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   "source": [
    "# Thinking in list comprehensions\n",
    "\n",
    "Here is a way of thinking about list comprehensions that may help you write more complex comprehensions in a natural way:"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "def make_powers_lc(n, inputs):\n",
    "    \"\"\"\n",
    "    Given list of inputs, return each input raised to the 1st-Nth power\n",
    "    \n",
    "    e.g.\n",
    "    >>> make_powers_lc(4, range(10))\n",
    "    [[0, 0, 0, 0],\n",
    "     [1, 1, 1, 1],\n",
    "     [2, 4, 8, 16],\n",
    "     [3, 9, 27, 81],\n",
    "     [4, 16, 64, 256],\n",
    "     [5, 25, 125, 625],\n",
    "     [6, 36, 216, 1296],\n",
    "     [7, 49, 343, 2401],\n",
    "     [8, 64, 512, 4096],\n",
    "     [9, 81, 729, 6561]]\n",
    "    \"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8eb3928f",
   "metadata": {},
   "outputs": [],
   "source": []
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  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1caa3d73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1]]"
      ]
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "# 1) start with shape: \n",
    "# Output will be a list of list of ints, \n",
    "# so create simplest version of that\n",
    "def make_powers_lc(n, inputs):\n",
    "    return [[1]]\n",
    "make_powers_lc(4, range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cc3309a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1], [1], [1], [1], [1], [1], [1], [1], [1], [1]]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2) expand outer list comprehension to have correct number of elements\n",
    "# using inputs as foundation, we haven't modified the first term yet\n",
    "def make_powers_lc(n, inputs):\n",
    "    return [[1] for x in inputs]\n",
    "make_powers_lc(4, range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8a531ebc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1],\n",
       " [1, 1, 1, 1]]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3) Now expand inner list to have correct number of elements.\n",
    "def make_powers_lc(n, inputs):\n",
    "    return [[1 for y in range(n)] for x in inputs]\n",
    "make_powers_lc(4, range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "80135012",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 0, 0, 0],\n",
       " [1, 1, 1, 1],\n",
       " [1, 2, 4, 8],\n",
       " [1, 3, 9, 27],\n",
       " [1, 4, 16, 64],\n",
       " [1, 5, 25, 125],\n",
       " [1, 6, 36, 216],\n",
       " [1, 7, 49, 343],\n",
       " [1, 8, 64, 512],\n",
       " [1, 9, 81, 729]]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 4) Fix initial term to do calculation\n",
    "def make_powers_lc(n, inputs):\n",
    "    return [[x**y for y in range(n)] for x in inputs]\n",
    "make_powers_lc(4, range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "513b22ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 0, 0, 0],\n",
       " [1, 1, 1, 1],\n",
       " [2, 4, 8, 16],\n",
       " [3, 9, 27, 81],\n",
       " [4, 16, 64, 256],\n",
       " [5, 25, 125, 625],\n",
       " [6, 36, 216, 1296],\n",
       " [7, 49, 343, 2401],\n",
       " [8, 64, 512, 4096],\n",
       " [9, 81, 729, 6561]]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 5) With correct shape, make modifications to ranges/etc. as needed\n",
    "def make_powers_lc(n, inputs):\n",
    "    return [[x**y for y in range(1, n+1)] for x in inputs]\n",
    "make_powers_lc(4, range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "15faca48",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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