{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CS 200: List Comprehensions\n",
    "\n",
    "\n",
    "<script language=\"JavaScript\">\n",
    "    document.write(\"Last modified: \" + document.lastModified)\n",
    "</script>\n",
    "\n",
    "### Video:\n",
    "\n",
    "See <a target=qq href=\"https://www.socratica.com/lesson/list-comprehensions\">List Comprehensions</a> from Socratica.\n",
    "\n",
    "List comprehensions are consise ways of executing functions on lists (and sets and dicts).  They are inspired by mathematical notation and the Haskell programming language.\n",
    "\n",
    "In math, the common ways to describe lists (or sets, or tuples, or vectors) are: \n",
    "\n",
    "<li>  S = {x² : x in {0 ... 9}} \n",
    "    </li>\n",
    "<li> V = (1, 2, 4, 8, ..., 2¹²) \n",
    "    </li>\n",
    "<li> M = {x | x in S and x even} \n",
    "    </li>\n",
    "\n",
    "       \n",
    "In other words, you'll find that the above definitions tell you the following:\n",
    "\n",
    "> S is a sequence that contains values between 0 and 9 included, and each value is raised to the power of two.\n",
    "    \n",
    "> The sequence V, on the other hand, contains the value 2 that is raised to a certain power x. The power x starts from 0 and goes till 12.\n",
    "\n",
    "> Lastly, the sequence M contains only the even elements from the sequence S.\n",
    "\n",
    "See https://www.datacamp.com/community/tutorials/python-list-comprehension\n",
    "    \n",
    "Below we give examples of equivalent computations using iteration, map, and list comprehensions.\n",
    "\n",
    "### Convert a string of digits into a list of digits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = []\n",
    "for n in str(12345):\n",
    "    a.append(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1', '2', '3', '4', '5']"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "a1 = list(map(lambda x: x, \"12345\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1', '2', '3', '4', '5']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "a2 = [x for x in str(12345)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1', '2', '3', '4', '5']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a == a1 == a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(lambda x: x*x, range(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-3, -2, 1, 6, 13, 22, 33, 46, 61, 78]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(lambda x:x-3,map(lambda x: x*x,range(10))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert a string of digits into a list of integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = []\n",
    "for n in str(12345):\n",
    "    b.append(int(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "b1 = list(map(int,\"12345\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "b2 = [int(x) for x in str(12345)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b == b1 == b2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert a string of digits into a list of squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = []\n",
    "for n in str(12345):\n",
    "    c.append(int(n) * int(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = list(map(lambda x: int(x) * int(x), \"12345\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "c2 = [int(x) * int(x) for x in str(12345)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c == c1 == c2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert a range of integers into a list of pairs (tuples) of integers and squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = []\n",
    "for n in range(5):\n",
    "    d.append((n, n*n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = list(map(lambda x: (int(x), int(x) * int(x)), range(5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1a = list(map(lambda x: (x, x*x), range(5)))  ## do not need the int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "d2 = [(n, n*n) for n in range(5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16)]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d == d1 == d1a == d2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3 id=\"enumerate\">Convert a list of characters into a list of pairs (tuples) of indices and characters</h3>\n",
    "\n",
    "(No map version.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "ee = enumerate([5,4,3,2,1])\n",
    "ee2 = list(ee)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<enumerate at 0x7fa0c8283240>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ee"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 5), (1, 4), (2, 3), (3, 2), (4, 1)]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ee2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "e = []\n",
    "for (x1,x2) in enumerate(\"abcde\"):\n",
    "    e.append((x1,x2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 'a'), (1, 'b'), (2, 'c'), (3, 'd'), (4, 'e')]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "e2 = [(x1,x2) for (x1,x2) in enumerate(\"abcde\")]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 'a'), (1, 'b'), (2, 'c'), (3, 'd'), (4, 'e')]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e == e2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Filter a range of integers, selecting only the even ones\n",
