From 9a4949ee010490cbfd9049d89dd73e8f7b919c77 Mon Sep 17 00:00:00 2001
From: Peter Norvig <peter.norvig@gmail.com>
Date: Sat, 28 Dec 2024 14:16:19 -0800
Subject: [PATCH] Add files via upload

---
 ipynb/Advent-2024.ipynb | 217 ++++++++++++++++++++++------------------
 1 file changed, 117 insertions(+), 100 deletions(-)

diff --git a/ipynb/Advent-2024.ipynb b/ipynb/Advent-2024.ipynb
index 0ba049e..ef2fd9a 100644
--- a/ipynb/Advent-2024.ipynb
+++ b/ipynb/Advent-2024.ipynb
@@ -670,7 +670,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  4.2:   .015 seconds, answer 1822              ok"
+       "Puzzle  4.2:   .016 seconds, answer 1822              ok"
       ]
      },
      "execution_count": 42,
@@ -1063,7 +1063,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  6.2:  1.943 seconds, answer 2162              ok"
+       "Puzzle  6.2:  1.977 seconds, answer 2162              ok"
       ]
      },
      "execution_count": 63,
@@ -1308,7 +1308,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  7.2:   .592 seconds, answer 150077710195188   ok"
+       "Puzzle  7.2:   .600 seconds, answer 150077710195188   ok"
       ]
      },
      "execution_count": 78,
@@ -1603,7 +1603,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  9.1:   .019 seconds, answer 6332189866718     ok"
+       "Puzzle  9.1:   .020 seconds, answer 6332189866718     ok"
       ]
      },
      "execution_count": 93,
@@ -1629,21 +1629,22 @@
     "\n",
     "To find all the slices that indicate files, it is easier to run through the disk map than the disk layout. The function `file_slices` quickly finds all such slices.\n",
     "\n",
-    "Finding a free space for a file is more difficult, because we need to find one that is big enough. I'll run through the whole layout from left-to-right each time. This will make it *O*(*n*<sup>2</sup>) rather than *O*(*n*), but hopefully it won't be too slow. (If I wanted to speed it up I could have an array of starting positions for each desired size of free space.)"
+    "Finding a free space for a file is more difficult, because we need to find one that is big enough. At first I coded a solution that ran through the whole layout from left-to-right each time. That made it *O*(*n*<sup>2</sup>). So I added a table: `starts[length]` tells me where to start looking for an empty space of size `length`. That speeds things up."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 95,
-   "id": "fcf4d832-3d7d-4987-aa57-e6e0f1df16bf",
+   "id": "8d34e96a-8ea9-4f92-b0aa-839b216ea14b",
    "metadata": {},
    "outputs": [],
    "source": [
     "def compress_layout2(disk_map: Ints) -> list:\n",
     "    \"\"\"Mutate layout by moving files one at a time from the end to the leftmost free space.\"\"\"\n",
     "    layout = disk_layout(disk_map)\n",
+    "    starts = defaultdict(int)\n",
     "    for file in file_slices(disk_map):\n",
-    "        if free := find_freespace(layout, file):\n",
+    "        if free := find_freespace(layout, file, starts):\n",
     "            layout[file], layout[free] = layout[free], layout[file]\n",
     "    return layout\n",
     "\n",
@@ -1658,11 +1659,12 @@
     "    slices.reverse()\n",
     "    return slices\n",
     "\n",
-    "def find_freespace(layout, file_slice) -> Optional[slice]:\n",
+    "def find_freespace(layout, file_slice, starts) -> Optional[slice]:\n",
     "    \"\"\"Find a slice position big enough to fit the given file slice, or return None if there is no position.\"\"\"\n",
     "    length = file_slice.stop - file_slice.start\n",
     "    run = 0\n",
-    "    for i in range(layout.index(empty), len(layout)):\n",
+    "    for i in range(layout.index(empty, starts[length]), len(layout)):\n",
+    "        starts[length] = i\n",
     "        if i >= file_slice.start:\n",
     "            return None # We only want to move a file left, not right\n",
     "        elif layout[i] is empty:\n",
@@ -1683,7 +1685,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle  9.2:  2.384 seconds, answer 6353648390778     ok"
