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   "source": [
    "<small><i>This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://bit.ly/code-notes).</i></small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Partition a linked list around a value x, such that all nodes less than x come before all nodes greater than or equal to x.\n",
    "\n",
    "* [Constraints and Assumptions](#Constraints-and-Assumptions)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints and Assumptions\n",
    "\n",
    "*Problem statements are often intentionally ambiguous.  Identifying constraints and stating assumptions can help to ensure you code the intended solution.*\n",
    "\n",
    "* Can we create additional data structures?\n",
    "    * Yes\n",
    "* Do you expect the function to return a new list?\n",
    "    * Yes\n",
    "* Can we assume the input x is valid?\n",
    "    * Yes\n",
    "* Can we assume we already have a linked list class that can be used for this problem?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Empty list\n",
    "* One element list\n",
    "* Left linked list is empty\n",
    "* Right linked list is empty\n",
    "* General case\n",
    "    * Partition = 10\n",
    "    * Input:  4, 3, 7, 8, 10, 1, 10, 12\n",
    "    * Output: 4, 3, 7, 8, 1, 10, 10, 12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* Create left and right linked lists\n",
    "* For each element in the list\n",
    "    * If elem < x, append to the left list\n",
    "    * else, append to the right list\n",
    "* Merge left and right lists\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run linked_list.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class MyLinkedList(LinkedList):\n",
    "    def partition(self, data):\n",
    "        if self.head is None:\n",
    "            return\n",
    "        left = MyLinkedList(None)\n",
    "        right = MyLinkedList(None)\n",
    "        curr = self.head\n",
    "        \n",
    "        # Build the left and right lists\n",
    "        while curr is not None:\n",
    "            if curr.data < data:\n",
    "                left.append(curr.data)\n",
    "            else:\n",
    "                right.append(curr.data)\n",
    "            curr = curr.next\n",
    "        curr_left = left.head\n",
    "        if curr_left is None:\n",
    "            return right\n",
    "        else:\n",
    "            # Merge the two lists\n",
    "            while curr_left.next is not None:\n",
    "                curr_left = curr_left.next\n",
    "            curr_left.next = right.head\n",
    "            return left"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*It is important to identify and run through general and edge cases from the [Test Cases](#Test-Cases) section by hand.  You generally will not be asked to write a unit test like what is shown below.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: Empty list\n",
      "Test: One element list, left list empty\n",
      "Test: Right list is empty\n",
      "Test: General case\n",
      "Success: test_partition\n"
     ]
    }
   ],
   "source": [
    "from nose.tools import assert_equal\n",
    "\n",
    "class Test(object):\n",
    "    def test_partition(self):\n",
    "        print('Test: Empty list')\n",
    "        linked_list = MyLinkedList(None)\n",
    "        linked_list.partition(10)\n",
    "        assert_equal(linked_list.get_all_data(), [])\n",
    "\n",
    "        print('Test: One element list, left list empty')\n",
    "        linked_list = MyLinkedList(Node(5))\n",
    "        linked_list.partition(0)\n",
    "        assert_equal(linked_list.get_all_data(), [5])\n",
    "\n",
    "        print('Test: Right list is empty')\n",
    "        linked_list = MyLinkedList(Node(5))\n",
    "        linked_list.partition(10)\n",
    "        assert_equal(linked_list.get_all_data(), [5])\n",
    "\n",
    "        print('Test: General case')\n",
    "        # Partition = 10\n",
    "        # Input: 4, 3, 7, 8, 10, 1, 10, 12\n",
    "        # Output: 4, 3, 7, 8, 1, 10, 10, 12\n",
    "        linked_list = MyLinkedList(Node(12))\n",
    "        linked_list.insert_to_front(10)\n",
    "        linked_list.insert_to_front(1)\n",
    "        linked_list.insert_to_front(10)\n",
    "        linked_list.insert_to_front(8)\n",
    "        linked_list.insert_to_front(7)\n",
    "        linked_list.insert_to_front(3)\n",
    "        linked_list.insert_to_front(4)\n",
    "        partitioned_list = linked_list.partition(10)\n",
    "        assert_equal(partitioned_list.get_all_data(), \n",
    "                     [4, 3, 7, 8, 1, 10, 10, 12])\n",
    "        \n",
    "        print('Success: test_partition')\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    test = Test()\n",
    "    test.test_partition()"
   ]
  }
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