From 008df35271c206f593f457430c85a218a21319a7 Mon Sep 17 00:00:00 2001
From: kzkedzierska <31040515+kzkedzierska@users.noreply.github.com>
Date: Mon, 4 Dec 2023 02:19:58 +0000
Subject: [PATCH] :art: improved the code (with suggestions from Github
 Copilot; added typing and docs

---
 2023/Day03.ipynb | 396 +++++++++++++++++++++++++----------------------
 1 file changed, 207 insertions(+), 189 deletions(-)

diff --git a/2023/Day03.ipynb b/2023/Day03.ipynb
index c55c3d0..0052f7c 100644
--- a/2023/Day03.ipynb
+++ b/2023/Day03.ipynb
@@ -53,81 +53,95 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {},
+   "outputs": [],
+   "source": [
+    "example_input = \"\"\"467..114..\n",
+    "...*......\n",
+    "..35..633.\n",
+    "......#...\n",
+    "617*......\n",
+    ".....+.58.\n",
+    "..592.....\n",
+    "......755.\n",
+    "...$.*....\n",
+    ".664.598..\"\"\"\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "({(3, 1): '*',\n",
-       "  (6, 3): '#',\n",
-       "  (3, 4): '*',\n",
-       "  (5, 5): '+',\n",
-       "  (3, 8): '$',\n",
-       "  (5, 8): '*'},\n",
-       " {(2, 0): 467,\n",
-       "  (7, 0): 114,\n",
-       "  (3, 2): 35,\n",
-       "  (8, 2): 633,\n",
-       "  (2, 4): 617,\n",
-       "  (8, 5): 58,\n",
-       "  (4, 6): 592,\n",
-       "  (8, 7): 755,\n",
-       "  (3, 9): 664,\n",
-       "  (7, 9): 598})"
+       "({(3, 1), (3, 4), (3, 8), (5, 5), (5, 8), (6, 3)},\n",
+       " {(0, 0): 467,\n",
+       "  (5, 0): 114,\n",
+       "  (2, 2): 35,\n",
+       "  (6, 2): 633,\n",
+       "  (0, 4): 617,\n",
+       "  (7, 5): 58,\n",
+       "  (2, 6): 592,\n",
+       "  (6, 7): 755,\n",
+       "  (1, 9): 664,\n",
+       "  (5, 9): 598})"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "example_input = \"\"\"467..114..\n",
-    "...*......\n",
-    "..35..633.\n",
-    "......#...\n",
-    "617*......\n",
-    ".....+.58.\n",
-    "..592.....\n",
-    "......755.\n",
-    "...$.*....\n",
-    ".664.598..\"\"\"\n",
-    "\n",
-    "def process_input(input, example = False):\n",
-    "\n",
-    "    symbol_dict = dict()\n",
-    "    numbers_dict = dict()\n",
+    "from typing import Tuple, Set, Dict\n",
+    "def process_input(input_file: str, \n",
+    "                  example: bool = False) -> Tuple[Set[Tuple[int, int]], \n",
+    "                                                  Dict[Tuple[int, int], int]]:\n",
+    "    \"\"\"\n",
+    "    Process the input file and return symbols and numbers dictionary.\n",
+    "\n",
+    "    Parameters:\n",
+    "    - input_file (str): Path to the input file or the input data itself.\n",
+    "    - example (bool): Flag indicating whether the input is an example or a file path.\n",
+    "\n",
+    "    Returns:\n",
+    "    - symbols (set): Set of symbols.\n",
+    "    - numbers_dict (dict): Dictionary of numbers with their coordinates as keys.\n",
+    "\n",
+    "    \"\"\"\n",
+    "    symbols = set()\n",
+    "    numbers_dict = {}\n",
     "    y = 0\n",
+    "\n",
     "    if not example:\n",
-    "        input = open(input).read()\n",
+    "        with open(input_file) as f:\n",
+    "            input_data = f.read()\n",
+    "    else:\n",
+    "        input_data = input_file\n",
     "\n",
-    "    for line in input.splitlines():\n",
+    "    for line in input_data.splitlines():\n",
+    "        line += \".\"  # Add sentinel to process last number\n",