+       "Puzzle  9.2:   .021 seconds, answer 6353648390778     ok"
       ]
      },
      "execution_count": 96,
@@ -1792,7 +1794,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 10.1:   .005 seconds, answer 744               ok"
+       "Puzzle 10.1:   .004 seconds, answer 744               ok"
       ]
      },
      "execution_count": 102,
@@ -1994,7 +1996,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.1:   .067 seconds, answer 194482            ok"
+       "Puzzle 11.1:   .068 seconds, answer 194482            ok"
       ]
      },
      "execution_count": 113,
@@ -2055,7 +2057,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.1:   .001 seconds, answer 194482            ok"
+       "Puzzle 11.1:   .002 seconds, answer 194482            ok"
       ]
      },
      "execution_count": 117,
@@ -2077,7 +2079,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 11.2:   .060 seconds, answer 232454623677743   ok"
+       "Puzzle 11.2:   .058 seconds, answer 232454623677743   ok"
       ]
      },
      "execution_count": 118,
@@ -2213,7 +2215,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.1:   .033 seconds, answer 1402544           ok"
+       "Puzzle 12.1:   .032 seconds, answer 1402544           ok"
       ]
      },
      "execution_count": 126,
@@ -2286,7 +2288,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.1:   .050 seconds, answer 1402544           ok"
+       "Puzzle 12.1:   .052 seconds, answer 1402544           ok"
       ]
      },
      "execution_count": 129,
@@ -2308,7 +2310,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 12.2:   .042 seconds, answer 862486            ok"
+       "Puzzle 12.2:   .043 seconds, answer 862486            ok"
       ]
      },
      "execution_count": 130,
@@ -2986,42 +2988,42 @@
        "</style>\n",
        "\n",
        "<div class=\"animation\">\n",
-       "  <img id=\"_anim_imgdc0d5558c9a0485aa3c468981a103eb2\">\n",
+       "  <img id=\"_anim_imge5889f6e232a4cbba19719532f4cbcc2\">\n",
        "  <div class=\"anim-controls\">\n",
-       "    <input id=\"_anim_sliderdc0d5558c9a0485aa3c468981a103eb2\" type=\"range\" class=\"anim-slider\"\n",
+       "    <input id=\"_anim_slidere5889f6e232a4cbba19719532f4cbcc2\" type=\"range\" class=\"anim-slider\"\n",
        "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
-       "           oninput=\"animdc0d5558c9a0485aa3c468981a103eb2.set_frame(parseInt(this.value));\">\n",
+       "           oninput=\"anime5889f6e232a4cbba19719532f4cbcc2.set_frame(parseInt(this.value));\">\n",
        "    <div class=\"anim-buttons\">\n",
-       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.slower()\">\n",
+       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.slower()\">\n",
        "          <i class=\"fa fa-minus\"></i></button>\n",
-       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.first_frame()\">\n",
+       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.first_frame()\">\n",
        "        <i class=\"fa fa-fast-backward\"></i></button>\n",
-       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.previous_frame()\">\n",
+       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.previous_frame()\">\n",
        "          <i class=\"fa fa-step-backward\"></i></button>\n",
-       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.reverse_animation()\">\n",
+       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.reverse_animation()\">\n",
        "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
-       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.pause_animation()\">\n",
+       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.pause_animation()\">\n",
        "          <i class=\"fa fa-pause\"></i></button>\n",
-       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.play_animation()\">\n",
+       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.play_animation()\">\n",
