{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Solution Notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Implement n stacks using a single array.\n", "\n", "* [Constraints](#Constraints)\n", "* [Test Cases](#Test-Cases)\n", "* [Algorithm](#Algorithm)\n", "* [Code](#Code)\n", "* [Unit Test](#Unit-Test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constraints\n", "\n", "* Are the stacks and array a fixed size?\n", " * Yes\n", "* Are the stacks equally sized?\n", " * Yes\n", "* Does pushing to a full stack result in an exception?\n", " * Yes\n", "* Does popping from an empty stack result in an exception?\n", " * Yes\n", "* Can we assume the user passed in stack index is valid?\n", " * Yes\n", "* Can we assume this fits memory?\n", " * Yes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Test Cases\n", "\n", "* Test the following on the three stacks:\n", " * Push to full stack -> Exception\n", " * Push to non-full stack\n", " * Pop on empty stack -> Exception\n", " * Pop on non-empty stack" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Algorithm\n", "\n", "### Absolute Index\n", "\n", "* return stack size * stack index + stack pointer\n", "\n", "Complexity:\n", "* Time: O(1)\n", "* Space: O(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)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class Stacks(object):\n", "\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] * self.num_stacks\n", " self.stack_array = [None] * self.num_stacks * self.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", " 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", " 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": "markdown", "metadata": {}, "source": [ "## Unit Test\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting test_n_stacks.py\n" ] } ], "source": [ "%%writefile test_n_stacks.py\n", "from nose.tools import assert_equal\n", "from nose.tools import raises\n", "\n", "\n", "class TestStacks(object):\n", "\n", " @raises(Exception)\n", " def test_pop_on_empty(self, num_stacks, stack_size):\n", " print('Test: Pop on empty stack')\n", " stacks = Stacks(num_stacks, stack_size)\n", " stacks.pop(0)\n", "\n", " @raises(Exception)\n", " def test_push_on_full(self, num_stacks, stack_size):\n", " print('Test: Push to full stack')\n", " stacks = Stacks(num_stacks, stack_size)\n", " for i in range(0, stack_size):\n", " stacks.push(2, i)\n", " stacks.push(2, stack_size)\n", "\n", " def test_stacks(self, num_stacks, stack_size):\n", " print('Test: Push to non-full stack')\n", " stacks = Stacks(num_stacks, stack_size)\n", " stacks.push(0, 1)\n", " stacks.push(0, 2)\n", " stacks.push(1, 3)\n", " stacks.push(2, 4)\n", "\n", " print('Test: Pop on non-empty stack')\n", " assert_equal(stacks.pop(0), 2)\n", " assert_equal(stacks.pop(0), 1)\n", " assert_equal(stacks.pop(1), 3)\n", " assert_equal(stacks.pop(2), 4)\n", "\n", " print('Success: test_stacks\\n')\n", "\n", "\n", "def main():\n", " num_stacks = 3\n", " stack_size = 100\n", " test = TestStacks()\n", " test.test_pop_on_empty(num_stacks, stack_size)\n", " test.test_push_on_full(num_stacks, stack_size)\n", " test.test_stacks(num_stacks, stack_size)\n", "\n", "\n", "if __name__ == '__main__':\n", " main()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test: Pop on empty stack\n", "Test: Push to full stack\n", "Test: Push to non-full stack\n", "Test: Pop on non-empty stack\n", "Success: test_stacks\n", "\n" ] } ], "source": [ "run -i test_n_stacks.py" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.0" } }, "nbformat": 4, "nbformat_minor": 0 }