13. List Comprehension.ipynb

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    "## List Comprehension\n",
    "\n",
    "List comprehensions were added with Python 2.0. Essentially, it is Python's way of implementing a well-known notation for sets as used by mathematicians.\n",
    "In mathematics the square numbers of the natural numbers are, for example, created by { x2 | x ∈ ℕ } or the set of complex integers { (x,y) | x ∈ ℤ ∧ y ∈ ℤ }.\n",
    "\n",
    "List comprehension is an elegant way to define and create list in Python. These lists have often the qualities of sets, but are not in all cases sets.\n",
    "\n",
    "List comprehension is a complete substitute for the lambda function as well as the functions map(), filter() and reduce(). For most people the syntax of list comprehension is easier to be grasped."
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     "text": [
      "[102.56, 97.7, 99.14, 100.03999999999999]\n"
     ]
    }
   ],
   "source": [
    "Celsius = [39.2, 36.5, 37.3, 37.8]\n",
    "Fahrenheit = [ ((float(9)/5)*x + 32) for x in Celsius ]  # this is lis comprehension\n",
    "print(Fahrenheit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "[('red', 'house'), ('red', 'car'), ('red', 'tree'), ('green', 'house'), ('green', 'car'), ('green', 'tree'), ('yellow', 'house'), ('yellow', 'car'), ('yellow', 'tree'), ('blue', 'house'), ('blue', 'car'), ('blue', 'tree')]\n"
     ]
    }
   ],
   "source": [
    "colours = [ \"red\", \"green\", \"yellow\", \"blue\" ]\n",
    "things = [ \"house\", \"car\", \"tree\" ]\n",
    "coloured_things = [ (x,y) for x in colours for y in things ]\n",
    "print(coloured_things)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generator Comprehension\n",
    "\n",
    "Generator comprehensions were introduced with Python 2.6. They are simply like a list comprehension but with parentheses - round brackets - instead of (square) brackets around it. Otherwise, the syntax and the way of working is like list comprehension, but a generator comprehension returns a generator instead of a list."
   ]
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     "text": [
      "<generator object <genexpr> at 0x0000019297C95F68>\n"
     ]
    }
   ],
   "source": [
    "x = (x **2 for x in range(20))\n",
    "print(x)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361]\n"
     ]
    }
   ],
   "source": [
    "x = list(x)\n",
    "print(x)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]\n"
     ]
    }
   ],
   "source": [
    "         # this return 'i' then 'i' pass to this statement then 'j' return\n",
    "noprimes = [j for i in range(2, 8) for j in range(i*2, 100, i)]\n",
    "primes = [x for x in range(2, 100) if x not in noprimes]\n",
    "print(primes)\n"
   ]
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   "execution_count": 19,
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     "text": [
      "[4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98]\n"
     ]
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     "data": {
      "text/plain": [
       "[2, 3, 4, 5, 6, 7]"
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     "execution_count": 19,
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   "source": [
    "print(noprimes)\n",
    "[i for i in range(2,8)]"
   ]
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  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
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     "name": "stdout",
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     "text": [
      "[4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98]\n"
     ]
    }
   ],
   "source": [
    "print([j for j in range(4,100,2)])"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Set Comprehension\n",
    "\n",
    "A set comprehension is similar to a list comprehension, but returns a set and not a list. Syntactically, we use curly brackets instead of square brackets to create a set. Set comprehension is the right functionality to solve our problem from the previous subsection. We are able to create the set of non primes without doublets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99}\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "n = 100\n",
    "sqrt_n = int(sqrt(n))\n",
    "no_primes = {j for i in range(2, sqrt_n+1) for j in range(i*2, n, i)}\n",
    "print(no_primes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}\n"
     ]
    }
   ],
   "source": [
    "primes = {i for i in range(2, n) if i not in no_primes}\n",
    "print(primes)"
   ]
  }
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