     "        num = \"\"\n",
     "        for x, c in enumerate(line):\n",
-    "            # if c in a number add to num\n",
-    "            if c in '0123456789':\n",
+    "            if c.isdigit():\n",
     "                num += c\n",
     "            else:\n",
-    "                # if num is not empty add to numbers_dict\n",
-    "                if num != \"\":\n",
-    "                    numbers_dict[(x-1, y)] = int(num)\n",
+    "                if num:\n",
+    "                    numbers_dict[(x-len(num), y)] = int(num)\n",
     "                    num = \"\"\n",
-    "                # if c is not a dot add to symbol_dict\n",
     "                if c != '.':\n",
-    "                    # I don't really need symbol_dict, a set would be enough\n",
-    "                    # but in case I might need it later, I'll keep it\n",
-    "                    symbol_dict[(x, y)] = c\n",
-    "        if num != \"\":\n",
-    "            numbers_dict[(x, y)] = int(num)\n",
+    "                    symbols.add((x, y))\n",
     "        y += 1\n",
     "\n",
-    "    return symbol_dict, numbers_dict\n",
+    "    return symbols, numbers_dict\n",
     "\n",
     "process_input(example_input, True)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -136,31 +150,34 @@
        "4361"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "def scan_grid(symbol_dict, numbers_dict):\n",
+    "def scan_grid(symbols: set, numbers_dict: dict) -> int:\n",
+    "    \"\"\"\n",
+    "    Scan the grid for parts numbers. Those are defined as numbers that are\n",
+    "    adjacent to a symbol. The sum of all parts numbers is the solution.\n",
+    "    \n",
+    "    Parameters:\n",
+    "        symbols: Set of coordinates of symbols.\n",
+    "        numbers_dict: Dictionary of coordinates of numbers and their value.\n",
+    "    \n",
+    "    Returns:\n",
+    "        Sum of all parts numbers.\n",
+    "    \"\"\"\n",
     "    parts_sum = 0\n",
-    "    # for each number in numbers_dict, check if in x+-1 and y+-1 there is a symbol\n",
     "    for (x, y), num in numbers_dict.items():\n",
-    "        # get the number of digits of num\n",
     "        num_digits = len(str(num))\n",
-    "        # check if there is a symbol in (x_min-1 to x_max+1) and y+-1\n",
-    "        x_min = x - num_digits\n",
-    "        x_max = x + 1\n",
-    "        # create all possible combinations of x1, y1 \n",
-    "        # where x is within x_min and x_max and y is y-1 or y+1\n",
-    "        xs = range(x_min, x_max+1)\n",
-    "        ys = [y-1, y+1]\n",
-    "        # take only the xs and ys >= 0\n",
-    "        xs = [x1 for x1 in xs if x1 >= 0]\n",
-    "        ys = [y1 for y1 in ys if y1 >= 0]\n",
+    "        x_min = x - 1\n",
+    "        x_max = x + num_digits\n",
+    "        xs = [x1 for x1 in range(x_min, x_max+1) if x1 >= 0]\n",
+    "        ys = [y1 for y1 in [y-1, y+1] if y1 >= 0]\n",
     "        pos = [(x1, y1) for x1 in xs for y1 in ys]\n",
     "        pos += [(x1, y) for x1 in [x_min, x_max] if x1 >= 0]\n",
-    "        if any([symbol_dict.get(p) for p in pos]):\n",
+    "        if any(p in symbols for p in pos):\n",
     "            parts_sum += num\n",
     "\n",
     "    return parts_sum\n",
@@ -177,7 +194,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -186,35 +203,37 @@
