diff --git a/README.md b/README.md index 6e30a33..a1f3378 100644 --- a/README.md +++ b/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 diff --git a/linked-lists/find-loop-start.ipynb b/linked-lists/find-loop-start.ipynb new file mode 100644 index 0000000..0b2caf4 --- /dev/null +++ b/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 +}