{
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   "cell_type": "markdown",
   "metadata": {},
   "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)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Given a positive integer, get the next largest number and the next smallest number with the same number of 1's as the given number.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is the output a positive int?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> Exception\n",
    "* 0 -> Exception\n",
    "* negative int -> Exception\n",
    "* General case:\n",
    "<pre>\n",
    "    * Input:         0000 0000 1101 0111\n",
    "    * Next largest:  0000 0000 1101 1011\n",
    "    * Next smallest: 0000 0000 1100 1111\n",
    "</pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "### get_next_largest\n",
    "\n",
    "* Find the right-most non trailing zero, call this index\n",
    "    * We'll use a mask of 1 and do a logical right shift on a copy of num to examine each bit starting from the right\n",
    "    * Count the number of zeroes to the right of index\n",
    "        * While num & 1 == 0 and num_copy != 0:\n",
    "            * Increment number of zeroes\n",
    "            * Logical shift right num_copy\n",
    "    * Count the number of ones to the right of index\n",
    "        * While num & 1 == 1 and num_copy != 0:\n",
    "            * Increment number of ones\n",
    "            * Logical shift right num_copy\n",
    "    * The index will be the sum of number of ones and number of zeroes\n",
    "    * Set the index bit\n",
    "    * Clear all bits to the right of index\n",
    "    * Set bits starting from 0\n",
    "        * Only set (number of ones - 1) bits because we set index to 1\n",
    "\n",
    "We should make a note that Python does not have a logical right shift operator built in.  We can either use a positive number of implement one for a 32 bit number:\n",
    "\n",
    "    num % 0x100000000 >> n\n",
    "\n",
    "### get_next_smallest\n",
    "\n",
    "* The algorithm for finding the next smallest number is very similar to finding the next largest number\n",
    "    * Instead of finding the right-most non-trailing zero, we'll find the right most non-trailing one and clear it\n",
    "    * Clear all bits to the right of index\n",
    "    * Set bits starting at 0 to the number of ones to the right of index, plus one\n",
    "\n",
    "Complexity:\n",
    "* Time: O(b), where b is the number of bits in num\n",
    "* Space: O(b), where b is the number of bits in num"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Bits(object):\n",
    "\n",
    "    def get_next_largest(self, num):\n",
    "        if num is None:\n",
    "            raise TypeError('num cannot be None')\n",
    "        if num <= 0:\n",
    "            raise ValueError('num cannot be 0 or negative')\n",
    "        num_ones = 0\n",
    "        num_zeroes = 0\n",
    "        num_copy = num\n",
    "        # We'll look for index, which is the right-most non-trailing zero\n",
    "        # Count number of zeroes to the right of index\n",
    "        while num_copy != 0 and num_copy & 1 == 0:\n",
    "            num_zeroes += 1\n",
    "            num_copy >>= 1\n",
    "        # Count number of ones to the right of index\n",
    "        while num_copy != 0 and num_copy & 1 == 1:\n",
    "            num_ones += 1\n",
    "            num_copy >>= 1\n",
    "        # Determine index and set the bit\n",
    "        index = num_zeroes + num_ones\n",
    "        num |= 1 << index\n",
    "        # Clear all bits to the right of index\n",
    "        num &= ~((1 << index) - 1)\n",
    "        # Set bits starting from 0\n",
    "        num |= ((1 << num_ones - 1) - 1)\n",
    "        return num\n",
    "\n",
    "    def get_next_smallest(self, num):\n",
    "        if num is None:\n",
    "            raise TypeError('num cannot be None')\n",
    "        if num <= 0:\n",
    "            raise ValueError('num cannot be 0 or negative')\n",
    "        num_ones = 0\n",
    "        num_zeroes = 0\n",
    "        num_copy = num\n",
    "        # We'll look for index, which is the right-most non-trailing one\n",
    "        # Count number of zeroes to the right of index\n",
    "        while num_copy != 0 and num_copy & 1 == 1:\n",
    "            num_ones += 1\n",
    "            num_copy >>= 1\n",
    "        # Count number of zeroes to the right of index\n",
    "        while num_copy != 0 and num_copy & 1 == 0:\n",
    "            num_zeroes += 1\n",
    "            num_copy >>= 1\n",
    "        # Determine index and clear the bit\n",
    "        index = num_zeroes + num_ones\n",
    "        num &= ~(1 << index)\n",
    "        # Clear all bits to the right of index\n",
    "        num &= ~((1 << index) - 1)\n",
    "        # Set bits starting from 0\n",
    "        num |= (1 << num_ones + 1) - 1\n",
    "        return num"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_get_next_largest.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_get_next_largest.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestBits(object):\n",
    "\n",
    "    def test_get_next_largest(self):\n",
    "        bits = Bits()\n",
    "        assert_raises(Exception, bits.get_next_largest, None)\n",
    "        assert_raises(Exception, bits.get_next_largest, 0)\n",
    "        assert_raises(Exception, bits.get_next_largest, -1)\n",
    "        num = int('011010111', base=2)\n",
    "        expected = int('011011011', base=2)\n",
    "        assert_equal(bits.get_next_largest(num), expected)\n",
    "        print('Success: test_get_next_largest')\n",
    "\n",
    "    def test_get_next_smallest(self):\n",
    "        bits = Bits()\n",
    "        assert_raises(Exception, bits.get_next_smallest, None)\n",
    "        assert_raises(Exception, bits.get_next_smallest, 0)\n",
    "        assert_raises(Exception, bits.get_next_smallest, -1)\n",
    "        num = int('011010111', base=2)\n",
    "        expected = int('011001111', base=2)\n",
    "        assert_equal(bits.get_next_smallest(num), expected)\n",
    "        print('Success: test_get_next_smallest')\n",
    "\n",
    "def main():\n",
    "    test = TestBits()\n",
    "    test.test_get_next_largest()\n",
    "    test.test_get_next_smallest()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_get_next_largest\n",
      "Success: test_get_next_smallest\n"
     ]
    }
   ],
   "source": [
    "%run -i test_get_next_largest.py"
   ]
  }
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