      "text": [
       "   | 0 | 1 | 2 | 3 |\n",
       " --------------------\n",
-      " 0 | . | . | . | . |\n",
-      " 1 | . | . | . | 1 |\n",
-      " 2 | 9 | 8 | 9 | * |\n",
-      " 3 | . | _ | - | - |\n"
+      "0  | . | . | . | . |\n",
+      "1  | . | . | . | 1 |\n",
+      "2  | 9 | 8 | 9 | * |\n",
+      "3  | . | _ | - | - |\n"
      ]
     }
    ],
    "source": [
-    "def print_matrix(input_string):\n",
+    "def print_matrix(input_string: str) -> None:\n",
+    "    \"\"\"\n",
+    "    Prints a matrix representation of the input string.\n",
+    "\n",
+    "    Args:\n",
+    "        input_string (str): The input string representing the matrix.\n",
+    "\n",
+    "    Returns:\n",
+    "        None\n",
+    "    \"\"\"\n",
     "    # Split the input string into rows\n",
     "    rows = input_string.split(\"\\n\")\n",
     "    # get the max length of the rows\n",
-    "    max_len = max([len(row) for row in rows])\n",
+    "    max_len = max(len(row) for row in rows)\n",
     "    \n",
     "    # Create a matrix of the max length\n",
-    "    matrix = [[' ' for i in range(max_len)] for j in range(len(rows))]\n",
+    "    matrix = [[char for char in row.ljust(max_len)] for row in rows]\n",
     "\n",
-    "    # Populate the matrix with characters from the input string\n",
-    "    for i, row in enumerate(rows):\n",
-    "        for j, char in enumerate(row):\n",
-    "            matrix[i][j] = char\n",
     "    # Print the matrix with row and column numbers\n",
-    "    print(f\"   | {' | '.join([str(i) if i < 10 else ' ' for i in range(max_len)])} |\")\n",
+    "    print(f\"   | {'| '.join(str(i).ljust(2) for i in range(max_len))}|\")\n",
     "    print(f\" {'-'*(max_len*4 + 4)}\")\n",
     "    for i, row in enumerate(matrix):\n",
-    "        if i < 10:\n",
-    "            print(f\" {i} | {' | '.join(row)} |\")\n",
-    "        else:\n",
-    "            print(f\"{i} | {' | '.join(row)} |\")\n",
+    "        print(f\"{str(i).ljust(2)} | {' | '.join(row)} |\")\n",
     "\n",
     "# Input string\n",
     "input_string = \"\"\"....\n",
@@ -228,7 +247,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -237,9 +256,9 @@
      "text": [
       "   | 0 | 1 | 2 | 3 | 4 | 5 |\n",
       " ----------------------------\n",
-      " 0 | 1 | 1 | 1 | $ | 1 | 2 |\n",
-      " 1 | + | . | . | . | . | . |\n",
-      " 2 | . | . | 1 | 3 | . | % |\n"
+      "0  | 1 | 1 | 1 | $ | 1 | 2 |\n",
+      "1  | + | . | . | . | . | . |\n",
+      "2  | . | . | 1 | 3 | . | % |\n"
      ]
     }
    ],
@@ -255,7 +274,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -264,9 +283,9 @@
      "text": [
       "   | 0 | 1 | 2 | 3 | 4 | 5 |\n",
       " ----------------------------\n",
-      " 0 | 1 | 1 | 1 | $ | 1 | 2 |\n",
-      " 1 | + | . | . | . | 8 | . |\n",
-      " 2 | . | . | 1 | 3 | . | % |\n"
+      "0  | 1 | 1 | 1 | $ | 1 | 2 |\n",
+      "1  | + | . | . | . | 8 | . |\n",
+      "2  | . | . | 1 | 3 | . | % |\n"
      ]
     }
    ],
@@ -282,7 +301,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -291,9 +310,9 @@
      "text": [
       "   | 0 | 1 | 2 | 3 | 4 | 5 |\n",
       " ----------------------------\n",
-      " 0 | . | . | $ | $ | . | . |\n",
-      " 1 | + | . | . | . | 8 | . |\n",
-      " 2 | . | . | 1 | 3 | . | % |\n"
+      "0  | . | . | $ | $ | . | . |\n",
+      "1  | + | . | . | . | 8 | . |\n",
