data-science-ipython-notebooks/python-data/structs.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Data Structures"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* tuple\n",
      "* list\n",
      "* dict\n",
      "* set"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## tuple"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A tuple is a one dimensional, fixed-length, immutable sequence.\n",
      "\n",
      "Create a tuple:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tup = (1, 2, 3)\n",
      "tup"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "(1, 2, 3)"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Convert to a tuple:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "list_1 = [1, 2, 3]\n",
      "type(tuple(list_1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "tuple"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create a nested tuple:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_tup = ([1, 2, 3], (4, 5))\n",
      "nested_tup"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "([1, 2, 3], (4, 5))"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Access a tuple's elements by index O(1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_tup[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "[1, 2, 3]"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Although tuples are immutable, their contents can contain mutable objects.  \n",
      "\n",
      "Modify a tuple's contents:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_tup[0].append(4)\n",
      "nested_tup[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[1, 2, 3, 4]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Concatenate tuples by creating a new tuple and copying objects:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(1, 3, 2) + (4, 5, 6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "(1, 3, 2, 4, 5, 6)"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Multiply tuples to copy references to objects (objects themselves are not copied):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "('foo', 'bar') * 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "('foo', 'bar', 'foo', 'bar')"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unpack tuples:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a, b = nested_tup\n",
      "a, b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "([1, 2, 3, 4], (4, 5))"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unpack nested tuples:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(a, b, c, d), (e, f) = nested_tup\n",
      "a, b, c, d, e, f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(1, 2, 3, 4, 4, 5)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A common use of variable unpacking is when iterating over sequences of tuples or lists:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "seq = [( 1, 2, 3), (4, 5, 6), (7, 8, 9)] \n",
      "for a, b, c in seq: \n",
      "    print(a, b, c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(1, 2, 3)\n",
        "(4, 5, 6)\n",
        "(7, 8, 9)\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## list"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A list is a one dimensional, variable-length, mutable sequence.\n",
      "\n",
      "Create a list:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "list_1 = [1, 2, 3]\n",
      "list_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "[1, 2, 3]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Convert to a list:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "type(list(tup))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "list"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create a nested list:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_list = [(1, 2, 3), [4, 5]]\n",
      "nested_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[(1, 2, 3), [4, 5]]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Access a list's elements by index O(1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_list[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[4, 5]"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Append an element to a list O(1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_list.append(6)\n",
      "nested_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "[(1, 2, 3), [4, 5], 6]"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Insert an element to a list at a specific index (note that insert is expensive as it has to shift subsequent elements O(n)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_list.insert(0, 'start')\n",
      "nested_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "['start', (1, 2, 3), [4, 5], 6]"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pop is expensive as it has to shift subsequent elements O(n).  The operation is O(1) if pop is used for the last element.\n",
      "\n",
      "Remove and return an element from a specified index:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_list.pop(0)\n",
      "nested_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[(1, 2, 3), [4, 5], 6]"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Locates the first such value and remove it O(n):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_list.remove((1, 2, 3))\n",
      "nested_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[[4, 5], 6]"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check if a list contains a value O(n):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "6 in nested_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Concatenate lists by creating a new list and copying objects:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "[1, 3, 2] + [4, 5, 6]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "[1, 3, 2, 4, 5, 6]"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Extend a list by appending elements (faster than concatenating lists, as it does not have to create a new list):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nested_list.extend([7, 8, 9])\n",
      "nested_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "[[4, 5], 6, 7, 8, 9]"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## dict"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A dict is also known as a hash map or associative array.  A dict is a mutable collection of key-value pairs.\n",
      "\n",
      "Note: Big O complexities are listed as average case, with most worst case complexities being O(n).\n",
      "\n",
      "Create a dict:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_1 = { 'a' : 'foo', 'b' : [0, 1, 2, 3] }\n",
