Implemented shoelace area

src/AoC_2023/Dazbo's_Advent_of_Code_2023.ipynb

@@ -4032,7 +4032,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Final Remarks and Useful Resources\n",
+    "### Altternative Solutions and Useful Resources\n",
     "\n",
     "There are a few other ways to solve this problem. \n",
     "\n",
@@ -4048,6 +4048,29 @@
     "- For simplicity, we could have easily replaced all non-loop pipe components with `.`. (Since we already know which points make up the loop itself.)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def shoelace_area(polygon: list[Point]) -> int:\n",
+    "    \"\"\" Use Shoelace formula to determine total area of a polygon:\n",
+    "    A = 1/2 sum(x * (y+1 - y-1)) \"\"\"\n",
+    "    total = 0\n",
+    "    for i, (point) in enumerate(polygon):\n",
+    "        next_index = (i+1) % len(polygon)\n",
+    "        prev_index = i-1\n",
+    "        total += point.x*(polygon[next_index].y - polygon[prev_index].y)\n",
+    "        \n",
+    "    return abs(total) // 2\n",
+    "\n",
+    "def interior_points(area: int, boundary_points: int):\n",
+    "    \"\"\" Use Pick's Theorem to determine total number of internal integer points, \n",
+    "    given a polygon area and number of boundary points. \"\"\"\n",
+    "    return area - (boundary_points // 2) + 1  "
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -4056,10 +4079,15 @@
    "source": [
     "def d10_with_shoelace_and_picks(grid: PipeGrid, furthest: Point, came_from: dict[Point, tuple]):\n",
     "    \"\"\" Determine number of tiles (which can be empty or non-loop pipe components) that are internal\n",
-    "    to the main loop. \"\"\"\n",
+    "    to the main loop.  Here we calculate the total polygon area with Shoelace formula\n",
+    "    and then determine the number of internal integer points with Pick's Theorem. \"\"\"\n",
     "    loop_path = get_loop_path(grid, furthest, came_from) # get complete enclosed main loop\n",
     "    logger.debug(f\"Loop path has length {len(loop_path)}.\")\n",
-    "    pass\n",
+    "    \n",
+    "    area = shoelace_area(loop_path)\n",
+    "    tiles = interior_points(area, len(loop_path))\n",
+    "    \n",
+    "    return tiles\n",
     "\n",
     "def d10_with_scale_up(grid: PipeGrid, furthest: Point, came_from: dict[Point, tuple]):\n",
     "    \"\"\" Determine number of tiles (which can be empty or non-loop pipe components) that are internal\n",