+      "2  | . | . | 1 | 3 | . | % |\n"
      ]
     }
    ],
@@ -309,7 +328,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -318,9 +337,9 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | 1 | . | 3 |\n",
-      " 1 | . | 5 | . |\n",
-      " 2 | 7 | . | 9 |\n"
+      "0  | 1 | . | 3 |\n",
+      "1  | . | 5 | . |\n",
+      "2  | 7 | . | 9 |\n"
      ]
     }
    ],
@@ -336,7 +355,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -345,9 +364,9 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | 1 | * | 3 |\n",
-      " 1 | * | 5 | * |\n",
-      " 2 | 7 | * | 9 |\n"
+      "0  | 1 | * | 3 |\n",
+      "1  | * | 5 | * |\n",
+      "2  | 7 | * | 9 |\n"
      ]
     }
    ],
@@ -363,7 +382,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -372,7 +391,7 @@
      "text": [
       "   | 0 | 1 | 2 | 3 |\n",
       " --------------------\n",
-      " 0 | . | $ | 1 | 2 |\n"
+      "0  | . | $ | 1 | 2 |\n"
      ]
     }
    ],
@@ -384,7 +403,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -393,7 +412,7 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | * | * | * |\n"
+      "0  | * | * | * |\n"
      ]
     }
    ],
@@ -405,7 +424,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -414,8 +433,8 @@
      "text": [
       "   | 0 | 1 | 2 | 3 | 4 |\n",
       " ------------------------\n",
-      " 0 | 3 | 3 | 3 | . | 3 |\n",
-      " 1 | . | . | . | * | . |\n"
+      "0  | 3 | 3 | 3 | . | 3 |\n",
+      "1  | . | . | . | * | . |\n"
      ]
     }
    ],
@@ -428,7 +447,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -437,9 +456,9 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | 1 | . | 3 |\n",
-      " 1 | . | 5 | * |\n",
-      " 2 | . | . | 9 |\n"
+      "0  | 1 | . | 3 |\n",
+      "1  | . | 5 | * |\n",
+      "2  | . | . | 9 |\n"
      ]
     }
    ],
@@ -453,7 +472,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -462,8 +481,8 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | * | . | * |\n",
-      " 1 | 1 | 2 | 3 |\n"
+      "0  | * | . | * |\n",
+      "1  | 1 | 2 | 3 |\n"
      ]
     }
    ],
@@ -476,7 +495,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -485,7 +504,7 @@
        "539637"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -527,45 +546,50 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [],
    "source": [
-    "def process_input_for_gears(input, example = False):\n",
-    "\n",
+    "def process_input_for_gears(input_file: str, \n",
+    "                            example: bool = False) -> Tuple[Set[Tuple[int, int]],\n",
+    "                                                            Dict[int, str],\n",
+    "                                                            Dict[Tuple[int, int], int]]:\n",
+    "    \"\"\"\n",
+    "    Process the input file and extract gears, numbers_idx, and numbers_dict.\n",
+    "\n",
+    "    Parameters:\n",
+    "        input_file (str): The path to the input file.\n",
+    "        example (bool): Flag indicating whether the input is an example or not.\n",
+    "\n",
+    "    Returns:\n",
+    "        tuple: A tuple containing gears (set), numbers_idx (dict), and numbers_dict (dict).\n",
+    "    \"\"\"\n",
     "    gears = set()\n",
     "    numbers_idx = dict()\n",
     "    numbers_dict = dict()\n",
     "    y = 0\n",
     "    idx = 0\n",
     "    if not example:\n",
-    "        input = open(input).read()\n",
