From 1d3888509809224dc336cdad05e30220d2bbf632 Mon Sep 17 00:00:00 2001 From: Donne Martin Date: Sat, 16 May 2015 08:46:58 -0400 Subject: [PATCH] Added notebook solving the following: Implement n stacks using a single array. --- README.md | 1 + stacks-queues/n-stacks.ipynb | 184 +++++++++++++++++++++++++++++++++++ 2 files changed, 185 insertions(+) create mode 100644 stacks-queues/n-stacks.ipynb diff --git a/README.md b/README.md index 034353c..c57f43f 100644 --- a/README.md +++ b/README.md @@ -32,6 +32,7 @@ Continually updated IPython Notebooks containing coding problems and solutions ( * [Implement a stack with push, pop, and peek methods using a linked list](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/stack.ipynb) * [Implement a queue with enqueue and dequeue methods using a linked list](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/queue.ipynb) +* [Implement n stacks using a single array](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/n-stacks.ipynb) ## License diff --git a/stacks-queues/n-stacks.ipynb b/stacks-queues/n-stacks.ipynb new file mode 100644 index 0000000..e6cd207 --- /dev/null +++ b/stacks-queues/n-stacks.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Implement n stacks using a single array.\n", + "\n", + "* [Clarifying Questions](#Clarifying-Questions)\n", + "* [Test Cases](#Test-Cases)\n", + "* [Algorithm](#Algorithm)\n", + "* [Code](#Code)\n", + "* [Pythonic-Code](#Pythonic-Code)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Clarifying Questions\n", + "\n", + "* Are the stacks and array a fixed size?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* Test the following on the three stacks:\n", + " * Push to full stack\n", + " * Push to non-full stack\n", + " * Pop on empty stack\n", + " * Pop on non-empty stack" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "* Initialize array\n", + "* Initialize stack pointers to -1\n", + "\n", + "### Push\n", + "\n", + "* If stack is full, throw exception\n", + "* Else\n", + " * Increment stack pointer\n", + " * Get the absolute array index\n", + " * Insert the value to this index\n", + "\n", + "Complexity:\n", + "* Time: O(1)\n", + "* Space: O(1)\n", + "\n", + "### Pop\n", + "\n", + "* If stack is empty, throw exception\n", + "* Else\n", + " * Store the value contained in the absolute array index\n", + " * Set the value in the absolute array index to None\n", + " * Decrement stack pointer\n", + " * return value\n", + "\n", + "Complexity:\n", + "* Time: O(1)\n", + "* Space: O(1)\n", + "\n", + "\n", + "### Absolute Index\n", + "\n", + "* return stack size * stack index + stack pointer\n", + "\n", + "Complexity:\n", + "* Time: O(1)\n", + "* Space: O(1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class Stacks(object):\n", + " def __init__(self, num_stacks, stack_size):\n", + " self.num_stacks = num_stacks\n", + " self.stack_size = stack_size\n", + " self.stack_pointers = [-1] * num_stacks\n", + " self.stack_array = [None] * num_stacks * stack_size\n", + "\n", + " def abs_index(self, stack_index):\n", + " return stack_index * self.stack_size + self.stack_pointers[stack_index]\n", + "\n", + " def push(self, stack_index, data):\n", + " if self.stack_pointers[stack_index] == self.stack_size - 1:\n", + " raise Exception('Stack is full')\n", + " else:\n", + " self.stack_pointers[stack_index] += 1\n", + " array_index = self.abs_index(stack_index)\n", + " self.stack_array[array_index] = data\n", + "\n", + " def pop(self, stack_index):\n", + " if self.stack_pointers[stack_index] == -1:\n", + " raise Exception('Stack is empty')\n", + " else:\n", + " array_index = self.abs_index(stack_index) \n", + " data = self.stack_array[array_index]\n", + " self.stack_array[array_index] = None\n", + " self.stack_pointers[stack_index] -= 1\n", + " return data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "num_stacks = 3\n", + "stack_size = 100\n", + "print('Pop on empty stack')\n", + "stacks = Stacks(num_stacks, stack_size)\n", + "try:\n", + " stacks.pop(0)\n", + "except Exception as e:\n", + " print(e)\n", + "print('Push to non-full stack')\n", + "stacks.push(0, 1)\n", + "stacks.push(0, 2)\n", + "stacks.push(1, 3)\n", + "stacks.push(2, 4)\n", + "print('Pop on non-empty stack')\n", + "print(stacks.pop(0))\n", + "print(stacks.pop(0))\n", + "print(stacks.pop(1))\n", + "print(stacks.pop(2))\n", + "print('Push to full stack')\n", + "for i in xrange(0, stack_size):\n", + " stacks.push(2, i)\n", + "try:\n", + " stacks.push(2, stack_size)\n", + "except Exception as e:\n", + " print(e)" + ] + } + ], + "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 +}