From 013ac4c1ec58003466eac2c2a61ba435dc283ed6 Mon Sep 17 00:00:00 2001 From: Donne Martin Date: Sun, 17 May 2015 05:33:48 -0400 Subject: [PATCH] Added notebook solving the following: Implement a stack with push, pop, and min methods running O(1) time. --- README.md | 1 + stacks-queues/stack-min.ipynb | 175 ++++++++++++++++++++++++++++++++++ 2 files changed, 176 insertions(+) create mode 100644 stacks-queues/stack-min.ipynb diff --git a/README.md b/README.md index c57f43f..32119af 100644 --- a/README.md +++ b/README.md @@ -33,6 +33,7 @@ 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) +* [Implement a stack that keeps track of its minimum element](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/stacks-queues/stack-min.ipynb) ## License diff --git a/stacks-queues/stack-min.ipynb b/stacks-queues/stack-min.ipynb new file mode 100644 index 0000000..8d0e630 --- /dev/null +++ b/stacks-queues/stack-min.ipynb @@ -0,0 +1,175 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem: Implement a stack with push, pop, and min methods running O(1) time.\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", + "* Is this a stack of ints?\n", + " * Yes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Cases\n", + "\n", + "* Push/pop on empty stack\n", + "* Push/pop on non-empty stack" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Algorithm\n", + "\n", + "We'll use a second stack to keep track of the minimum values.\n", + "\n", + "### Min\n", + "\n", + "* If the second stack is empty, return the max int value\n", + "* Else, return the top of the stack, without popping it\n", + "\n", + "Complexity:\n", + "* Time: O(1)\n", + "* Space: O(1)\n", + "\n", + "### Push\n", + "\n", + "* Push the data\n", + "* If the data is less than min\n", + " * Push data to second stack\n", + "\n", + "Complexity:\n", + "* Time: O(1)\n", + "* Space: O(n)\n", + "\n", + "### Pop\n", + "\n", + "* Pop the data\n", + "* If the data is equal to min\n", + " * Pop the top of the second stack\n", + "* Return the data\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": [ + "%run stack.py" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import sys\n", + "\n", + "class MyStack(Stack):\n", + " def __init__(self, top=None):\n", + " self.min_vals = Stack()\n", + " super(MyStack, self).__init__(top)\n", + "\n", + " def min(self):\n", + " if self.min_vals.top is None:\n", + " return sys.maxint\n", + " else:\n", + " return self.min_vals.peek()\n", + "\n", + " def push(self, data):\n", + " super(MyStack, self).push(data)\n", + " if data < self.min():\n", + " self.min_vals.push(data)\n", + "\n", + " def pop(self):\n", + " data = super(MyStack, self).pop()\n", + " if data == self.min():\n", + " self.min_vals.pop()\n", + " return data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "print('Push on empty stack, non-empty stack')\n", + "stack = MyStack()\n", + "stack.push(5)\n", + "print('Push:', stack.peek(), 'Min after push:', stack.min())\n", + "stack.push(1)\n", + "print('Push:', stack.peek(), 'Min after push:', stack.min())\n", + "stack.push(3)\n", + "print('Push:', stack.peek(), 'Min after push:', stack.min())\n", + "stack.push(0)\n", + "print('Push:', stack.peek(), 'Min after push:', stack.min())\n", + "print('Pop on non-empty stack')\n", + "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n", + "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n", + "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n", + "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n", + "print('Stack contents:', stack.peek())\n", + "print('Pop empty stack:', stack.pop())" + ] + } + ], + "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 +}