+    "        with open(input_file) as f:\n",
+    "            input_data = f.read()\n",
+    "    else:\n",
+    "        input_data = input_file\n",
     "\n",
-    "    for line in input.splitlines():\n",
+    "    for line in input_data.splitlines():\n",
+    "        line += \".\"  # Add sentinel to process last number\n",
     "        num = \"\"\n",
     "        for x, c in enumerate(line):\n",
-    "            # if c in a number add to num\n",
-    "            if c in '0123456789':\n",
+    "            if c.isdigit():\n",
     "                num += c\n",
     "            else:\n",
-    "                # if num is not empty add to numbers_dict\n",
-    "                if num != \"\":\n",
+    "                if num:\n",
     "                    numbers_idx[idx] = num\n",
-    "                    # for each position of the number add the idx\n",
     "                    for i in range(len(num)):\n",
-    "                        numbers_dict[(x-i-1, y)] = idx\n",
+    "                        numbers_dict[(x - i - 1, y)] = idx\n",
     "                    num = \"\"\n",
     "                    idx += 1\n",
-    "                # if c is not a dot add to symbol_dict\n",
     "                if c == '*':\n",
     "                    gears.add((x, y))\n",
-    "        if num != \"\":\n",
-    "            numbers_idx[idx] = num\n",
-    "            # for each position of the number add the idx\n",
-    "            for i in range(len(num)):\n",
-    "                numbers_dict[(x-i, y)] = idx\n",
-    "            num = \"\"\n",
-    "            idx += 1\n",
     "        y += 1\n",
     "\n",
     "    return gears, numbers_idx, numbers_dict\n"
@@ -573,49 +597,43 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "467835"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "def scan_grid_for_gears(gears, numbers_idx, numbers_dict):\n",
+    "def scan_grid_for_gears(gears: set, \n",
+    "                        numbers_idx: dict, \n",
+    "                        numbers_dict: dict) -> int:\n",
+    "    \"\"\"\n",
+    "    Scans the grid for gears and calculates the sum of the products of the corresponding numbers.\n",
+    "\n",
+    "    Parameters:\n",
+    "        gears (set): List of coordinates representing the positions of gears.\n",
+    "        numbers_idx (dict): Dictionary mapping gear indices to numbers.\n",
+    "        numbers_dict (dict): Dictionary mapping positions to gear indices.\n",
+    "\n",
+    "    Returns:\n",
+    "        gears_sum (int): Sum of the products of the corresponding numbers.\n",
+    "\n",
+    "    \"\"\"\n",
     "    gears_sum = 0\n",
-    "    # for each '*' in symbol_dict, check if in x+-1 and y+-1 there are exactly two numbers\n",
     "    for (x, y) in gears:\n",
-    "        # check if there are exactly two numbers in (x-1 to x+1) and (y-1 to y+1)\n",
-    "        xs = [x-1, x, x+1]\n",
-    "        ys = [y-1, y, y+1]\n",
-    "        # take only the xs and ys >= 0\n",
-    "        xs = [x1 for x1 in xs if x1 >= 0]\n",
-    "        ys = [y1 for y1 in ys if y1 >= 0]\n",
+    "        xs = [x1 for x1 in [x-1, x, x+1] if x1 >= 0]\n",
+    "        ys = [y1 for y1 in [y-1, y, y+1] if y1 >= 0]\n",
     "        pos = [(x1, y1) for x1 in xs for y1 in ys if (x1, y1) != (x, y)]\n",
-    "        # get the idx of the numbers in the positions\n",
