cs110_pcw_4_2.ipynb

{
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    "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
    "\n",
    "Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your name and collaborators below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "NAME = \"Evan\"\n",
    "COLLABORATORS = \"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
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   "source": [
    "# CS110 Pre-class Work 4.2\n",
    "\n",
    "## Part A. The Hire-Assistant Problem.\n",
    "\n",
    "Imagine that you need to hire a new assistant. Every day an agency sends a new assistant for you to interview. If the assistant is better than your current assistant, then you fire your current assistant and you hire the better assistant. You may assume that assistant quality is uniformly distributed between 0 and 1.\n",
    "\n",
    "## Question 1.\n",
    "Write a function, named hire_assistant, that takes applicants (a list of the numbers that represent the level of qualification of the applicants; the higher the number, the better qualified), and returns the number hires if the applicants are presented in the exact same order as the input list applicants. Note that your function should not randomize anything (or else it would be called a randomized algorithm)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   "outputs": [],
   "source": [
    "def hire_assistant(applicants):\n",
    "    \"\"\"\n",
    "    Return the number of assistant hired.\n",
    "    Inputs:\n",
    "    - applicants: a list of the numbers that represent the level of qualification of \n",
    "    the applicants; the higher the number, the better qualified\n",
    "    \n",
    "    Outputs:\n",
    "    - hires: Number of assistants hired\n",
    "    \"\"\"\n",
    "    hired = 0\n",
    "    best = float(\"-inf\")\n",
    "    for i in range(len(applicants)):\n",
    "        if applicants[i] > best:\n",
    "            best = applicants[i]\n",
    "            hired +=1\n",
    "            \n",
    "    return hired\n",
    "    \n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
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  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
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   },
   "outputs": [],
   "source": [
    "assert(hire_assistant([1])==1)\n",
    "assert(hire_assistant([-1, -2, -3, -4])==1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": false,
    "nbgrader": {
     "checksum": "950e8b4c047988bb6493460be72d1bc7",
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   },
   "source": [
    "## Question 2. \n",
    "Assuming the applicants are presented in a random order, write a function that receives the number of applicants as input and returns the average number of assistants hired.\n",
    "\n",
    "**N.B.:** Don’t forget to run the simulation several times for each given number of applicants to better estimate the number of hires (please refer to task 3 of the Study Guide)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "7038d9d8cc9239d5ca15f5d21aa986e3",
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   },
   "outputs": [],
   "source": [
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def experimental_hires(N):\n",
    "    # YOUR CODE HERE\n",
    "    hired = 0\n",
    "    best = float(\"-inf\")\n",
    "    rand_list = []\n",
    "    for i in range(N):\n",
    "        nexte = random.randrange(1,N+1)\n",
    "        while nexte in rand_list:\n",
    "            nexte = random.randrange(1,N+1)\n",
    "        rand_list.append(nexte) \n",
    "   \n",
    "    for i in range(N):\n",
    "        if rand_list[i] > best:\n",
    "            best = rand_list[i]\n",
    "            hired +=1\n",
    "            \n",
    "    return hired\n",
    "    raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_list = [*range(200)]\n",
    "experimental_data = []\n",
    "analytical_data = []\n",
    "for i in range(len(n_list)):\n",
    "    tot_hire = 0\n",
    "    for j in range(30):\n",
    "        tot_hire += experimental_hires(i)\n",
    "    ave_hire = tot_hire/30\n",
    "    experimental_data.append(ave_hire)\n",
    "    analytical_data.append(analytical_hires(i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "editable": false,
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   },
   "source": [
    "## Question 3.\n",
    "\n",
    "Use the function below, `analytical_hires(N)`, which returns the analytical expected number of hires, given the number of applicants, along with the function you created in question 2 to create a graph with two curves such that:\n",
    "* The x-axis shows the total number of applicants (make sure label the x-axis)\n",
    "* The y-axis shows the average number of hires (make sure label the y-axis)\n",
    "* The graph contains two curves;\n",
    "    * Curve 1: the theoretical performance estimates computed calls to the function `analytical_hires`.\n",
    "    * Curve 2: the simulated or experimental estimates using the function you created in question 2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "1e514458253b863a6c69ce09ccd2d9de",
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     "grade_id": "cell-4092502cb05933d4",
     "locked": true,
     "schema_version": 1,
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   },
   "outputs": [],
   "source": [
    "def analytical_hires(N):\n",
    "    \"\"\"\n",
    "    Return the analytical expected number of hires if there are N applicants\n",
    "    Inputs:\n",
    "    - N: Number of applicants\n",
    "    Outputs:\n",
    "    - hires: Average number of assistants hired\n",
    "    \"\"\"\n",
    "    # from the textbook, we know that the analytical result is \n",
    "    # 1 + 1/2 + 1/3 + ... + 1/N\n",
    "    hires = 0\n",
    "    for n in range(N):\n",
    "        hires += 1/(n+1)\n",
    "    return hires"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.878030948121446"
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     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_list,analytical_data,color=\"b\")\n",
    "plt.plot(n_list,experimental_data,color=\"r\")\n",
    "plt.legend((\"Analytical\",\"Experimental\"))\n",
    "plt.xlabel(\"Number of Applicants\")\n",
    "plt.ylabel(\"Results\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "055b3a48707a83f9330ab3b00c45144a",
     "grade": true,
     "grade_id": "cell-f9c07920c069ce20",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "f5c0fc54ac7e38140eacf7a0d3877a00",
     "grade": false,
     "grade_id": "cell-8720f8d8a6a98422",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Question 4.\n",
    "\n",
    "Plot a graph with the x-axis showing the total number of applicants and the y-axis showing the probability that exactly one assistant is hired."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "99500575978918dad34be4dfe49fff36",
     "grade": true,
     "grade_id": "cell-d3fe1b7d6d175ad7",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# YOUR CODE HERE\n",
    "#Probability of hiring exactly 1 applicant is equal to the probability that the best applicant interviews first, or 1/n\n",
    "\n",
    "one_hire = []\n",
    "for i in range(1,201):\n",
    "    one_hire.append(1/i)\n",
    "\n",
    "plt.plot(n_list,one_hire)\n",
    "plt.xlabel(\"Number of Applicants\")\n",
    "plt.ylabel(\"P(One Hire)\")\n",
    "plt.show()\n",
    "\n",
    "#raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "5721e2312411a707d06a42f45aa28d6a",
     "grade": false,
     "grade_id": "cell-2bd2500c3ca4cf02",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## [Optional] Question 5.\n",
    "Assume that an assistant is able to perform an amount of work each day that is equal to their “quality”. You have a total amount of work M that needs to be accomplished. Your costs are as follows:\n",
    "* X = daily salary for the assistant,\n",
    "* Y = fee to the employment agency,\n",
    "* Z = retrenchment fee for the old assistant.\n",
    "\n",
    "Try to formulate an optimal stopping rule (i.e., at what point should one stop requesting new potential hires from the agency?) Make any necessary assumptions to ensure the problem is well-formulated.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "43b6a51878665a39b0ede1313448eaa6",
     "grade": true,
     "grade_id": "cell-af2f0291eced6982",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "33ac7721d636faf76ce7bdbda1b443d6",
     "grade": false,
     "grade_id": "cell-92211f5b42929c46",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Part B. The Hat Check Problem.\n",
    "\n",
    "There is a coat check at a party, where an attendant stores everyone’s hat while they attend the party. The attendant receives the N hats from everyone attending (all attendees come with a hat). Unfortunately, the coat check attendant forgets which hat belongs to whom. Rather than admitting a mistake, the attendant simply returns random hats back to the party-goers. \n",
    "\n",
    "What is the average number of correct hats returned? Here are some guiding questions to help you to simulate this problem. \n",
    "\n",
    "## Question 1. \n",
    "Knowing that everyone’s hats are unique and every guest has a hat. Do you need to generate a random sample in a similar way as what you did for the hiring assistant problem? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "259c6115bee56676178f28ab36d6db2f",
     "grade": true,
     "grade_id": "cell-e786799fc4eb1499",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "No, we can simply take the probability  of 1/remaining number of hats - that someone will recieve the correct hat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "c9f8182f3dd59f572cb797f373fb7464",
     "grade": false,
     "grade_id": "cell-e2f68e2bd4c2d099",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Question 2. \n",
    "Which of the following commands do you think is the Pythonic way to implement that? \n",
    "```\n",
    "import numpy as np\n",
    "n = 100 #the number of party attendants `\n",
    "```\n",
    "**Command 1. **\n",
    "```\n",
    "hat_list = [np.random.integers(0,n) for i in range(n)]`\n",
    "```\n",
    "**Command 2.**\n",
    "```\n",
    "hat_list = list(range(n)) \n",
    "np.random.shuffle(hat_list) \n",
    "```\n",
    "**Command 3.**\n",
    "```\n",
    "hat_list = np.random.sample(n)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "b5e83025692b2772640e9e58f0f36af1",
     "grade": true,
     "grade_id": "cell-b8da78e72c1c0738",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "command 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "ec25d5c32cc709928fa50666f21d9808",
     "grade": false,
     "grade_id": "cell-8915979a0b8cf6ce",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Question 3.\n",
    "Now write a function `hat_check(N)` that has: \n",
    "* Input: N the number of party attendants. \n",
    "* Output: the number of hats correctly returned despite the fact that hats are randomly handed back to the guests.\n",
    "\n",
    "You should use the command you picked for question 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "c37f6cdc2ca8cbb92644fa2746445779",
     "grade": true,
     "grade_id": "cell-c8499aeb1b1d76c7",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def hat_check(N):\n",
    "    correct_returns = 0\n",
    "    hat_list = list(range(N))\n",
    "    np.random.shuffle(hat_list)\n",
    "    for i in range(N):\n",
    "        if hat_list[i] == i:\n",
    "            correct_returns +=1\n",
    "            \n",
    "    return correct_returns\n",
    "\n",
    "#raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "1ff8b95312de63513a2107ffb7ab9d5a",
     "grade": false,
     "grade_id": "cell-086d4cc0fc5b0155",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Question 4.\n",
    "\n",
    "Plot a curve with the x-axis showing the total number of party attendants and the y-axis showing the average number of hats correctly returned. As always, remember to run several trials. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "c4d1251529b962f3d3ce28f6ac9f244e",
     "grade": true,
     "grade_id": "cell-597031ea2a5a512a",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "correct_return_data = []\n",
    "for i in range(len(n_list)):\n",
    "    tot_return = 0\n",
    "    for j in range(30):\n",
    "        tot_return += hat_check(i)\n",
    "    ave_return = tot_return/30\n",
    "    correct_return_data.append(ave_return)\n",
    "\n",
    "\n",
    "#raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_list,correct_return_data)\n",
    "plt.xlabel(\"Number of Hats\")\n",
    "plt.ylabel(\"Correct Returns\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "aad5d529ed9af56148bfc12691cdb950",
     "grade": false,
     "grade_id": "cell-f74b2078132a5177",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## [Optional] Question 5.\n",
    "As $N$ tends to infinity, the number of correct hats returned tends towards a well-known statistical distribution. State the distribution with all its parameters. Plot several samples using your code. Does the empirical distribution match your theoretical prediction?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "33f94a80e6d5d9c371e6c39790bd67eb",
     "grade": true,
     "grade_id": "cell-32fe26c1d99fdd2a",
     "locked": false,
     "points": 0,
     "schema_version": 1,
     "solution": true
    }
   },
   "source": [
    "As N--> inf, correct_returns -->. This is because the probability that each individual recieves the correct hat = 1/n, multiplied by n individuals n(1/n) = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "correct_return_data = []\n",
    "ns = np.logspace(1,20,base=2,num=20)\n",
    "for i in ns:\n",
    "    tot_return = 0\n",
    "    for j in range(30):\n",
    "        tot_return += hat_check(int(i))\n",
    "    ave_return = tot_return/30\n",
    "    correct_return_data.append(ave_return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.000000e+00 4.000000e+00 8.000000e+00 1.600000e+01 3.200000e+01\n",
      " 6.400000e+01 1.280000e+02 2.560000e+02 5.120000e+02 1.024000e+03\n",
      " 2.048000e+03 4.096000e+03 8.192000e+03 1.638400e+04 3.276800e+04\n",
      " 6.553600e+04 1.310720e+05 2.621440e+05 5.242880e+05 1.048576e+06]\n"
     ]
    }
   ],
   "source": [
    "#print(np.logspace(1,20,base=2,num=20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ns,correct_return_data)\n",
    "plt.xlabel(\"Number of Hats\")\n",
    "plt.ylabel(\"Correct Returns\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "This empirical prediction does not exactly match the experimental results. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}