        "          <i class=\"fa fa-play\"></i></button>\n",
-       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.next_frame()\">\n",
+       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.next_frame()\">\n",
        "          <i class=\"fa fa-step-forward\"></i></button>\n",
-       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.last_frame()\">\n",
+       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.last_frame()\">\n",
        "          <i class=\"fa fa-fast-forward\"></i></button>\n",
-       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animdc0d5558c9a0485aa3c468981a103eb2.faster()\">\n",
+       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anime5889f6e232a4cbba19719532f4cbcc2.faster()\">\n",
        "          <i class=\"fa fa-plus\"></i></button>\n",
        "    </div>\n",
-       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectdc0d5558c9a0485aa3c468981a103eb2\"\n",
+       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selecte5889f6e232a4cbba19719532f4cbcc2\"\n",
        "          class=\"anim-state\">\n",
-       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_dc0d5558c9a0485aa3c468981a103eb2\"\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_e5889f6e232a4cbba19719532f4cbcc2\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio1_dc0d5558c9a0485aa3c468981a103eb2\">Once</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_dc0d5558c9a0485aa3c468981a103eb2\"\n",
+       "      <label for=\"_anim_radio1_e5889f6e232a4cbba19719532f4cbcc2\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_e5889f6e232a4cbba19719532f4cbcc2\"\n",
        "             checked>\n",
-       "      <label for=\"_anim_radio2_dc0d5558c9a0485aa3c468981a103eb2\">Loop</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_dc0d5558c9a0485aa3c468981a103eb2\"\n",
+       "      <label for=\"_anim_radio2_e5889f6e232a4cbba19719532f4cbcc2\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_e5889f6e232a4cbba19719532f4cbcc2\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio3_dc0d5558c9a0485aa3c468981a103eb2\">Reflect</label>\n",
+       "      <label for=\"_anim_radio3_e5889f6e232a4cbba19719532f4cbcc2\">Reflect</label>\n",
        "    </form>\n",
        "  </div>\n",
        "</div>\n",
@@ -3031,9 +3033,9 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_imgdc0d5558c9a0485aa3c468981a103eb2\";\n",
-       "    var slider_id = \"_anim_sliderdc0d5558c9a0485aa3c468981a103eb2\";\n",
-       "    var loop_select_id = \"_anim_loop_selectdc0d5558c9a0485aa3c468981a103eb2\";\n",
+       "    var img_id = \"_anim_imge5889f6e232a4cbba19719532f4cbcc2\";\n",
+       "    var slider_id = \"_anim_slidere5889f6e232a4cbba19719532f4cbcc2\";\n",
+       "    var loop_select_id = \"_anim_loop_selecte5889f6e232a4cbba19719532f4cbcc2\";\n",
        "    var frames = new Array(3);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
@@ -4770,14 +4772,14 @@
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        animdc0d5558c9a0485aa3c468981a103eb2 = new Animation(frames, img_id, slider_id, 200.0,\n",
+       "        anime5889f6e232a4cbba19719532f4cbcc2 = new Animation(frames, img_id, slider_id, 200.0,\n",
        "                                 loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "text/plain": [
-       "<matplotlib.animation.FuncAnimation at 0x31c3b3f20>"
+       "<matplotlib.animation.FuncAnimation at 0x31ce7ac00>"
       ]
      },
      "execution_count": 156,
@@ -5010,42 +5012,42 @@
        "</style>\n",
        "\n",
        "<div class=\"animation\">\n",
-       "  <img id=\"_anim_imgea6b17f8e6f745568d5445b9aa800110\">\n",
+       "  <img id=\"_anim_img7295292aa9074d0193a9f80b1d46cca1\">\n",
        "  <div class=\"anim-controls\">\n",
-       "    <input id=\"_anim_sliderea6b17f8e6f745568d5445b9aa800110\" type=\"range\" class=\"anim-slider\"\n",
+       "    <input id=\"_anim_slider7295292aa9074d0193a9f80b1d46cca1\" type=\"range\" class=\"anim-slider\"\n",
        "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
