{
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   "cell_type": "code",
   "execution_count": null,
   "id": "639168a7-1fd7-4585-a665-95bcc723108f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import matplotlib.ticker as ticker\n",
    "from matplotlib.ticker import MultipleLocator\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de43d55b-fe6a-4677-9e2e-2af7edf8538c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Constant: The full search interval is (1, MAX_VALUE)\n",
    "MAX_VALUE = 1024"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "83c1f4db-09a8-424e-a7d9-871dac77c82b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def binary_search(n):\n",
    "    \"\"\"\n",
    "    Perform a binary search for the value n.\n",
    "    Return the count of probes until found.\n",
    "    \"\"\"\n",
    "    # Initial interval bounds.\n",
    "    low = 0\n",
    "    high = MAX_VALUE\n",
    "    \n",
    "    count = 0\n",
    "    middle = -1\n",
    "    \n",
    "    while (middle != n) and (count < 11):\n",
    "        middle = (low + high)//2\n",
    "        count += 1\n",
    "\n",
    "        if middle < n:\n",
    "            low = middle   # search the upper half next\n",
    "        elif middle > n:\n",
    "            high = middle  # search the lower half next\n",
    "        \n",
    "    return count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e319c078-5698-4879-aa6f-5c1448c6d39b",
   "metadata": {},
   "outputs": [],
   "source": [
    "counts = [0]*MAX_VALUE       # list of counts of probes for the values \n",
    "colors = ['BLUE']*MAX_VALUE  # list of colors of the horizonal bars\n",
    "frequencies = [0]*11         # list of frequencies of the counts\n",
    "\n",
    "# Search for each value n in the range.\n",
    "for n in range(1, MAX_VALUE):\n",
    "    count = binary_search(n)\n",
    "    \n",
    "    # Set the count for this value\n",
    "    # and update the count's frequency.\n",
    "    counts[n] = count \n",
    "    frequencies[count] += 1\n",
    "    \n",
    "    # Determine the horizontal bar's color\n",
    "    # for this value based on its count.\n",
    "    if count < 3:\n",
    "        colors[n] = 'RED'\n",
    "    elif count < 6:\n",
    "        colors[n] = 'ORANGE'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec89d43a-4457-4230-9fa0-82723773ae4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A simple bar chart of the count frequencies.\n",
    "plt.bar(x=range(0, 11), height=frequencies)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e57e41b3-79ad-4691-854a-f64789598e03",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A horizontal bar chart of each value's probe count.\n",
    "\n",
    "# Set the graph's size.\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(6, 150)\n",
    "\n",
    "# Set the axes' tick intervals.\n",
    "ax = fig.add_subplot(111)\n",
    "ax.xaxis.set_major_locator(ticker.MultipleLocator(1))  # x axis\n",
    "ax.yaxis.set_major_locator(ticker.MultipleLocator(2))  # y axis\n",
    "\n",
    "# Set the lower and upper limits of the y axis.\n",
    "plt.ylim(0, MAX_VALUE)\n",
    "\n",
    "# Create a horizontal bar chart.\n",
    "# Assign a color to each bar based on its count.\n",
    "plt.barh(y=range(0, MAX_VALUE), width=counts, height=0.8,\n",
    "         color=colors)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "621a57f6-57e4-4437-b082-1da85a4c5b68",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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