Added cumulative sum solution to d11

src/AoC_2023/Dazbo's_Advent_of_Code_2023.ipynb

@@ -4653,6 +4653,88 @@
     "logger.info(f\"Soln={soln}\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Alternative Solution\n",
+    "\n",
+    "This solution is very efficient.\n",
+    "\n",
+    "- Read in the character values into a list of lists.\n",
+    "- Create a cumulative sum array, to store the cumulative integer index of each row.\n",
+    "  - For each row, if it contains a galaxy, add 1 to the sum.\n",
+    "  - Else, add the expansion value.\n",
+    "- Now transpose with `zip(*grid)` and then build a col cumulative sum array in the same way.\n",
+    "- Now we can get the vertical distance between any pair of galaxies by obtaining the difference\n",
+    "  of the cumulative sums of their row indexes.\n",
+    "- And we can get the horizontal distance between any pair of galaxies by obtaining the \n",
+    "  differnce of the cumulative sums of their col indexes.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def solve_with_cumulative_sum(data, expansion_value:int=2):\n",
+    "    grid = [[char for char in line] for line in data]\n",
+    "    # logger.debug(\"\\n\" + \"\\n\".join(\"\".join(line) for line in grid))\n",
+    "    \n",
+    "    row_sum_array = [0] # cumulative sum of row indexes\n",
+    "    col_sum_array = [0] # cumulative sum of col indexes\n",
+    "    for row in grid:\n",
+    "        add_val = expansion_value if all(char == \".\" for char in row) else 1\n",
+    "        row_sum_array.append(row_sum_array[-1] + add_val)\n",
+    "        \n",
+    "    cols = list(zip(*grid)) # transpose\n",
+    "    for col in cols:\n",
+    "        add_val = expansion_value if all(char == \".\" for char in col) else 1\n",
+    "        col_sum_array.append(col_sum_array[-1] + add_val)\n",
+    "    \n",
+    "    hash_points = set()\n",
+    "    for y, row in enumerate(grid):\n",
+    "        for x, char in enumerate(row):\n",
+    "            if char == \"#\":\n",
+    "                hash_points.add((x,y))\n",
+    "    \n",
+    "    shortest_paths = []\n",
+    "    for ((ax, ay), (bx, by)) in combinations(hash_points, 2): # all combinations of 2 points\n",
+    "        shortest_paths.append(abs(row_sum_array[by]-row_sum_array[ay]) + \n",
+    "                              abs(col_sum_array[bx]-col_sum_array[ax]))\n",
+    "    \n",
+    "    return sum(shortest_paths)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sample_input = \"\"\"\\\n",
+    "...#......\n",
+    ".......#..\n",
+    "#.........\n",
+    "..........\n",
+    "......#...\n",
+    ".#........\n",
+    ".........#\n",
+    "..........\n",
+    ".......#..\n",
+    "#...#.....\n",
+    "\"\"\"\n",
+    "\n",
+    "validate(solve_with_cumulative_sum(sample_input.splitlines(), expansion_value=2), 374) \n",
+    "validate(solve_with_cumulative_sum(sample_input.splitlines(), expansion_value=100), 8410) \n",
+    "\n",
+    "logger.info(\"Tests passed!\")\n",
+    "\n",
+    "logger.info(f\"Part 1 with cumulative sum={solve_with_cumulative_sum(input_data, expansion_value=2)}\")\n",
+    "logger.info(f\"Part 2 with cumulative sum={solve_with_cumulative_sum(input_data, expansion_value=1000000)}\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},