-       "           oninput=\"animea6b17f8e6f745568d5445b9aa800110.set_frame(parseInt(this.value));\">\n",
+       "           oninput=\"anim7295292aa9074d0193a9f80b1d46cca1.set_frame(parseInt(this.value));\">\n",
        "    <div class=\"anim-buttons\">\n",
-       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.slower()\">\n",
+       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.slower()\">\n",
        "          <i class=\"fa fa-minus\"></i></button>\n",
-       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.first_frame()\">\n",
+       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.first_frame()\">\n",
        "        <i class=\"fa fa-fast-backward\"></i></button>\n",
-       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.previous_frame()\">\n",
+       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.previous_frame()\">\n",
        "          <i class=\"fa fa-step-backward\"></i></button>\n",
-       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.reverse_animation()\">\n",
+       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.reverse_animation()\">\n",
        "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
-       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.pause_animation()\">\n",
+       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.pause_animation()\">\n",
        "          <i class=\"fa fa-pause\"></i></button>\n",
-       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.play_animation()\">\n",
+       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.play_animation()\">\n",
        "          <i class=\"fa fa-play\"></i></button>\n",
-       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.next_frame()\">\n",
+       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.next_frame()\">\n",
        "          <i class=\"fa fa-step-forward\"></i></button>\n",
-       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.last_frame()\">\n",
+       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.last_frame()\">\n",
        "          <i class=\"fa fa-fast-forward\"></i></button>\n",
-       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animea6b17f8e6f745568d5445b9aa800110.faster()\">\n",
+       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim7295292aa9074d0193a9f80b1d46cca1.faster()\">\n",
        "          <i class=\"fa fa-plus\"></i></button>\n",
        "    </div>\n",
-       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectea6b17f8e6f745568d5445b9aa800110\"\n",
+       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select7295292aa9074d0193a9f80b1d46cca1\"\n",
        "          class=\"anim-state\">\n",
-       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_ea6b17f8e6f745568d5445b9aa800110\"\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_7295292aa9074d0193a9f80b1d46cca1\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio1_ea6b17f8e6f745568d5445b9aa800110\">Once</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_ea6b17f8e6f745568d5445b9aa800110\"\n",
+       "      <label for=\"_anim_radio1_7295292aa9074d0193a9f80b1d46cca1\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_7295292aa9074d0193a9f80b1d46cca1\"\n",
        "             checked>\n",
-       "      <label for=\"_anim_radio2_ea6b17f8e6f745568d5445b9aa800110\">Loop</label>\n",
-       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_ea6b17f8e6f745568d5445b9aa800110\"\n",
+       "      <label for=\"_anim_radio2_7295292aa9074d0193a9f80b1d46cca1\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_7295292aa9074d0193a9f80b1d46cca1\"\n",
        "             >\n",
-       "      <label for=\"_anim_radio3_ea6b17f8e6f745568d5445b9aa800110\">Reflect</label>\n",
+       "      <label for=\"_anim_radio3_7295292aa9074d0193a9f80b1d46cca1\">Reflect</label>\n",
        "    </form>\n",
        "  </div>\n",
        "</div>\n",
@@ -5055,9 +5057,9 @@
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