    "\n",
    "Uses <code>filter</code> instead of <code>map</code>\n",
    "\n",
    "Uses <code>if</code> inside list comprehension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = []\n",
    "for x in range(10):\n",
    "    if x % 2 == 0:\n",
    "        f.append(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 4, 6, 8]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "f1 = list(filter (lambda x: x % 2 == 0, range(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 4, 6, 8]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "f2 = [x for x in range(10) if x % 2 == 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 4, 6, 8]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f == f1 == f2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Filters range of integers, selecting the ones greater than 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = []\n",
    "for x in range(10):\n",
    "    if x > 4:\n",
    "        g.append(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "g1 = list(filter (lambda x: x > 4, range(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "g2 = [x for x in range(10) if x > 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = ['morse', 'stiles', '', 'franklin', 'edwards','', \"\", '', 'branford', '', 'trumbull', '', '', 'hopper']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['morse',\n",
       " 'stiles',\n",
       " '',\n",
       " 'franklin',\n",
       " 'edwards',\n",
       " '',\n",
       " '',\n",
       " '',\n",
       " 'branford',\n",
       " '',\n",
       " 'trumbull',\n",
       " '',\n",
       " '',\n",
       " 'hopper']"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['morse', 'stiles', 'franklin', 'edwards', 'branford', 'trumbull', 'hopper']"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(filter(None, l))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['morse', 'stiles', 'franklin', 'edwards', 'branford', 'trumbull', 'hopper']"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x for x in l if x]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### reduce combines values in a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = 0\n",
    "for x in range(101):\n",
    "    h += x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5050"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "h1 = reduce(lambda x, y: x+y, range(101))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5050"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h == h1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating prime numbers\n",
    "\n",
    "See https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "noprimes = [j for i in range(2, 8) for j in range(i*2, 100, i)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4,\n",
       " 6,\n",
       " 8,\n",
       " 10,\n",
       " 12,\n",
       " 14,\n",
       " 16,\n",
       " 18,\n",
       " 20,\n",
       " 22,\n",
       " 24,\n",
       " 26,\n",
       " 28,\n",
       " 30,\n",
       " 32,\n",
       " 34,\n",
       " 36,\n",
       " 38,\n",
       " 40,\n",
       " 42,\n",
       " 44,\n",
       " 46,\n",
       " 48,\n",
       " 50,\n",
       " 52,\n",
       " 54,\n",
       " 56,\n",
       " 58,\n",
       " 60,\n",
       " 62,\n",
       " 64,\n",
       " 66,\n",
       " 68,\n",
       " 70,\n",
       " 72,\n",
       " 74,\n",
       " 76,\n",
       " 78,\n",
       " 80,\n",
       " 82,\n",
       " 84,\n",
       " 86,\n",
       " 88,\n",
       " 90,\n",
       " 92,\n",
       " 94,\n",
       " 96,\n",
       " 98,\n",
       " 6,\n",
       " 9,\n",
       " 12,\n",
       " 15,\n",
       " 18,\n",
       " 21,\n",
       " 24,\n",
       " 27,\n",
       " 30,\n",
       " 33,\n",
       " 36,\n",
       " 39,\n",
       " 42,\n",
       " 45,\n",
       " 48,\n",
       " 51,\n",
       " 54,\n",
       " 57,\n",
       " 60,\n",
       " 63,\n",
       " 66,\n",
       " 69,\n",
       " 72,\n",
       " 75,\n",
       " 78,\n",
       " 81,\n",
       " 84,\n",
       " 87,\n",
       " 90,\n",
       " 93,\n",
       " 96,\n",
       " 99,\n",
       " 8,\n",
       " 12,\n",
       " 16,\n",
       " 20,\n",
       " 24,\n",
       " 28,\n",
       " 32,\n",
       " 36,\n",
       " 40,\n",
       " 44,\n",
       " 48,\n",
       " 52,\n",
       " 56,\n",
       " 60,\n",
       " 64,\n",
       " 68,\n",
       " 72,\n",
       " 76,\n",
       " 80,\n",
       " 84,\n",
       " 88,\n",
       " 92,\n",
       " 96,\n",
       " 10,\n",
       " 15,\n",
       " 20,\n",
       " 25,\n",
       " 30,\n",
       " 35,\n",
       " 40,\n",
       " 45,\n",
       " 50,\n",
       " 55,\n",
       " 60,\n",
       " 65,\n",
       " 70,\n",
       " 75,\n",
       " 80,\n",
       " 85,\n",
       " 90,\n",
       " 95,\n",
       " 12,\n",
       " 18,\n",
       " 24,\n",
       " 30,\n",
       " 36,\n",
       " 42,\n",
       " 48,\n",
       " 54,\n",
       " 60,\n",
       " 66,\n",
       " 72,\n",
       " 78,\n",
       " 84,\n",
       " 90,\n",
       " 96,\n",
       " 14,\n",
       " 21,\n",
       " 28,\n",
       " 35,\n",
       " 42,\n",
       " 49,\n",
       " 56,\n",
       " 63,\n",
       " 70,\n",
       " 77,\n",
       " 84,\n",
       " 91,\n",
