{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f2a6d772",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Improved Quadratic Equation Solver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90807e9d",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "**CS1302 Introduction to Computer Programming**\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c090b397",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In this notebook, we will improve the quadratic equation solver in the previous lab using conditional executions.  \n",
    "First of all, run the following to setup the environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "947b618f",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interact\n",
    "import math\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6eb68c8c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Discriminant"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7db9c46b",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Recall that a quadratic equation is\n",
    "\n",
    "$$\n",
    "ax^2+bx+c=0\n",
    "$$\n",
    "\n",
    "where $a$, $b$, and $c$ are real-valued coefficients, and $x$ is the unknown variable."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57cdc489",
   "metadata": {},
   "source": [
    "````{prf:definition} Discriminant\n",
    "\n",
    "The disciminant of a quadratic equation is defined as\n",
    "\n",
    "$$\n",
    "\\Delta := b^2 - 4ac.\n",
    "$$ (discriminant)\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a682a686",
   "metadata": {},
   "source": [
    "The discriminant $\\Delta$ discriminates the roots $\\frac{-b\\pm \\sqrt{\\Delta}}{2a}$ of a quadratic equation:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2654072e",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{prf:proposition} \n",
    "\n",
    "The roots of a quadratic equation {eq}`quadratic` are the same (repeated) equal to $-\\frac{b}{2a}$ when the discriminant is zero, i.e., $\\Delta=0$.\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35ce4c61",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Exercise** Complete the following function by assigning `roots` only one root when the discriminant is zero. E.g., if $(a,b,c)=(1,-2,1)$, then `roots` should be assigned the value `1.0` instead of `1.0, 1.0`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5d5f7ec5",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ab6fbcdff876e3cfc8767e7377284ccb",
     "grade": false,
     "grade_id": "zero_determininant",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def get_roots(a, b, c):\n",
    "    d = b ** 2 - 4 * a * c  # discriminant\n",
    "    if math.isclose(d, 0):\n",
    "        # YOUR CODE HERE\n",
    "        raise NotImplementedError()\n",
    "    return roots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc790249",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{hint}\n",
    "\n",
    "Consider using the [if statement](https://docs.python.org/3/reference/compound_stmts.html#if) as follows:\n",
    "\n",
    "```Python\n",
    "def get_roots(a, b, c):\n",
    "    d = b ** 2 - 4 * a * c  # discriminant\n",
    "    if math.isclose(d, 0):\n",
    "        roots = ___  # repeated root\n",
    "    else:\n",
    "        d **= 0.5\n",
    "        roots = ___, ___\n",
    "    return roots\n",
    "```\n",
    "\n",
    "This is a solution template where `___` needs to be filled in with appropriate code. If you have a more efficient/simpler implementation, you need *not* follow the solution template. E.g., to challenge your understanding of short-circuit evaluation, you can write your solution using boolean operations without any if statement.\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9c3cf252",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "16860060eb7229216c52e0e6c7e96484",
     "grade": true,
     "grade_id": "test-zero_determinant",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "hide-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'roots' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-caa994877248>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-3-caa994877248>\u001b[0m in \u001b[0;36mtest_get_roots\u001b[0;34m(roots, a, b, c)\u001b[0m\n\u001b[1;32m      4\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimag\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mroots_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     assert (\n\u001b[1;32m      8\u001b[0m         \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mroots\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"__len__\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-2-45ff55ce66e0>\u001b[0m in \u001b[0;36mget_roots\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m      4\u001b[0m         \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m         \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mroots\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'roots' is not defined"