-       "    var img_id = \"_anim_imgea6b17f8e6f745568d5445b9aa800110\";\n",
-       "    var slider_id = \"_anim_sliderea6b17f8e6f745568d5445b9aa800110\";\n",
-       "    var loop_select_id = \"_anim_loop_selectea6b17f8e6f745568d5445b9aa800110\";\n",
+       "    var img_id = \"_anim_img7295292aa9074d0193a9f80b1d46cca1\";\n",
+       "    var slider_id = \"_anim_slider7295292aa9074d0193a9f80b1d46cca1\";\n",
+       "    var loop_select_id = \"_anim_loop_select7295292aa9074d0193a9f80b1d46cca1\";\n",
        "    var frames = new Array(1);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
@@ -5446,14 +5448,14 @@
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
-       "        animea6b17f8e6f745568d5445b9aa800110 = new Animation(frames, img_id, slider_id, 200.0,\n",
+       "        anim7295292aa9074d0193a9f80b1d46cca1 = new Animation(frames, img_id, slider_id, 200.0,\n",
        "                                 loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "text/plain": [
-       "<matplotlib.animation.FuncAnimation at 0x31c28bef0>"
+       "<matplotlib.animation.FuncAnimation at 0x31cdecd70>"
       ]
      },
      "execution_count": 159,
@@ -5487,7 +5489,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 14.2:  1.828 seconds, answer 6876              ok"
+       "Puzzle 14.2:  1.866 seconds, answer 6876              ok"
       ]
      },
      "execution_count": 161,
@@ -5609,7 +5611,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 15.1:   .026 seconds, answer 1563092           ok"
+       "Puzzle 15.1:   .027 seconds, answer 1563092           ok"
       ]
      },
      "execution_count": 166,
@@ -5877,7 +5879,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 16.1:   .146 seconds, answer 103512            ok"
+       "Puzzle 16.1:   .147 seconds, answer 103512            ok"
       ]
      },
      "execution_count": 178,
@@ -5941,7 +5943,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 16.2:   .848 seconds, answer 554               ok"
+       "Puzzle 16.2:   .860 seconds, answer 554               ok"
       ]
      },
      "execution_count": 181,
@@ -6547,7 +6549,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 19.1:   .040 seconds, answer 242               ok"
+       "Puzzle 19.1:   .039 seconds, answer 242               ok"
       ]
      },
      "execution_count": 211,
@@ -6594,7 +6596,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 19.2:   .186 seconds, answer 595975512785325   ok"
+       "Puzzle 19.2:   .185 seconds, answer 595975512785325   ok"
       ]
      },
      "execution_count": 214,
@@ -6762,7 +6764,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 20.1:   .029 seconds, answer 1343              ok"
+       "Puzzle 20.1:   .028 seconds, answer 1343              ok"
       ]
      },
      "execution_count": 224,
@@ -6799,7 +6801,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 20.2:   .761 seconds, answer 982891            ok"
+       "Puzzle 20.2:   .768 seconds, answer 982891            ok"
       ]
      },
      "execution_count": 226,
@@ -7281,7 +7283,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 22.1:   .318 seconds, answer 14273043166       ok"
+       "Puzzle 22.1:   .331 seconds, answer 14273043166       ok"
       ]
      },
      "execution_count": 255,
@@ -7325,7 +7327,7 @@
     "Some details:\n",
     "- A `defaultdict(int)` is a great data structure for the 4-tuple to bananas mapping (a `Counter` is also good).\n",
     "- A `deque` with `maxlen=4` is a good data structure for keeping the evolving 4-tuple; just append to the deque and it automatically drops old deltas.\n",
-    "- In `price_timeline` I call `nth_secret(secret, 1)`, so I wish I had made a separate `next_secret` function in Part 1; it would probably speed things up by a percent or two."
+    "- In `price_timeline` I could call `nth_secret(secret, 1)`, but I decided to make a separate `next_secret` function. I probably should have done that for Part 1."