       " 98]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noprimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "primes = [x for x in range(2, 100) if x not in noprimes]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2,\n",
       " 3,\n",
       " 5,\n",
       " 7,\n",
       " 11,\n",
       " 13,\n",
       " 17,\n",
       " 19,\n",
       " 23,\n",
       " 29,\n",
       " 31,\n",
       " 37,\n",
       " 41,\n",
       " 43,\n",
       " 47,\n",
       " 53,\n",
       " 59,\n",
       " 61,\n",
       " 67,\n",
       " 71,\n",
       " 73,\n",
       " 79,\n",
       " 83,\n",
       " 89,\n",
       " 97]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "primes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "149"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(noprimes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "noprimes contains duplicates. If we convert it to a set, we will eliminate the duplicates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 2, 3, 4, 5, 6, 7}"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set([1,2,3,4,1,2,3,4,5,6,7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "setnoprimes = set(noprimes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{4,\n",
       " 6,\n",
       " 8,\n",
       " 9,\n",
       " 10,\n",
       " 12,\n",
       " 14,\n",
       " 15,\n",
       " 16,\n",
       " 18,\n",
       " 20,\n",
       " 21,\n",
       " 22,\n",
       " 24,\n",
       " 25,\n",
       " 26,\n",
       " 27,\n",
       " 28,\n",
       " 30,\n",
       " 32,\n",
       " 33,\n",
       " 34,\n",
       " 35,\n",
       " 36,\n",
       " 38,\n",
       " 39,\n",
       " 40,\n",
       " 42,\n",
       " 44,\n",
       " 45,\n",
       " 46,\n",
       " 48,\n",
       " 49,\n",
       " 50,\n",
       " 51,\n",
       " 52,\n",
       " 54,\n",
       " 55,\n",
       " 56,\n",
       " 57,\n",
       " 58,\n",
       " 60,\n",
       " 62,\n",
       " 63,\n",
       " 64,\n",
       " 65,\n",
       " 66,\n",
       " 68,\n",
       " 69,\n",
       " 70,\n",
       " 72,\n",
       " 74,\n",
       " 75,\n",
       " 76,\n",
       " 77,\n",
       " 78,\n",
       " 80,\n",
       " 81,\n",
       " 82,\n",
       " 84,\n",
       " 85,\n",
       " 86,\n",
       " 87,\n",
       " 88,\n",
       " 90,\n",
       " 91,\n",
       " 92,\n",
       " 93,\n",
       " 94,\n",
       " 95,\n",
       " 96,\n",
       " 98,\n",
       " 99}"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "setnoprimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(setnoprimes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Set comprehensions\n",
    "\n",
    "By using {} instead of [] we can create set comprehensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = [x if x % 2 else x + 1 for x in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1, 3, 3, 5, 5, 7, 7, 9, 9]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "s2 = {x if x % 2 else x + 1 for x in range(10)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 3, 5, 7, 9}"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create literal sets using {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "s3 = {1, 2, 3, 1, 2, 3}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 2, 3}"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "noprimesset = {j for i in range(2, 8) for j in range(i*2, 100, i)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{4,\n",
       " 6,\n",
       " 8,\n",
       " 9,\n",
       " 10,\n",
       " 12,\n",
       " 14,\n",
       " 15,\n",
       " 16,\n",
       " 18,\n",
       " 20,\n",
       " 21,\n",
       " 22,\n",
       " 24,\n",
       " 25,\n",
       " 26,\n",
       " 27,\n",
       " 28,\n",
       " 30,\n",
       " 32,\n",
       " 33,\n",
       " 34,\n",
       " 35,\n",
       " 36,\n",
       " 38,\n",
       " 39,\n",
       " 40,\n",
       " 42,\n",
       " 44,\n",
       " 45,\n",
       " 46,\n",
       " 48,\n",
       " 49,\n",
       " 50,\n",
       " 51,\n",
       " 52,\n",
       " 54,\n",
       " 55,\n",
       " 56,\n",
       " 57,\n",
       " 58,\n",
       " 60,\n",
       " 62,\n",
       " 63,\n",
       " 64,\n",
       " 65,\n",
       " 66,\n",
       " 68,\n",
       " 69,\n",
       " 70,\n",
       " 72,\n",
       " 74,\n",
       " 75,\n",
       " 76,\n",
       " 77,\n",
       " 78,\n",
       " 80,\n",
       " 81,\n",
       " 82,\n",
       " 84,\n",
       " 85,\n",
       " 86,\n",
       " 87,\n",
       " 88,\n",
       " 90,\n",
       " 91,\n",
       " 92,\n",
       " 93,\n",
       " 94,\n",
       " 95,\n",
       " 96,\n",
       " 98,\n",
       " 99}"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noprimesset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "73"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(noprimesset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dictionary comprehensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = {i : x*x for (i,x) in enumerate(range(10))}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0, 1: 1, 2: 4, 3: 9, 4: 16, 5: 25, 6: 36, 7: 49, 8: 64, 9: 81}"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "End of list comprehension notebook"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
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