     ]
    }
   ],
   "source": [
    "# tests\n",
    "def test_get_roots(roots, a, b, c):\n",
    "    def mysort(c):\n",
    "        return c.real, c.imag\n",
    "\n",
    "    roots_ = get_roots(a, b, c)\n",
    "    assert (\n",
    "        hasattr(roots, \"__len__\")\n",
    "        and np.isclose(\n",
    "            sorted(list(roots), key=mysort), sorted(list(roots_), key=mysort)\n",
    "        ).all()\n",
    "        or roots == roots_ or np.isclose(roots, roots_)\n",
    "    )\n",
    "\n",
    "\n",
    "test_get_roots((-1.0, 0.0), 1, 1, 0)\n",
    "test_get_roots(0.0, 1, 0, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c8e24bc2",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "ea74289e50129048beb923088ce499c8",
     "grade": true,
     "grade_id": "hidden_test-zero_determinant",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f7aa15e",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Exercise** Why use `math.isclose(d, 0)` instead of `d == 0`?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21bf7b7a",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "12889805830e3af64988ae0de141f1b7",
     "grade": true,
     "grade_id": "isclose",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1338a121",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear equation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f50e4e2",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If $a=0$, the earlier formula for the roots are invalid due to division by zero. Nevertheless, the equation remains valid:\n",
    "\n",
    "$$\n",
    "bx + c=0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14b834b0",
   "metadata": {},
   "source": [
    "**Exercise** Improve the function `get_roots` to return the root $-\\frac{c}{b}$ when $a=0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "06935007",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "790fe0b27e9e6efe7e54afa74e32dbad",
     "grade": false,
     "grade_id": "linear",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def get_roots(a, b, c):\n",
    "    d = b ** 2 - 4 * a * c\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return roots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83dc5b7c",
   "metadata": {},
   "source": [
    "````{hint} \n",
    "\n",
    "Solution template:\n",
    "```Python\n",
    "def get_roots(a, b, c):\n",
    "    d = b ** 2 - 4 * a * c    # discriminant\n",
    "    if ___:\n",
    "        roots = ___\n",
    "    elif math.isclose(d, 0):\n",
    "        roots = ___  # repeated root\n",
    "    else:\n",
    "        d **= 0.5\n",
    "        roots = ___\n",
    "    return roots\n",
    "```\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "81c78d2d",
   "metadata": {
    "code_folding": [],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "5c1bddf43ef773f22d90ffad549ccc45",
     "grade": true,
     "grade_id": "test-linear",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-output",
     "hide-input"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-2d9728339754>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-3-caa994877248>\u001b[0m in \u001b[0;36mtest_get_roots\u001b[0;34m(roots, a, b, c)\u001b[0m\n\u001b[1;32m      4\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimag\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mroots_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     assert (\n\u001b[1;32m      8\u001b[0m         \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mroots\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"__len__\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-ba623ea41c29>\u001b[0m in \u001b[0;36mget_roots\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mroots\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "test_get_roots((-1.0, -0.0), 1, 1, 0)\n",
    "test_get_roots(0.0, 1, 0, 0)\n",
    "test_get_roots(0.5, 0, -2, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0acfdccb",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "0b77d8b49baaccd677119a45a0a2a230",
     "grade": true,
     "grade_id": "hidden_test-linear",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b79e5149",
   "metadata": {},
   "source": [
    "## Degenerate cases"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5791fbf9",
   "metadata": {},
   "source": [
    "What if $a=b=0$? In that case, the equation becomes\n",
    "\n",
    "$$\n",
    "c = 0\n",
    "$$\n",
    "which is always satisfied if $c=0$ but never satisfied if $c\\neq 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ff6b07d",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Exercise** Improve the function `get_roots` to return root(s) under all cases:\n",
    "- If $a=0$ and $b\\neq 0$, assign `roots` to the single root $-\\frac{c}{b}$. \n",
    "- If $a=b=0$ and $c\\neq 0$, assign `roots` to `None`.  \n",
    "    Note that `None` is an object, not a string.\n",
    "- If $a=b=c=0$, there are infinitely many roots. Assign to `roots` the tuple `-float('inf'), float('inf')`.  \n",