      "dict_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "{'a': 'foo', 'b': [0, 1, 2, 3]}"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Access a dict's elements by index O(1)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_1['b']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "[0, 1, 2, 3]"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Insert or set a dict's elements by index O(1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_1[5] = 'bar'\n",
      "dict_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "{5: 'bar', 'a': 'foo', 'b': [0, 1, 2, 3]}"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check if a dict contains a key O(1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "5 in dict_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Delete a value from a dict O(1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_2 = dict(dict_1)\n",
      "del dict_2[5]\n",
      "dict_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "{'a': 'foo', 'b': [0, 1, 2, 3]}"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Remove and return an element from a specified index O(1):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "value = dict_2.pop('b')\n",
      "print(value)\n",
      "print(dict_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0, 1, 2, 3]\n",
        "{'a': 'foo'}\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Get or pop can be called with a default value if the key is not found.  By default, get() will return None and pop() will throw an exception if the key is not found."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "value = dict_1.get('z', 0)\n",
      "value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "0"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Return a default value if the key is not found:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(dict_1.setdefault('b', None))\n",
      "print(dict_1.setdefault('z', None))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0, 1, 2, 3]\n",
        "None\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "By contrast to setdefault(), defaultdict lets you specify the default when the container is initialized, which works well if the default is appropriate for all keys:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from collections import defaultdict\n",
      "\n",
      "seq = ['foo', 'bar', 'baz']\n",
      "first_letter = defaultdict(list)\n",
      "for elem in seq:\n",
      "    first_letter[elem[0]].append(elem)\n",
      "first_letter"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "defaultdict(<type 'list'>, {'b': ['bar', 'baz'], 'f': ['foo']})"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "dict keys must be \"hashable\", i.e. they must be immutable objects like scalars (int, float, string) or tuples whose objects are all immutable.  Lists are mutable and therefore are not hashable, although you can convert the list portion to a tuple as a quick fix."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(hash('string'))\n",
      "print(hash((1, 2, (3, 4))))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-9167918882415130555\n",
        "-2725224101759650258\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Get the list of keys in no particular order (although keys() outputs the keys in the same order).  In Python 3, keys() returns an iterator instead of a list."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_1.keys()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "['a', 'b', 5, 'z']"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Get the list of values in no particular order (although values() outputs the keys in the same order).  In Python 3, keys() returns an iterator instead of a list."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_1.values()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "['foo', [0, 1, 2, 3], 'bar', None]"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Iterate through a dictionary's keys and values:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for key, value in dict_1.items():\n",
      "    print key, value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "a foo\n",
        "b [0, 1, 2, 3]\n",
        "5 bar\n",
        "z None\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Merge one dict into another:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_1.update({'e' : 'elephant', 'f' : 'fish'})\n",
      "dict_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "{5: 'bar',\n",
        " 'a': 'foo',\n",
        " 'b': [0, 1, 2, 3],\n",
        " 'e': 'elephant',\n",
        " 'f': 'fish',\n",
        " 'z': None}"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Pair up two sequences element-wise in a dict:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mapping = dict(zip(range(7), reversed(range(7))))\n",
      "mapping"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "{0: 6, 1: 5, 2: 4, 3: 3, 4: 2, 5: 1, 6: 0}"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## set"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A set is an unordered sequence of unique elements.  \n",
      "\n",
      "Create a set:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_1 = set([0, 1, 2, 3, 4, 5])\n",
      "set_1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "{0, 1, 2, 3, 4, 5}"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_2 = {1, 2, 3, 5, 8, 13}\n",
      "set_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "{1, 2, 3, 5, 8, 13}"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sets support set operations like union, intersection, difference, and symmetric difference."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Union O(len(set_1) + len(set_2)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_1 | set_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "{0, 1, 2, 3, 4, 5, 8, 13}"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Intersection O(min(len(set_1), len(set_2)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_1 & set_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "{1, 2, 3, 5}"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Difference O(len(set_1)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_1 - set_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "{0, 4}"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Symmetric Difference O(len(set_1)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_1 ^ set_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "{0, 4, 8, 13}"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Subset O(len(set_3)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_3 = {1, 2, 3}\n",
      "set_3.issubset(set_2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Superset O(len(set_3)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set_2.issuperset(set_3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Equal O(min(len(set_1), len(set_2)):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "{1, 2, 3} == {3, 2, 1}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 45
    }
   ],
   "metadata": {}
  }
 ]
}