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    "## Problem: Find the start of a linked list loop.\n",
    "\n",
    "* [Clarifying Questions](#Clarifying-Questions)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clarifying Questions\n",
    "\n",
    "* This is a singly linked list?\n",
    "    * Yes\n",
    "* Can we assume we are always passed a circular linked list?\n",
    "    * No"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Empty list\n",
    "* Not a circular linked list\n",
    "    * One element\n",
    "    * Two elements\n",
    "    * Three or more elements\n",
    "* General case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* Check for an empty list\n",
    "* Use two pointers i, j, initialized to the head\n",
    "* j is incremented twice as fast as i\n",
    "    * If j's next is NULL, we do not have a circular list\n",
    "* When i and j meet, move j to the head\n",
    "* Increment i and j one node at a time until they meet\n",
    "* Where they meet is the start of the loop\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: In-place"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run linked_list.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class MyLinkedList(LinkedList):\n",
    "    def find_loop_start(self):\n",
    "        if self.head is None or self.head.next is None:\n",
    "            return\n",
    "        i = self.head\n",
    "        j = self.head\n",
    "        i = i.next\n",
    "        j = j.next.next\n",
    "        while j != i:\n",
    "            i = i.next\n",
    "            if j is None or j.next is None:\n",
    "                return\n",
    "            j = j.next.next\n",
    "        j = self.head\n",
    "        while j != i:\n",
    "            i = i.next\n",
    "            j = j.next\n",
    "        return i.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "collapsed": false
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   "outputs": [],
   "source": [
    "print('Empty list')\n",
    "linked_list = MyLinkedList()\n",
    "print(linked_list.find_loop_start())\n",
    "print('Not a circular linked list')\n",
    "print('One element')\n",
    "head = Node(1)\n",
    "linked_list = MyLinkedList(head)\n",
    "print(linked_list.find_loop_start())\n",
    "print('Two elements')\n",
    "linked_list.append(2)\n",
    "print(linked_list.find_loop_start())\n",
    "print('Three or more elements')\n",
    "linked_list.append(3)\n",
    "print(linked_list.find_loop_start())\n",
    "print('General case')\n",
    "node0 = Node(0)\n",
    "node1 = Node(1)\n",
    "node2 = Node(2)\n",
    "node3 = Node(3)\n",
    "node4 = Node(4)\n",
    "node5 = Node(5)\n",
    "node6 = Node(6)\n",
    "node7 = Node(7)\n",
    "node8 = Node(8)\n",
    "node9 = Node(9)\n",
    "node10 = Node(10)\n",
    "node0.next = node1\n",
    "node1.next = node2\n",
    "node2.next = node3\n",
    "node3.next = node4\n",
    "node4.next = node5\n",
    "node5.next = node6\n",
    "node6.next = node7\n",
    "node7.next = node8\n",
    "node8.next = node9\n",
    "node9.next = node10\n",
    "node10.next = node3\n",
    "linked_list = MyLinkedList(node0)\n",
    "print(linked_list.find_loop_start())"
   ]
  }
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