    "    Note that `float('inf')` converts the string `'inf'` to a floating point value that represents $\\infty$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d37bac31",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "474f601f43c279d150f959b1672c2f86",
     "grade": false,
     "grade_id": "degenerate",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    },
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "def get_roots(a, b, c):\n",
    "    d = b ** 2 - 4 * a * c\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    return roots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b3467af",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "````{hint} \n",
    "\n",
    "Use nested `if` statements as in the solution template:\n",
    "\n",
    "```Python\n",
    "def get_roots(a, b, c):\n",
    "    d = b**2 - 4 * a * c\n",
    "    if ___:\n",
    "        if ___:\n",
    "            if ___:\n",
    "                roots = -float('inf'), float('inf')\n",
    "            else:\n",
    "                roots = None\n",
    "        else:\n",
    "            ___\n",
    "    elif math.isclose(d, 0):\n",
    "        roots = ___  # repeated root\n",
    "    else:\n",
    "        d **= 0.5\n",
    "        roots = ___\n",
    "    return roots\n",
    "```\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cdb68285",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "5d991e44c6b5378dbe741263bcf09984",
     "grade": true,
     "grade_id": "test-degenerate",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "hide-input",
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-6500f6940609>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# tests\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'inf'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'inf'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mtest_get_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-3-caa994877248>\u001b[0m in \u001b[0;36mtest_get_roots\u001b[0;34m(roots, a, b, c)\u001b[0m\n\u001b[1;32m      4\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimag\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mroots_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_roots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     assert (\n\u001b[1;32m      8\u001b[0m         \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mroots\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"__len__\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-8-ba623ea41c29>\u001b[0m in \u001b[0;36mget_roots\u001b[0;34m(a, b, c)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0;31m# YOUR CODE HERE\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mroots\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNotImplementedError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# tests\n",
    "test_get_roots((-1.0, 0.0), 1, 1, 0)\n",
    "test_get_roots(0.0, 1, 0, 0)\n",
    "test_get_roots((-float('inf'), float('inf')), 0, 0, 0)\n",
    "test_get_roots(None, 0, 0, 1)\n",
    "test_get_roots(0.5, 0, -2, 1)\n",
    "test_get_roots(1.0, 1, -2, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f2f6f89c",
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "8ee8bbfeb16c1bf80e555537f093154d",
     "grade": true,
     "grade_id": "test_test-degenerate",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# hidden tests"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1182418",
   "metadata": {},
   "source": [
    "After you have complete the exercises, you can run your robust solver below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6a49dc1c",
   "metadata": {
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "-"
    },
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "aef5c25097ff4a19842a443cd947489b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='a', max=10, min=-10), IntSlider(value=2, description='b'…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# quadratic equations solver\n",
    "@interact(a=(-10,10,1),b=(-10,10,1),c=(-10,10,1))\n",
    "def quadratic_equation_solver(a=1,b=2,c=1):\n",
    "    print('Root(s):',get_roots(a,b,c))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "162e7ff3",
   "metadata": {},
   "source": [
    "## Flowcharts (optional)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25ce40d8",
   "metadata": {},
   "source": [
    "Let's play a game to test your understanding of boolean expressions. Run the following program and choose your input so that 1, 2, 3 are each printed in a separate line as follows:\n",
    "``` \n",
    "1\n",
    "2\n",
    "3\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6538bbe1",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-12-3db6e2a1edbe>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "input(1) or input(2) and input(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "523d3f85",
   "metadata": {},
   "source": [
    "````{hint}\n",
    "\n",