    ]
   },
   {
@@ -7347,18 +7349,25 @@
     "    return bananas\n",
     "    \n",
     "def price_timeline(secret, n=2000) -> Dict[Deltas, int]:\n",
-    "    \"\"\"Each {delta-4-tuple: price} in the timeline of this secret number for `n` steps.\"\"\"\n",
+    "    \"\"\"Each {delta-4-tuple: price} in the timeline of this secret number, for `n` steps.\"\"\"\n",
     "    timeline = {}             # {delta-4-tuple: price} pairs\n",
     "    deltas = deque(maxlen=4)  # The 4 most recent price deltas  \n",
     "    price = secret % 10       # Initial price\n",
     "    for _ in range(n):\n",
-    "        secret = nth_secret(secret, 1)\n",
+    "        secret = next_secret(secret)\n",
     "        price, previous_price = secret % 10, price\n",
     "        deltas.append(price - previous_price)\n",
     "        D = tuple(deltas)\n",
     "        if len(D) == 4 and D not in timeline:\n",
     "            timeline[D] = price\n",
-    "    return timeline"
+    "    return timeline\n",
+    "\n",
+    "def next_secret(secret: int) -> int:\n",
+    "    \"\"\"Compute the next secret number after this secret number.\"\"\"\n",
+    "    secret ^= (secret *   64) % 16777216\n",
+    "    secret ^= (secret //  32) % 16777216\n",
+    "    secret ^= (secret * 2048) % 16777216\n",
+    "    return secret"
    ]
   },
   {
@@ -7370,7 +7379,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 22.2:  1.267 seconds, answer 1667              ok"
+       "Puzzle 22.2:  1.157 seconds, answer 1667              ok"
       ]
      },
      "execution_count": 258,
@@ -7767,7 +7776,7 @@
     {
      "data": {
       "text/plain": [
-       "Puzzle 23.2:   .004 seconds, answer bo,dd,eq,ik,lo,lu,ph,ro,rr,rw,uo,wx,yg ok"
+       "Puzzle 23.2:   .003 seconds, answer bo,dd,eq,ik,lo,lu,ph,ro,rr,rw,uo,wx,yg ok"
       ]
      },
      "execution_count": 281,
@@ -8331,7 +8340,7 @@
     "\n",
     "Here are all the puzzle answers and timings. I got all the puzzles correct! And I did it before midnight (my time) on December 25th, a rarity for me. \n",
     "\n",
-    "The median run time is about 5 milliseconds, with 4 puzzles taking over a second. I didn't count the time that `parse` takes, but that is less than a millisecond per day."
+    "The median run time is about 5 milliseconds, with 3 puzzles taking over a second. I didn't count the time that `parse` takes, but that is less than a millisecond per day."
    ]
   },
   {
@@ -8351,58 +8360,66 @@
       "Puzzle  3.1:   .001 seconds, answer 156388521         ok\n",
       "Puzzle  3.2:   .000 seconds, answer 75920122          ok\n",
       "Puzzle  4.1:   .021 seconds, answer 2401              ok\n",
-      "Puzzle  4.2:   .015 seconds, answer 1822              ok\n",
+      "Puzzle  4.2:   .016 seconds, answer 1822              ok\n",
       "Puzzle  5.1:   .001 seconds, answer 5762              ok\n",
       "Puzzle  5.2:   .001 seconds, answer 4130              ok\n",
       "Puzzle  6.1:   .002 seconds, answer 5329              ok\n",
-      "Puzzle  6.2:  1.943 seconds, answer 2162              ok\n",
+      "Puzzle  6.2:  1.977 seconds, answer 2162              ok\n",
       "Puzzle  7.1:   .014 seconds, answer 1985268524462     ok\n",
-      "Puzzle  7.2:   .592 seconds, answer 150077710195188   ok\n",
+      "Puzzle  7.2:   .600 seconds, answer 150077710195188   ok\n",
       "Puzzle  8.1:   .003 seconds, answer 220               ok\n",
       "Puzzle  8.2:   .003 seconds, answer 813               ok\n",
-      "Puzzle  9.1:   .019 seconds, answer 6332189866718     ok\n",
-      "Puzzle  9.2:  2.384 seconds, answer 6353648390778     ok\n",
