interactive-coding-challenges/math_probability/power_two/power_two_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: Determine if a number is a power of two.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
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    "## Constraints\n",
    "\n",
    "* Is the input number an int?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Is the output a boolean?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
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   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> TypeError\n",
    "* 0 -> False\n",
    "* 1 -> True\n",
    "* 2 -> True\n",
    "* 15 -> False\n",
    "* 16 -> True"
   ]
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   "source": [
    "## Algorithm\n",
    "\n",
    "We can use bit manipulation to determine if a number is a power of two.  \n",
    "\n",
    "For a number to be a power of two, there must only be one bit that is a `1`.  \n",
    "\n",
    "We can use the following bit manipulation trick to determine this:\n",
    "\n",
    "`n & (n - 1)`\n",
    "\n",
    "Here's an example why:\n",
    "\n",
    "<pre>\n",
    "0000 1000 = n\n",
    "0000 0001 = 1\n",
    "0000 0111 = n-1\n",
    "\n",
    "0000 1000 = n\n",
    "0000 0111 = n-1\n",
    "0000 0000 = n & n-1, result = 0\n",
    "</pre>\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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   "source": [
    "class Solution(object):\n",
    "\n",
    "    def is_power_of_two(self, n):\n",
    "        if n is None:\n",
    "            raise TypeError('n cannot be None')\n",
    "        if n <= 0:\n",
    "            return False\n",
    "        return (n & (n - 1)) == 0"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
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     "text": [
      "Overwriting test_is_power_of_two.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_is_power_of_two.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestSolution(object):\n",
    "\n",
    "    def test_is_power_of_two(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.is_power_of_two, None)\n",
    "        assert_equal(solution.is_power_of_two(0), False)\n",
    "        assert_equal(solution.is_power_of_two(1), True)\n",
    "        assert_equal(solution.is_power_of_two(2), True)\n",
    "        assert_equal(solution.is_power_of_two(15), False)\n",
    "        assert_equal(solution.is_power_of_two(16), True)\n",
    "        print('Success: test_is_power_of_two')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestSolution()\n",
    "    test.test_is_power_of_two()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_is_power_of_two\n"
     ]
    }
   ],
   "source": [
    "%run -i test_is_power_of_two.py"
   ]
  }
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