    "The following flowchart describes the [short-circuit evaluation](https://docs.python.org/3/reference/expressions.html?highlight=precedence#boolean-operations) for the boolean expression as follows:\n",
    "\n",
    "![1or2and3](images/1or2and3.svg)\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b47ac95",
   "metadata": {},
   "source": [
    "**How to read the flowchart?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2927ac8",
   "metadata": {},
   "source": [
    "A flowchart uses arrows to connects a set of [annotated blocks][bb]. The rules were first specified by ANSI and later adopted in [ISO 5807][iso].\n",
    "\n",
    "[bb]: https://en.wikipedia.org/wiki/Flowchart#Building_blocks\n",
    "[iso]: https://webstore.ansi.org/Standards/ISO/ISO58071985"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d243b088",
   "metadata": {},
   "source": [
    "For the above game, start from the first decision block at the top and choose the input appropriately to transition along the `yes` arrows."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37cccfe1",
   "metadata": {},
   "source": [
    "**Why use a program flowchart?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72ec7d45",
   "metadata": {},
   "source": [
    "A program flowchart is a powerful way of describing an algorithm quickly. Unlike a text-based programming language:\n",
    "- The rules governing the program flow can be shown explicitly by arrows.\n",
    "- The annotated graphical blocks can convey the meaning faster using visual clues."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b43a1cce",
   "metadata": {},
   "source": [
    "A programmer can draft a program in flowchart without worrying about syntax (indentation, colon, ...). E.g., the above flow chart can be implemented as follows using the if statement instead of the boolean operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bf7e6714",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-70de8affeb10>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m         \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "if not input(1):\n",
    "    if input(2):\n",
    "        input(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78b80f5b",
   "metadata": {},
   "source": [
    "**How to convert the program to a flowchart automatically?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60d2f454",
   "metadata": {},
   "source": [
    "To draw a flowchart, we can use a vector graphics editor. [Inkscape](https://inkscape.org/) is an open source software the runs in Linux/Mac/Windows. To run on mobile devices, you can run it with the desktop launcher in your jupyter server."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ad88765",
   "metadata": {},
   "source": [
    "A web application you can run without a desktop is [`ipydrawio`](https://ipydrawio.readthedocs.io/en/stable/):\n",
    "- In the file tab, create a file called `test.dio.svg` and double click it.\n",
    "- After you finished drawing the flowchart, save it and use it as an [SVG image](https://en.wikipedia.org/wiki/Scalable_Vector_Graphics)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa59af83",
   "metadata": {},
   "source": [
    "The most convenient way, of course, is to ask python to convert a python code to a flowchart automatically. This can be done with [`pyflowchart`](https://github.com/cdfmlr/pyflowchart):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a1d3d7d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyflowchart import Flowchart\n",
    "\n",
    "def code2flow(code):\n",
    "    '''\n",
    "    Given input code (as a string), returns the flowchart (as a string) that can be rendered by\n",
    "    http://flowchart.js.org\n",
    "    '''\n",
    "    return Flowchart.from_code(code, simplify=False).flowchart()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "597ae38d",
   "metadata": {},
   "source": [
    "Pass the code as a string to `code2flow`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6dc3afb5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cond3=>condition: if (not input(1))\n",
      "cond8=>condition: if input(2)\n",
      "sub12=>subroutine: input(3)\n",
      "\n",
      "cond3(yes)->cond8\n",
      "cond8(yes)->sub12\n",
      "\n"
     ]
    }
   ],
   "source": [
    "fc = code2flow('''\n",
    "if not input(1):\n",
    "    if input(2):\n",
    "        input(3)\n",
    "''')\n",
    "print(fc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "966db20a",
   "metadata": {},
   "source": [
    "The output is a string in a [domain-specific language (DSL)][dsl] that can be [rendered here with flowchart.js][fc]. Simply overwrite a demo textbox there with the printed flowchart code above.\n",
    "\n",
    "[dsl]: https://en.wikipedia.org/wiki/Domain-specific_language\n",
    "[fc]: http://flowchart.js.org"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a25db98c",
   "metadata": {},
   "source": [
    "**How to write a documentation with flowcharts?  \n",