-      "Puzzle 10.1:   .005 seconds, answer 744               ok\n",
+      "Puzzle  9.1:   .020 seconds, answer 6332189866718     ok\n",
+      "Puzzle  9.2:   .021 seconds, answer 6353648390778     ok\n",
+      "Puzzle 10.1:   .004 seconds, answer 744               ok\n",
       "Puzzle 10.2:   .006 seconds, answer 1651              ok\n",
-      "Puzzle 11.1:   .001 seconds, answer 194482            ok\n",
-      "Puzzle 11.2:   .060 seconds, answer 232454623677743   ok\n",
-      "Puzzle 12.1:   .050 seconds, answer 1402544           ok\n",
-      "Puzzle 12.2:   .042 seconds, answer 862486            ok\n",
+      "Puzzle 11.1:   .002 seconds, answer 194482            ok\n",
+      "Puzzle 11.2:   .058 seconds, answer 232454623677743   ok\n",
+      "Puzzle 12.1:   .052 seconds, answer 1402544           ok\n",
+      "Puzzle 12.2:   .043 seconds, answer 862486            ok\n",
       "Puzzle 13.1:   .000 seconds, answer 29598             ok\n",
       "Puzzle 13.2:   .000 seconds, answer 93217456941970    ok\n",
       "Puzzle 14.1:   .000 seconds, answer 216027840         ok\n",
-      "Puzzle 14.2:  1.828 seconds, answer 6876              ok\n",
+      "Puzzle 14.2:  1.866 seconds, answer 6876              ok\n",
       "Puzzle 15.1:   .029 seconds, answer 1563092           ok\n",
       "Puzzle 15.2:   .042 seconds, answer 1582688           ok\n",
-      "Puzzle 16.1:   .146 seconds, answer 103512            ok\n",
-      "Puzzle 16.2:   .848 seconds, answer 554               ok\n",
+      "Puzzle 16.1:   .147 seconds, answer 103512            ok\n",
+      "Puzzle 16.2:   .860 seconds, answer 554               ok\n",
       "Puzzle 17.1:   .000 seconds, answer 2,1,0,1,7,2,5,0,3 ok\n",
       "Puzzle 17.2:   .004 seconds, answer 267265166222235   ok\n",
       "Puzzle 18.1:   .014 seconds, answer 344               ok\n",
       "Puzzle 18.2:   .032 seconds, answer 46,18             ok\n",
       "Puzzle 19.1:   .004 seconds, answer 242               ok\n",
-      "Puzzle 19.2:   .186 seconds, answer 595975512785325   ok\n",
+      "Puzzle 19.2:   .185 seconds, answer 595975512785325   ok\n",
       "Puzzle 20.1:   .023 seconds, answer 1343              ok\n",
-      "Puzzle 20.2:   .761 seconds, answer 982891            ok\n",
+      "Puzzle 20.2:   .768 seconds, answer 982891            ok\n",
       "Puzzle 21.1:   .000 seconds, answer 205160            ok\n",
       "Puzzle 21.2:   .004 seconds, answer 252473394928452   ok\n",
-      "Puzzle 22.1:   .318 seconds, answer 14273043166       ok\n",
-      "Puzzle 22.2:  1.267 seconds, answer 1667              ok\n",
+      "Puzzle 22.1:   .331 seconds, answer 14273043166       ok\n",
+      "Puzzle 22.2:  1.157 seconds, answer 1667              ok\n",
       "Puzzle 23.1:   .001 seconds, answer 1170              ok\n",
-      "Puzzle 23.2:   .004 seconds, answer bo,dd,eq,ik,lo,lu,ph,ro,rr,rw,uo,wx,yg ok\n",
+      "Puzzle 23.2:   .003 seconds, answer bo,dd,eq,ik,lo,lu,ph,ro,rr,rw,uo,wx,yg ok\n",
       "Puzzle 24.1:   .001 seconds, answer 36035961805936    ok\n",
       "Puzzle 24.2:   .000 seconds, answer jqf,mdd,skh,wpd,wts,z11,z19,z37 ok\n",
       "Puzzle 25.1:   .022 seconds, answer 3196              ok\n",
       "\n",
       "Correct: 49/49\n",
       "\n",
-      "Time in seconds: 0.005 median, 0.218 mean, 10.699 total.\n"
+      "Time in seconds: 0.004 median, 0.170 mean, 8.342 total.\n"
      ]
     }
    ],
    "source": [
     "summary(answers)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4f23c694-7302-4d45-8bef-751b9a7356f2",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {