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   "cell_type": "markdown",
   "id": "124fe12d",
   "metadata": {},
   "source": [
    "# [Largest Product in a Grid](https://projecteuler.net/problem=11)\n",
    "\n",
    "Here's that whole grid in a NumPy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7d93e5b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "grid = np.array([[08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08],\n",
    "                 [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00],\n",
    "                 [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65],\n",
    "                 [52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91],\n",
    "                 [22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80],\n",
    "                 [24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50],\n",
    "                 [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70],\n",
    "                 [67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21],\n",
    "                 [24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72],\n",
    "                 [21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95],\n",
    "                 [78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92],\n",
    "                 [16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57],\n",
    "                 [86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58],\n",
    "                 [19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40],\n",
    "                 [04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66],\n",
    "                 [88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69],\n",
    "                 [04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36],\n",
    "                 [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16],\n",
    "                 [20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54],\n",
    "                 [01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4924c1d",
   "metadata": {},
   "source": [
    "Now we'll just iterate through every 4x4 subgrid of this grid, and for each subgrid, compute the product of the rows, columns, and diagonals, and record the largest product we see."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7ac0e53c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "70600674\n"
     ]
    }
   ],
   "source": [
    "maximum = 0\n",
    "for i in range(0, 16):\n",
    "    for j in range(0, 16):\n",
    "        subgrid = grid[i:i+4, j:j+4]\n",
    "        \n",
    "        cols = subgrid.prod(axis=0)\n",
    "        rows = subgrid.prod(axis=1)\n",
    "        diag = np.diag(subgrid).prod()\n",
    "        anti_diag = np.diag(np.fliplr(subgrid)).prod()\n",
    "        \n",
    "        maximum = max(maximum, *cols, *rows, diag, anti_diag)\n",
    "\n",
    "print(maximum)"
   ]
  }
 ],
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