interactive-coding-challenges/math_probability/add_digits/add_digits_solution.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": [
    "# Solution Notebook"
   ]
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   "metadata": {},
   "source": [
    "## Problem: Given an int, repeatedly add its digits until the result is one digit.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## Constraints\n",
    "\n",
    "* Can we assume num is not negative?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "<pre>\n",
    "* None input -> TypeError\n",
    "* negative input -> ValueError\n",
    "* 9 -> 9\n",
    "* 138 -> 3\n",
    "* 65536 -> 7\n",
    "</pre>"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## Algorithm\n",
    "\n",
    "The naive solution simply isolates each digit with with modulo and integer division.  We'll add each isolated digit to  a list and sum the values.\n",
    "\n",
    "<pre>\n",
    "138 % 10 = 8 -> isolated\n",
    "138 // 10 = 13\n",
    "13 % 10 = 3 -> isolated\n",
    "13 // 10 = 1\n",
    "1 % 10 = 1 -> isolated\n",
    "</pre>\n",
    "\n",
    "A more optimal solution exists, by recognizing this is a digital root.  See the [Wikipedia article](https://en.wikipedia.org/wiki/Digital_root) for more information.\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "source": [
    "class Solution(object):\n",
    "\n",
    "    def add_digits(self, num):\n",
    "        if num is None:\n",
    "            raise TypeError('num cannot be None')\n",
    "        if num < 0:\n",
    "            raise ValueError('num cannot be negative')\n",
    "        digits = []\n",
    "        while num != 0:\n",
    "            digits.append(num % 10)\n",
    "            num //= 10\n",
    "        digits_sum = sum(digits)\n",
    "        if digits_sum >= 10:\n",
    "            return self.add_digits(digits_sum)\n",
    "        else:\n",
    "            return digits_sum\n",
    "\n",
    "    def add_digits_optimized(self, num):\n",
    "        if num is None:\n",
    "            raise TypeError('num cannot be None')\n",
    "        if num < 0:\n",
    "            raise ValueError('num cannot be negative')\n",
    "        if num == 0:\n",
    "            return 0\n",
    "        elif num % 9 == 0:\n",
    "            return 9\n",
    "        else:\n",
    "            return num % 9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_add_digits.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_add_digits.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestAddDigits(object):\n",
    "\n",
    "    def test_add_digits(self, func):\n",
    "        assert_raises(TypeError, func, None)\n",
    "        assert_raises(ValueError, func, -1)\n",
    "        assert_equal(func(0), 0)\n",
    "        assert_equal(func(9), 9)\n",
    "        assert_equal(func(138), 3)\n",
    "        assert_equal(func(65536), 7) \n",
    "        print('Success: test_add_digits')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestAddDigits()\n",
    "    solution = Solution()\n",
    "    test.test_add_digits(solution.add_digits)\n",
    "    try:\n",
    "        test.test_add_digits(solution.add_digits_optimized)\n",
    "    except NameError:\n",
    "        # Alternate solutions are only defined\n",
    "        # in the solutions file\n",
    "        pass\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
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   "cell_type": "code",
   "execution_count": 3,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_add_digits\n",
      "Success: test_add_digits\n"
     ]
    }
   ],
   "source": [
    "%run -i test_add_digits.py"
   ]
  }
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