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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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"## Constraints and Assumptions\n",
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"\n",
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"* None"
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"*Problem statements are often intentionally ambiguous. Identifying constraints and stating assumptions can help to ensure you code the intended solution.*\n",
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"\n",
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"* Can we assume we already have a stack class that can be used for this problem?\n",
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" * Yes"
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]
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},
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{
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@ -54,7 +58,7 @@
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" * hanoi(n-1, buffer, dest) \n",
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"\n",
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"Complexity:\n",
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"* Time: O(2^n - 1)\n",
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"* Time: O(2^n)\n",
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"* Space: O(m) where m is the number of recursion levels"
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]
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},
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@ -67,7 +71,7 @@
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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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"execution_count": 1,
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"metadata": {
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"collapsed": true
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},
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@ -78,7 +82,7 @@
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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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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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@ -94,32 +98,68 @@
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" hanoi(num_disks-1, buff, dest, src)"
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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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"## Unit Test\n",
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"\n",
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"*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.*"
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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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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Test: NULL towers\n",
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"Test: 0 disks\n",
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"Test: 1 disk\n",
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"Test: 2 or more disks\n",
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"Success: test_hanoi\n"
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]
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}
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],
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"source": [
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"print('NULL towers')\n",
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"hanoi(num_disks, None, None, None)\n",
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"first = Stack()\n",
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"second = Stack()\n",
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"third = Stack()\n",
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"print('0 disks')\n",
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"hanoi(num_disks, first, third, second)\n",
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"print('1 disk')\n",
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"first.push(5)\n",
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"hanoi(num_disks, first, third, second)\n",
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"print(third.pop())\n",
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"print('2 or more disks')\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"class Test(object):\n",
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" def test_hanoi(self):\n",
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" num_disks = 3\n",
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" src = Stack()\n",
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" buff = Stack()\n",
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" dest = Stack()\n",
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"\n",
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" print('Test: NULL towers')\n",
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" hanoi(num_disks, None, None, None)\n",
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"\n",
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" print('Test: 0 disks')\n",
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" hanoi(num_disks, src, dest, buff)\n",
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" assert_equal(dest.pop(), None)\n",
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"\n",
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" print('Test: 1 disk')\n",
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" src.push(5)\n",
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" hanoi(num_disks, src, dest, buff)\n",
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" assert_equal(dest.pop(), 5)\n",
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"\n",
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" print('Test: 2 or more disks')\n",
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" for i in xrange(num_disks, -1, -1):\n",
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" first.push(i)\n",
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"hanoi(num_disks, first, third, second)\n",
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" src.push(i)\n",
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" hanoi(num_disks, src, dest, buff)\n",
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" for i in xrange(0, num_disks):\n",
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" print(third.pop())"
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" assert_equal(dest.pop(), i)\n",
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"\n",
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" print('Success: test_hanoi')\n",
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"\n",
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"if __name__ == '__main__':\n",
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" test = Test()\n",
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" test.test_hanoi()"
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]
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}
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],
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