    "What about other DSL for special contents such as diagrams, equations, lists, ...?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85801459",
   "metadata": {},
   "source": [
    "[Markdown](https://en.wikipedia.org/wiki/Markdown) is becoming popular in writing documentations. jupyter notebooks, jupyterbook, github, ... all supports markdown, but to different extents:\n",
    "\n",
    "- Jupyter notebook such as this one supports [CommonMark](https://commonmark.org).\n",
    "- Our [cs1302 jupyterbook](https://www.cs.cityu.edu.hk/~ccha23/cs1302book) is written in [MyST](https://myst-parser.readthedocs.io/en/latest/syntax/syntax.html) markdown.\n",
    "- Github uses [Github Flavored Markdown (GFM).](https://github.github.com/gfm/)\n",
    "\n",
    "Unfortunately, none of them support the flowchart code currently."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcff4b9a",
   "metadata": {},
   "source": [
    "Nevertheless, many editors such as [Typora](https://typora.io) supports advanced Markdown language with live preview. We can also extend VS Code to do the same using [Markdown Preview Enhanced](https://shd101wyy.github.io/markdown-preview-enhanced/#/) as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72d1ee09",
   "metadata": {},
   "source": [
    "````{tip}\n",
    "\n",
    "You can install any extension on the VS Code interface of the JupyterHub server. To render flowchart code:\n",
    "\n",
    "1. Open `Launcher` (click on the **+** sign in the top left or press `Shift + Ctrl + L`) and click on `VS Code` to create a VSCode tab\n",
    "2. Click the extension tab on the left and search for *Markdown Preview Enhanced*.\n",
    "3. Click install and refresh the browser.\n",
    "4. Click the file explorer tab and create a new file say `test.md` file.\n",
    "5. Insert the flowchart in DSL to the `test.md` [as follows](https://shd101wyy.github.io/markdown-preview-enhanced/#/diagrams?id=flow-charts):  \n",
    "    ````Markdown\n",
    "    ```flow\n",
    "    cond3=>condition: if (not input(1))\n",
    "    cond8=>condition: if input(2)\n",
    "    sub12=>subroutine: input(3)\n",
    "\n",
    "    cond3(yes)->cond8\n",
    "    cond8(yes)->sub12\n",
    "    ```\n",
    "    ````\n",
    "6. To show the live preview, click the `open preview` button of Markdown Preview Enhanced located on the tool bar at the top right-hand corner.\n",
    "\n",
    "You can also using `drawio` in VS Code using [the extension here](https://marketplace.visualstudio.com/items?itemName=hediet.vscode-drawio).\n",
    "\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51794064",
   "metadata": {},
   "source": [
    "Finally, note that the flow chart does not implement how short-circuit evaluation returns values. E.g., consider entering `a` for all the inputs and see the difference in the output of the boolean expression and the code that implements the flowchart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "297f6b93",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-16-3db6e2a1edbe>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "input(1) or input(2) and input(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "aa70d6b1",
   "metadata": {
    "tags": [
     "remove-output"
    ]
   },
   "outputs": [
    {
     "ename": "StdinNotImplementedError",
     "evalue": "raw_input was called, but this frontend does not support input requests.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-70de8affeb10>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m         \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/my-conda-envs/jb/lib/python3.8/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m    843\u001b[0m         \"\"\"\n\u001b[1;32m    844\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_allow_stdin\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 845\u001b[0;31m             raise StdinNotImplementedError(\n\u001b[0m\u001b[1;32m    846\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    847\u001b[0m             )\n",
      "\u001b[0;31mStdinNotImplementedError\u001b[0m: raw_input was called, but this frontend does not support input requests."
     ]
    }
   ],
   "source": [
    "if not input(1):\n",
    "    if input(2):\n",
    "        input(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30b5387c",
   "metadata": {},
   "source": [
    "**Exercise** (Optional) Can you implement the boolean expression exactly with the same return value using only conditionals but not boolean operators?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "802ac09c",
   "metadata": {},
   "source": [
    "````{hint}\n",
    "\n",
    "Consider using [conditional expression](https://docs.python.org/3/reference/expressions.html#conditional-expressions) and [assignment expression](https://docs.python.org/3/reference/expressions.html#grammar-token-assignment-expression).\n",
    "\n",
    "````"
   ]
  }
 ],
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