interactive-coding-challenges/math_probability/check_prime/check_prime_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: Check if a number is prime.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
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   "source": [
    "## Constraints\n",
    "\n",
    "* Is it correct that 1 is not considered a prime number?\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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   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> Exception\n",
    "* Not an int -> Exception\n",
    "* Less than 2 -> False\n",
    "* General case"
   ]
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   "source": [
    "## Algorithm\n",
    "\n",
    "For a number to be prime, it must be 2 or greater and cannot be divisible by another number other than itself (and 1).\n",
    "\n",
    "We'll check by dividing all numbers from 2 to the input number to determine if the number is prime.\n",
    "\n",
    "As an optimization, we can divide from 2 to the square root of the input number.  For each value that divides the input number evenly, there is a complement b where a * b = n.  If a > sqrt(n) then b < sqrt(n) because sqrt(n^2) = n.\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n) where n is the value of the input number\n",
    "* Space: O(1)\n",
    "\n",
    "### Sieve of Eratosthenes\n",
    "\n",
    "The Sieve of Eratosthenes provides a more efficient way of computing and generating primes.  See the challenge [\"Generate a list of primes\"]() for more details."
   ]
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   "metadata": {},
   "source": [
    "## Code"
   ]
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  {
   "cell_type": "code",
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   "source": [
    "import math\n",
    "\n",
    "\n",
    "class Math(object):\n",
    "\n",
    "    def check_prime(self, num):\n",
    "        if num is None:\n",
    "            raise TypeError('num cannot be None')\n",
    "        if num < 2:\n",
    "            return False\n",
    "        for i in range(2, num):\n",
    "            if num % i == 0:\n",
    "                return False\n",
    "        return True\n",
    "\n",
    "    def check_prime_optimized(self, num):\n",
    "        if num is None:\n",
    "            raise TypeError('num cannot be None')\n",
    "        if num < 2:\n",
    "            return False\n",
    "        for i in range(2, int(math.sqrt(num)+1)):\n",
    "            if num % i == 0:\n",
    "                return False\n",
    "        return True"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_check_prime.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_check_prime.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestMath(object):\n",
    "\n",
    "    def test_check_prime(self):\n",
    "        math = Math()\n",
    "        assert_raises(TypeError, math.check_prime, None)\n",
    "        assert_raises(TypeError, math.check_prime, 98.6)\n",
    "        assert_equal(math.check_prime(0), False)\n",
    "        assert_equal(math.check_prime(1), False)\n",
    "        assert_equal(math.check_prime(97), True)\n",
    "        print('Success: test_check_prime')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestMath()\n",
    "    test.test_check_prime()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_check_prime\n"
     ]
    }
   ],
   "source": [
    "%run -i test_check_prime.py"
   ]
  }
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