interactive-coding-challenges/recursion_dynamic/magic_index/magic_index_challenge.ipynb

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   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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   "source": [
    "# Challenge Notebook"
   ]
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   "metadata": {},
   "source": [
    "## Problem: Find the magic index in an array, where array[i] = i.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)\n",
    "* [Solution Notebook](#Solution-Notebook)"
   ]
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   "source": [
    "## Constraints\n",
    "\n",
    "* Is the array sorted?\n",
    "    * Yes\n",
    "* Are the elements in the array distinct?\n",
    "    * No\n",
    "* Does a magic index always exist?\n",
    "    * No\n",
    "* If there is no magic index, do we just return -1?\n",
    "    * Yes\n",
    "* Are negative values allowed in the array?\n",
    "    * Yes\n",
    "* If there are multiple magic values, what do we return?\n",
    "    * Return the left-most one\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
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   "source": [
    "## Test Cases\n",
    "\n",
    "* None input -> -1\n",
    "* Empty array -> -1\n",
    "\n",
    "<pre>\n",
    "a[i]  -4 -2  2  6  6  6  6 10\n",
    "  i    0  1  2  3  4  5  6  7\n",
    "</pre>\n",
    "\n",
    "Result: 2\n",
    "\n",
    "<pre>\n",
    "a[i]  -4 -2  1  6  6  6  6 10\n",
    "  i    0  1  2  3  4  5  6  7\n",
    "</pre>\n",
    "\n",
    "Result: 6\n",
    "\n",
    "<pre>\n",
    "a[i]  -4 -2  1  6  6  6  7 10\n",
    "  i    0  1  2  3  4  5  6  7\n",
    "</pre>\n",
    "\n",
    "Result: -1"
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   "cell_type": "markdown",
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   "source": [
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook]().  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "class MagicIndex(object):\n",
    "\n",
    "    def find_magic_index(self, array):\n",
    "        # TODO: Implement me\n",
    "        pass"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The following unit test is expected to fail until you solve the challenge.**"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "# %load test_find_magic_index.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestFindMagicIndex(object):\n",
    "\n",
    "    def test_find_magic_index(self):\n",
    "        magic_index = MagicIndex()\n",
    "        assert_equal(magic_index.find_magic_index(None), -1)\n",
    "        assert_equal(magic_index.find_magic_index([]), -1)\n",
    "        array = [-4, -2, 2, 6, 6, 6, 6, 10]\n",
    "        assert_equal(magic_index.find_magic_index(array), 2)\n",
    "        array = [-4, -2, 1, 6, 6, 6, 6, 10]\n",
    "        assert_equal(magic_index.find_magic_index(array), 6)\n",
    "        array = [-4, -2, 1, 6, 6, 6, 7, 10]\n",
    "        assert_equal(magic_index.find_magic_index(array), -1)\n",
    "        print('Success: test_find_magic')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestFindMagicIndex()\n",
    "    test.test_find_magic_index()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Notebook\n",
    "\n",
    "Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
   ]
  }
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