Added notebook solving the following: Find the start of a linked list loop.

README.md

@@ -27,6 +27,7 @@ Continually updated IPython Notebooks containing coding problems and solutions (
 * [Delete a node in the middle of a linked list, given access to only that node](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/delete-mid.ipynb)
 * [Partition a linked list around a given value](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/partition.ipynb)
 * [Add two numbers whose digits are stored in a linked list in reverse order](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/add-reverse.ipynb)
+* [Find the start of a linked list loop](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/linked-lists/find-loop-start.ipynb)
 
 ## Stacks and Queues
 

linked-lists/find-loop-start.ipynb

@@ -0,0 +1,177 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 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,
+   "metadata": {
+    "collapsed": false
+   },
+   "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())"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}