-    "        idxs = [numbers_dict.get(p) for p in pos if numbers_dict.get(p) is not None]\n",
-    "        idxs = list(set(idxs))\n",
+    "        idxs = {numbers_dict.get(p) for p in pos if numbers_dict.get(p) is not None}\n",
     "        if len(idxs) == 2:\n",
-    "            # get the numbers\n",
-    "            nums = [numbers_idx.get(i) for i in idxs]\n",
-    "            # multiply the numbers\n",
-    "            gears_sum += int(nums[0]) * int(nums[1])\n",
+    "            nums = list(map(int, [numbers_idx.get(i) for i in idxs]))\n",
+    "            gears_sum += nums[0] * nums[1]\n",
     "\n",
     "    return gears_sum\n",
     "\n",
-    "scan_grid_for_gears(*process_input_for_gears(example_input, True))"
+    "assert(scan_grid_for_gears(*process_input_for_gears(example_input, True)) == 467835)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -624,9 +642,9 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | 1 | . | 3 |\n",
-      " 1 | . | 5 | * |\n",
-      " 2 | . | . | 9 |\n"
+      "0  | 1 | . | 3 |\n",
+      "1  | . | 5 | * |\n",
+      "2  | . | . | 9 |\n"
      ]
     }
    ],
@@ -640,7 +658,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -649,8 +667,8 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | * | . | * |\n",
-      " 1 | 1 | 2 | 3 |\n"
+      "0  | * | . | * |\n",
+      "1  | 1 | 2 | 3 |\n"
      ]
     }
    ],
@@ -663,7 +681,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -672,8 +690,8 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | . | * | . |\n",
-      " 1 | 1 | . | 3 |\n"
+      "0  | . | * | . |\n",
+      "1  | 1 | . | 3 |\n"
      ]
     }
    ],
@@ -686,7 +704,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
@@ -695,7 +713,7 @@
      "text": [
       "   | 0 | 1 | 2 |\n",
       " ----------------\n",
-      " 0 | * | * | * |\n"
+      "0  | * | * | * |\n"
      ]
     }
    ],
@@ -707,7 +725,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
@@ -716,9 +734,9 @@
      "text": [
       "   | 0 | 1 | 2 | 3 | 4 | 5 |\n",
       " ----------------------------\n",
-      " 0 | 1 | 1 | 1 | * | 1 | 2 |\n",
-      " 1 | * | . | . | . | 8 | . |\n",
-      " 2 | . | . | 1 | 3 | . | * |\n"
+      "0  | 1 | 1 | 1 | * | 1 | 2 |\n",
+      "1  | * | . | . | . | 8 | . |\n",
+      "2  | . | . | 1 | 3 | . | * |\n"
      ]
     }
    ],
@@ -734,7 +752,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
@@ -743,9 +761,9 @@
      "text": [
       "   | 0 | 1 | 2 | 3 | 4 | 5 |\n",
       " ----------------------------\n",
-      " 0 | 1 | 1 | 1 | * | 1 | 2 |\n",
-      " 1 | * | . | . | . | 8 | . |\n",
-      " 2 | . | . | 1 | 3 | * | * |\n"
+      "0  | 1 | 1 | 1 | * | 1 | 2 |\n",
+      "1  | * | . | . | . | 8 | . |\n",
+      "2  | . | . | 1 | 3 | * | * |\n"
      ]
     }
    ],
@@ -761,7 +779,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
@@ -770,9 +788,9 @@
      "text": [
       "   | 0 | 1 | 2 | 3 | 4 | 5 |\n",
       " ----------------------------\n",
-      " 0 | 1 | 1 | 1 | * | 1 | 2 |\n",
-      " 1 | * | . | * | . | 8 | . |\n",
-      " 2 | . | . | 1 | 3 | * | * |\n"
+      "0  | 1 | 1 | 1 | * | 1 | 2 |\n",
+      "1  | * | . | * | . | 8 | . |\n",
+      "2  | . | . | 1 | 3 | * | * |\n"
      ]
     }
    ],
@@ -788,7 +806,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
@@ -797,7 +815,7 @@
        "82818007"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }