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authorJack Sangdahl <[email protected]>2024-12-12 21:01:58 -0700
committerJack Sangdahl <[email protected]>2024-12-12 21:01:58 -0700
commit532be33588fd033fc7f814e725372923cf79a6c4 (patch)
treeaadebd96897ed3c2979a4986b30bbd7df4ddc657 /data-types-exercise.ipynb
downloadcsci3155-532be33588fd033fc7f814e725372923cf79a6c4.tar.gz
csci3155-532be33588fd033fc7f814e725372923cf79a6c4.zip
Unit 1
Signed-off-by: Jack Sangdahl <[email protected]>
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "3d02434f",
+ "metadata": {},
+ "source": [
+ "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`, \"???\", \"YOUR ANSWER HERE\", as well as your name and collaborators below:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "id": "8a89a7aa",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mNAME\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"Jack Sangdahl\"\u001b[39m\n",
+ "\u001b[36mCOLLABORATORS\u001b[39m: \u001b[32mString\u001b[39m = \u001b[32m\"N/A\"\u001b[39m"
+ ]
+ },
+ "execution_count": 47,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val NAME = \"Jack Sangdahl\"\n",
+ "val COLLABORATORS = \"N/A\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d009c835",
+ "metadata": {},
+ "source": [
+ "---"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9d34c7c8-c787-4f41-bd3a-5628797aa728",
+ "metadata": {},
+ "source": [
+ "# Exercise: Expressions and Data Types\n",
+ "\n",
+ "<!-- 3 Expressions -->\n",
+ "\n",
+ "<!-- 4 Binding and Scope -->\n",
+ "\n",
+ "The purpose of this assignment is to warm-up with Scala.\n",
+ "\n",
+ "### Learning Goals\n",
+ "\n",
+ "The primary learning goals of this assignment are to build intuition for\n",
+ "the following:\n",
+ "\n",
+ "- thinking in terms of types, values, and expressions; and\n",
+ "- imperative iteration.\n",
+ "\n",
+ "### Instructions\n",
+ "\n",
+ "This assignment asks you to write Scala code. There are restrictions\n",
+ "associated with how you can solve these problems. Please pay careful\n",
+ "heed to those. If you are unsure, ask the course staff.\n",
+ "\n",
+ "Note that `???` indicates that there is a missing function or code\n",
+ "fragment that needs to be filled in. In Scala, it is also an expression\n",
+ "that throws a `NotImplementedError` exception. Make sure that you remove\n",
+ "the `???` and replace it with the answer.\n",
+ "\n",
+ "Use the test cases provided to test your implementations. You are also\n",
+ "encouraged to write your own test cases to help debug your work.\n",
+ "However, please delete any extra cells you may have created lest they\n",
+ "break an autograder.\n",
+ "\n",
+ "## Type Checking\n",
+ "\n",
+ "In the following, I have left off the return type of function `g`. The\n",
+ "body of `g` is well-typed if we can come up with a valid return type. In\n",
+ "this question, we will reason for ourselves that `g` is indeed\n",
+ "well-typed."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "id": "0db88593",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mg\u001b[39m"
+ ]
+ },
+ "execution_count": 48,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def g(x: Int) = /*e1*/({\n",
+ " // env1\n",
+ " val (a, b) = /*e2*/(\n",
+ " // env2\n",
+ " (1, (x, 3))\n",
+ " )\n",
+ " /*e3*/(\n",
+ " // env3\n",
+ " if (x == 0) (b, 1) else (b, a + 2)\n",
+ " )\n",
+ "})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "27d6ff35-074c-4171-a7f5-a035015e7b83",
+ "metadata": {},
+ "source": [
+ "We have added parentheses around 3 key sub-expressions of the body of\n",
+ "`g` (e.g., `/*e1*/(`$\\ldots$`)`) and noted that there are corresponding\n",
+ "environments (e.g., `// env1` for each sub-expression).\n",
+ "\n",
+ "### Q1.1: What is the type environment `env1`? Briefly explain.\n",
+ "\n",
+ "Use either format shown in the notes (e.g.,\n",
+ "$[ x_1 : \\tau_1, \\ldots, x_n : \\tau_n ]$)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "672c616d-04fb-41cf-aad5-6f025548b7b7",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "markdown",
+ "checksum": "e41ca86f62e024565d1f2956f3950f48",
+ "grade": true,
+ "grade_id": "q1_1",
+ "locked": false,
+ "points": 2,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "source": [
+ "The type environment of `env1` alone is $[\\:\\mathtt{env1} \\mapsto\\mathtt{Int}\\:]$. At this point, the only variable in scope is the parameter `x: Int`, so `env1` also maps to `Int`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d577d0ca-7375-4e10-a89f-6a9f067a8f9f",
+ "metadata": {},
+ "source": [
+ "### Q1.2: What is the type environment `env2`? Briefly explain."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "62ae6788-7ed6-4acd-9d5c-40192d303dc9",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "markdown",
+ "checksum": "4660b9558a8195d26712214909a62db2",
+ "grade": true,
+ "grade_id": "q1_2",
+ "locked": false,
+ "points": 2,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "source": [
+ "The type environment of `env2` is $[\\:\\mathtt{env2} \\mapsto\\mathtt{Int}\\:]$. `env2` references the known type of `x: Int`, which also maps `env2` to `Int`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "93547002-40ae-42f1-a910-38131a7d26f6",
+ "metadata": {},
+ "source": [
+ "### Q1.3: Derive the type of expression `e2`.\n",
+ "\n",
+ "Showing the type for each sub-expression of `e2`; stop when you reach\n",
+ "literals or variable uses."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4114c6c1-7098-466c-bf92-69aa4a321664",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "markdown",
+ "checksum": "315ba92969984b267763af81ebd0f5d0",
+ "grade": true,
+ "grade_id": "q1_3",
+ "locked": false,
+ "points": 10,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "source": [
+ "```scala\n",
+ "(1, (x, 3)): (Int, (Int, Int))\n",
+ "- if 1: Int\n",
+ "- if (x, 3): (Int, Int)\n",
+ " - if x: Int\n",
+ " - if 3: Int\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "934b39f4-9eb5-4186-8e8d-f05f24d0f578",
+ "metadata": {},
+ "source": [
+ "#### Notes\n",
+ "\n",
+ "Use the format shown in the notes. Here’s such a derivation for the type\n",
+ "of the expression `(1 + 2) + (3 + 4)`.\n",
+ "\n",
+ "``` scala\n",
+ "(1 + 2) + (3 + 4): Int\n",
+ "- if 1 + 2: Int\n",
+ " - if 1: Int\n",
+ " - if 2: Int\n",
+ "- if 3 + 4: Int\n",
+ " - if 3: Int\n",
+ " - if 4: Int\n",
+ "```\n",
+ "\n",
+ "### Q1.4: What is the type environment `env3`? Briefly explain."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2e94876a-32b9-477c-9aa1-91253dde0d30",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "markdown",
+ "checksum": "e5b9bc3f55c403acbbb1e709d2b68f12",
+ "grade": true,
+ "grade_id": "q1_4",
+ "locked": false,
+ "points": 2,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "source": [
+ "The type environment of `env3` alone is $[\\:\\mathtt{env3} \\mapsto\\mathtt{x: Int, a: Int, b: (Int, Int)}\\:]$. At this point, `env3` includes the variables `x`, `a`, and `b`. We know `x: Int` from the function argument, `a: Int` from the tuple deconstruction, and `b: (Int, Int)` also from the tuple deconstruction."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7faf5604-c103-44b1-a711-334dfdab5d6c",
+ "metadata": {},
+ "source": [
+ "### Q1.5: Derive the type of expression `e3`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ceae2d55-bef9-4cc5-a3dc-cfd11db90e43",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "markdown",
+ "checksum": "52869852b70e53b19066a880678a23b7",
+ "grade": true,
+ "grade_id": "q1_5",
+ "locked": false,
+ "points": 2,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "source": [
+ "```scala\n",
+ "if (x == 0) (b, 1) else (b, a + 2): ((Int, Int), Int)\n",
+ "- if x == 0: Boolean\n",
+ " - if (b, 1): Int\n",
+ " - if b: Int\n",
+ " - if 1: Int\n",
+ " - if (b, a + 2): Int\n",
+ " - if b: Int\n",
+ " - if a + 2: Int\n",
+ " - if a: Int\n",
+ " - if 2: Int\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bab903c4-188f-46ed-86dd-9495e781ff51",
+ "metadata": {},
+ "source": [
+ "### Q1.6: Confirm your derivations by adding type assertions to each sub-expression of `g` and adding the return type of `g`.\n",
+ "\n",
+ "That is, replace sub-expressions $e$ of `g` with expressions $e$ `:`\n",
+ "$\\tau$. You may need to add some parentheses—`(` $e$ `:` $\\tau$ `)`—to\n",
+ "preserve the syntactic structure. Skip adding typing assertions for\n",
+ "literals and variable uses.\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "b472b0a7",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "c4abe7222641b8ec119ec31036e39b95",
+ "grade": true,
+ "grade_id": "q1_6",
+ "locked": false,
+ "points": 9,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mg\u001b[39m"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def g(x: Int) = /*e1*/({\n",
+ " // env1\n",
+ " val (a: Int, b: (Int, Int)) = /*e2*/(\n",
+ " // env2\n",
+ " (1, (x, 3)): (Int, (Int, Int))\n",
+ " )\n",
+ " /*e3*/(\n",
+ " // env3\n",
+ " if (x == 0: Boolean) (b, 1): ((Int, Int), Int) else (b, a + 2): ((Int, Int), Int)\n",
+ " ): ((Int, Int), Int)\n",
+ "}): ((Int, Int), Int) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d5e75af2-a72c-4fed-a247-aa90d3f8f0ad",
+ "metadata": {},
+ "source": [
+ "*Hint*: There are 8 sub-expressions that are not literals nor variable\n",
+ "uses that need typing assertions (i.e., $e$ `:` $\\tau$), plus 1 more\n",
+ "annotation for the return type of `g`.\n",
+ "\n",
+ "## Unit Testing\n",
+ "\n",
+ "When starting to program in the large, it is useful to use a testing\n",
+ "framework to manage tests and integrate with IDEs. One that is commonly\n",
+ "used in Scala is [ScalaTest](https://www.scalatest.org/).\n",
+ "\n",
+ "While it is somewhat overkill for testing small exercises like the ones\n",
+ "to come, we practice here writing tests using ScalaTest.\n",
+ "\n",
+ "To load the ScalaTest library, run the following cell:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "id": "8fea5968",
+ "metadata": {
+ "deletable": false,
+ "editable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "bdf4aa1ba5caa128e0dbcd6cc1ad5766",
+ "grade": false,
+ "grade_id": "testing",
+ "locked": true,
+ "schema_version": 3,
+ "solution": false,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[32mimport \u001b[39m\u001b[36mRUN this cell FIRST before testing\n",
+ "import $ivy.$ , org.scalatest._, events._, flatspec._\n",
+ "\u001b[39m\n",
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mreport\u001b[39m\n",
+ "defined \u001b[32mfunction\u001b[39m \u001b[36massertPassed\u001b[39m\n",
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mtest\u001b[39m"
+ ]
+ },
+ "execution_count": 50,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "// RUN this cell FIRST before testing\n",
+ "import $ivy.`org.scalatest::scalatest:3.2.19`, org.scalatest._, events._, flatspec._\n",
+ "def report(suite: Suite) = suite.execute(stats = true)\n",
+ "def assertPassed(suite: Suite) =\n",
+ " suite.run(None, Args(new Reporter {\n",
+ " def apply(e: Event) = e match {\n",
+ " case e @ (_: TestFailed) => assert(false, s\"${e.message} (${e.testName})\")\n",
+ " case _ => ()\n",
+ " }\n",
+ " }))\n",
+ "def test(suite: Suite) = {\n",
+ " report(suite)\n",
+ " assertPassed(suite)\n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "67ac4efd-c505-4a4f-a6f5-91610f977849",
+ "metadata": {},
+ "source": [
+ "### Q2.1: Unit Test `plus`\n",
+ "\n",
+ "For this question, **edit the next two code cells** to fix the\n",
+ "implementation of `plus` and add the appropriate assertion for the third\n",
+ "test case `\"add (3,4) == 7\"`.\n",
+ "\n",
+ "Our goal is unit test the following complicated function (that we’ve\n",
+ "gotten wrong!):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 51,
+ "id": "6bc42853",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mplus\u001b[39m"
+ ]
+ },
+ "execution_count": 51,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def plus(n: Int, m: Int): Int = n + m"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2fd19eae-bb49-4616-94f4-e2383aad90c9",
+ "metadata": {},
+ "source": [
+ "To use ScalaTest, we create “Spec” objects using ScalaTest methods like\n",
+ "`should` that define an embedded domain-specific language (DSL) for\n",
+ "defining tests:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "id": "1255cbba",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[36mRun starting. Expected test count is: 3\u001b[0m\n",
+ "\u001b[32mcmd52$Helper$$anon$1:\u001b[0m\n",
+ "\u001b[32mplus\u001b[0m\n",
+ "\u001b[32m- should add 1 + 1 == 2\u001b[0m\n",
+ "\u001b[32m- should add 2 + 2 == 4\u001b[0m\n",
+ "\u001b[32m- should add 3 + 4 == 7\u001b[0m\n",
+ "\u001b[36mRun completed in 2 milliseconds.\u001b[0m\n",
+ "\u001b[36mTotal number of tests run: 3\u001b[0m\n",
+ "\u001b[36mSuites: completed 1, aborted 0\u001b[0m\n",
+ "\u001b[36mTests: succeeded 3, failed 0, canceled 0, ignored 0, pending 0\u001b[0m\n",
+ "\u001b[32mAll tests passed.\u001b[0m\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mplusSuite\u001b[39m: \u001b[32mAnyFlatSpec\u001b[39m = cmd52$Helper$$anon$1"
+ ]
+ },
+ "execution_count": 52,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val plusSuite = new AnyFlatSpec {\n",
+ " // Define a *subject* to test (e.g., \"plus\").\n",
+ " // After `should`, name a test (e.g, \"add (1, 1) == 2\").\n",
+ " // After `in`, specify assertions (e.g., `assert(plus(1,1) == 2))\n",
+ " \"plus\" should \"add 1 + 1 == 2\" in {\n",
+ " // Specify assertions here.\n",
+ " assert(plus(1,1) == 2)\n",
+ " }\n",
+ "\n",
+ " it should \"add 2 + 2 == 4\" in {\n",
+ " // It is convenient to distinguish the expected result from the code that\n",
+ " // you're testing, which affects the error messages when the test fails.\n",
+ " assertResult(2 + 2) {\n",
+ " plus(2,2)\n",
+ " }\n",
+ " }\n",
+ " it should \"add 3 + 4 == 7\" in {\n",
+ " assertResult(3 + 4) {\n",
+ " plus(3, 4)\n",
+ " }\n",
+ " }\n",
+ "}\n",
+ "report(plusSuite)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 53,
+ "id": "27368277",
+ "metadata": {
+ "deletable": false,
+ "editable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "8ac2636aa17b31fca777bf3064b8d491",
+ "grade": true,
+ "grade_id": "q2_1",
+ "locked": true,
+ "points": 3,
+ "schema_version": 3,
+ "solution": false,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mres53\u001b[39m: \u001b[32mStatus\u001b[39m = org.scalatest.CompositeStatus@48f724de"
+ ]
+ },
+ "execution_count": 53,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "assertPassed(plusSuite)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "be1d876b-25dc-451a-86db-ed1cf1fed54e",
+ "metadata": {},
+ "source": [
+ "## Run-Time Library\n",
+ "\n",
+ "Most languages come with a standard library with support for things like\n",
+ "data structures, mathematical operators, string processing, etc.\n",
+ "Standard library functions may be implemented in the object language\n",
+ "(perhaps for portability) or the meta language (perhaps for\n",
+ "implementation efficiency).\n",
+ "\n",
+ "For this question, we will implement some library functions in Scala,\n",
+ "our meta language, that we can imagine will be part of the run-time for\n",
+ "our object language interpreter. In actuality, the main purpose of this\n",
+ "exercise is to warm-up with Scala programming.\n",
+ "\n",
+ "### Q3.1: Write and test a function `abs`\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "id": "3f001698",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "d1bacc19634bfb1bf864bd58b41906c4",
+ "grade": false,
+ "grade_id": "q3_1_code",
+ "locked": false,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mabs\u001b[39m"
+ ]
+ },
+ "execution_count": 54,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def abs(n: Double): Double = ({\n",
+ " if (n < 0) {\n",
+ " -n\n",
+ " } else {\n",
+ " n\n",
+ " }\n",
+ "})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "71c5328d-b26d-497d-adaf-6ef22d22688f",
+ "metadata": {},
+ "source": [
+ "that returns the absolute value of `n`. This a function that takes a\n",
+ "value of type `Double` and returns a value of type `Double`. This\n",
+ "function corresponds to the JavaScript library function `Math.abs`.\n",
+ "\n",
+ "#### Notes\n",
+ "\n",
+ "- Do not use any Scala library functions.\n",
+ "\n",
+ "#### Tests\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "id": "d913e614",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[36mRun starting. Expected test count is: 4\u001b[0m\n",
+ "\u001b[32mcmd55$Helper$$anon$1:\u001b[0m\n",
+ "\u001b[32mabs\u001b[0m\n",
+ "\u001b[32m- should abs(2) == 2\u001b[0m\n",
+ "\u001b[32m- should abs(-2) == 2\u001b[0m\n",
+ "\u001b[32m- should abs(0) == 0\u001b[0m\n",
+ "\u001b[32m- should abs(1) == 1\u001b[0m\n",
+ "\u001b[36mRun completed in 3 milliseconds.\u001b[0m\n",
+ "\u001b[36mTotal number of tests run: 4\u001b[0m\n",
+ "\u001b[36mSuites: completed 1, aborted 0\u001b[0m\n",
+ "\u001b[36mTests: succeeded 4, failed 0, canceled 0, ignored 0, pending 0\u001b[0m\n",
+ "\u001b[32mAll tests passed.\u001b[0m\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mabsSuite\u001b[39m: \u001b[32mAnyFlatSpec\u001b[39m = cmd55$Helper$$anon$1"
+ ]
+ },
+ "execution_count": 55,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val absSuite = new AnyFlatSpec {\n",
+ " \"abs\" should \"abs(2) == 2\" in {\n",
+ " assert(abs(2) == 2)\n",
+ " }\n",
+ " it should \"abs(-2) == 2\" in {\n",
+ " assert(abs(-2) == 2)\n",
+ " }\n",
+ " it should \"abs(0) == 0\" in {\n",
+ " assert(abs(0) === 0)\n",
+ " }\n",
+ " it should \"abs(1) == 1\" in {\n",
+ " assert(abs(1) === 1)\n",
+ " }\n",
+ "}\n",
+ "report(absSuite)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "id": "1956942b",
+ "metadata": {
+ "deletable": false,
+ "editable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "8ae14654f39c831149cca3cd7bc9901f",
+ "grade": true,
+ "grade_id": "q3_1",
+ "locked": true,
+ "points": 4,
+ "schema_version": 3,
+ "solution": false,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mres56\u001b[39m: \u001b[32mStatus\u001b[39m = org.scalatest.CompositeStatus@4fd24e85"
+ ]
+ },
+ "execution_count": 56,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "assertPassed(absSuite)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "21898c2c-2b50-42c1-85f9-df4be93e8284",
+ "metadata": {},
+ "source": [
+ "### Q3.2: Write and test a function `xor`\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 57,
+ "id": "3c119212",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "ac179e4aa90d501026fc34ffbf524ab7",
+ "grade": false,
+ "grade_id": "q3_2_code",
+ "locked": false,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mxor\u001b[39m"
+ ]
+ },
+ "execution_count": 57,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def xor(a: Boolean, b: Boolean): Boolean = a ^ b"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5b47755a-a0e7-44ee-acc5-10a06d925697",
+ "metadata": {},
+ "source": [
+ "that returns the exclusive-or of `a` and `b`. The exclusive-or returns\n",
+ "`true` if and only if exactly one of `a` or `b` is `true`.\n",
+ "\n",
+ "#### Notes\n",
+ "\n",
+ "- For practice, do not use the Boolean operators. Instead, only use\n",
+ " the `if`- expression and the Boolean literals (i.e., `true` or\n",
+ " `false`).\n",
+ "\n",
+ "#### Tests\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 58,
+ "id": "f723c395",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[36mRun starting. Expected test count is: 4\u001b[0m\n",
+ "\u001b[32mcmd58$Helper$$anon$1:\u001b[0m\n",
+ "\u001b[32mxor\u001b[0m\n",
+ "\u001b[32m- should !xor(true, true)\u001b[0m\n",
+ "\u001b[32m- should xor(true, false)\u001b[0m\n",
+ "\u001b[32m- should xor(false, true)\u001b[0m\n",
+ "\u001b[32m- should !xor(false, false)\u001b[0m\n",
+ "\u001b[36mRun completed in 11 milliseconds.\u001b[0m\n",
+ "\u001b[36mTotal number of tests run: 4\u001b[0m\n",
+ "\u001b[36mSuites: completed 1, aborted 0\u001b[0m\n",
+ "\u001b[36mTests: succeeded 4, failed 0, canceled 0, ignored 0, pending 0\u001b[0m\n",
+ "\u001b[32mAll tests passed.\u001b[0m\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mxorSuite\u001b[39m: \u001b[32mAnyFlatSpec\u001b[39m = cmd58$Helper$$anon$1"
+ ]
+ },
+ "execution_count": 58,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val xorSuite = new AnyFlatSpec {\n",
+ " \"xor\" should \"!xor(true, true)\" in {\n",
+ " assert(!xor(true, true))\n",
+ " }\n",
+ " it should \"xor(true, false)\" in {\n",
+ " assert(xor(true, false))\n",
+ " }\n",
+ " it should \"xor(false, true)\" in {\n",
+ " assert(xor(false, true))\n",
+ " }\n",
+ " it should \"!xor(false, false)\" in {\n",
+ " assert(!xor(false, false))\n",
+ " }\n",
+ "}\n",
+ "report(xorSuite)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "id": "5fc09530",
+ "metadata": {
+ "deletable": false,
+ "editable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "475a7a4bd08579befea92b998fc9a712",
+ "grade": true,
+ "grade_id": "q3_2",
+ "locked": true,
+ "points": 4,
+ "schema_version": 3,
+ "solution": false,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mres59\u001b[39m: \u001b[32mStatus\u001b[39m = org.scalatest.CompositeStatus@2780f927"
+ ]
+ },
+ "execution_count": 59,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "assertPassed(xorSuite)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4b0a894d-67f5-480a-bbcb-2abe33b45784",
+ "metadata": {},
+ "source": [
+ "## Imperative Iteration and Complexity\n",
+ "\n",
+ "### Q4.1: Write a function `filterPairsByBound`\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 60,
+ "id": "a9436132",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "ed640d35faac5ce44926effc28995737",
+ "grade": false,
+ "grade_id": "q4_1_code",
+ "locked": false,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mfilterPairsByBound\u001b[39m"
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def filterPairsByBound(list: List[(Int, Int)], k: Int): List[(Int, Int)] =\n",
+ " list.filter { // iterate through the tuples in list\n",
+ " case (n1, n2) => // for each pair (n1, n2)...\n",
+ " // return appropriate value when leq k \n",
+ " // using our abs() function from Q3.1\n",
+ " abs(n1 - n2) <= k\n",
+ " }"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d95cdad4-4de8-440e-8a25-b1f9d901091a",
+ "metadata": {},
+ "source": [
+ "that given a list of pairs of integers, for example,"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 61,
+ "id": "15116cf9",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36minput1_l\u001b[39m: \u001b[32mList\u001b[39m[(\u001b[32mInt\u001b[39m, \u001b[32mInt\u001b[39m)] = \u001b[33mList\u001b[39m(\n",
+ " (\u001b[32m1\u001b[39m, \u001b[32m5\u001b[39m),\n",
+ " (\u001b[32m2\u001b[39m, \u001b[32m7\u001b[39m),\n",
+ " (\u001b[32m15\u001b[39m, \u001b[32m14\u001b[39m),\n",
+ " (\u001b[32m18\u001b[39m, \u001b[32m19\u001b[39m),\n",
+ " (\u001b[32m14\u001b[39m, \u001b[32m28\u001b[39m),\n",
+ " (\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m),\n",
+ " (\u001b[32m35\u001b[39m, \u001b[32m24\u001b[39m)\n",
+ ")"
+ ]
+ },
+ "execution_count": 61,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val input1_l = List( (1, 5), (2, 7), (15, 14), (18, 19), (14, 28), (0,0), (35, 24) )"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "46a2bbe6-ac0c-4fd1-a4e2-15f66b895bf8",
+ "metadata": {},
+ "source": [
+ "output a list consisting of just those pairs $(n_1, n_2)$ in the\n",
+ "original list wherein $|n_1 - n_2| \\leq k$ where $k$ is an integer given\n",
+ "as input. Ensure that the order of the elements in the output list is\n",
+ "the same as that in the input list.\n",
+ "\n",
+ "For the list `input1`, the expected output, with `k == 1`, the expected\n",
+ "output is as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 62,
+ "id": "c378241a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36minput1_k\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m1\u001b[39m\n",
+ "\u001b[36moutput1\u001b[39m: \u001b[32mList\u001b[39m[(\u001b[32mInt\u001b[39m, \u001b[32mInt\u001b[39m)] = \u001b[33mList\u001b[39m((\u001b[32m15\u001b[39m, \u001b[32m14\u001b[39m), (\u001b[32m18\u001b[39m, \u001b[32m19\u001b[39m), (\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m))"
+ ]
+ },
+ "execution_count": 62,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val input1_k = 1\n",
+ "val output1 = List( (15,14), (18,19), (0,0) )\n",
+ "assert(filterPairsByBound(input1_l, input1_k) == output1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b55b49e4-2a4b-4dc6-80de-c600151fcf5a",
+ "metadata": {},
+ "source": [
+ "With `k == 4`, the expected output is as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 63,
+ "id": "d05fe5b9",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36minput2_k\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m4\u001b[39m\n",
+ "\u001b[36moutput2\u001b[39m: \u001b[32mList\u001b[39m[(\u001b[32mInt\u001b[39m, \u001b[32mInt\u001b[39m)] = \u001b[33mList\u001b[39m((\u001b[32m1\u001b[39m, \u001b[32m5\u001b[39m), (\u001b[32m15\u001b[39m, \u001b[32m14\u001b[39m), (\u001b[32m18\u001b[39m, \u001b[32m19\u001b[39m), (\u001b[32m0\u001b[39m, \u001b[32m0\u001b[39m))"
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val input2_k = 4\n",
+ "val output2 = List( (1, 5), (15, 14), (18, 19), (0,0) )\n",
+ "assert(filterPairsByBound(input1_l, input2_k) == output2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "984c452b-5302-48a6-8fe1-e1a1ff22cbaa",
+ "metadata": {},
+ "source": [
+ "#### Notes\n",
+ "\n",
+ "- Your function must be called `filterPairsByBound` with two\n",
+ " arguments: (1) a list of pairs of integers, and (2) the $k$ value.\n",
+ " It must return a list of pairs of integers.\n",
+ "- You can use `for`-loops (or `foreach`) and the following operators\n",
+ " for concatenating elements to a list:\n",
+ " - `:+` appends an element to the back of a list.\n",
+ " - `:::` concatenates two lists together.\n",
+ " - `::` prepends an element to the front of a list.\n",
+ "- You can use the `List` API method `reverse`. You may also use the\n",
+ " `Int` `abs` method to obtain the absolute value of an integer (or\n",
+ " use your `abs` function above).\n",
+ "- You should not use any other `List` API functions including\n",
+ " `filter`, `map`, `foldLeft`, `foldRight`, etc. Plenty of time to\n",
+ " learn them properly later on.\n",
+ "- Do not try to convert your list to an array or vector so that you\n",
+ " can mutate it.\n",
+ "- If you are unable to solve the problem without violating the\n",
+ " restrictions or unsure, ask us.\n",
+ "- You will need to use `var` given the above restrictions.\n",
+ "\n",
+ "#### Hints\n",
+ "\n",
+ "- In Scala, pairs of integers have the type `(Int, Int)`.\n",
+ "- A list containing pairs of integers has the type `List[(Int, Int)]`.\n",
+ "- Recall from the notes, here is how one iterates over the elements of\n",
+ " a list in Scala:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 64,
+ "id": "757f5f83",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1\n",
+ "2\n",
+ "3\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mlist\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m)"
+ ]
+ },
+ "execution_count": 64,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val list = List(1, 2, 3)\n",
+ "\n",
+ "for (elt <- list) {\n",
+ " // do stuff with elt\n",
+ " println(elt)\n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e8155fd8-8f76-4131-86e7-3d9bc3f583b4",
+ "metadata": {},
+ "source": [
+ "- Append an element to the end of a list and update a `var`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 65,
+ "id": "d20926f0",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div class=\"jp-RenderedText\">\n",
+ "<pre><code><span style=\"color: rgb(0, 187, 187)\"><span class=\"ansi-cyan-fg\">resultList</span></span>: <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">List</span></span>[<span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">Int</span></span>] = <span style=\"color: yellow\"><span class=\"ansi-yellow-fg\">List</span></span>(<span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">1</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">2</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">3</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">42</span></span>)\n",
+ "<span style=\"color: rgb(0, 187, 187)\"><span class=\"ansi-cyan-fg\">elt</span></span>: <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">Int</span></span> = <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">42</span></span></code></pre>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ "\u001b[36mresultList\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m42\u001b[39m)\n",
+ "\u001b[36melt\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m42\u001b[39m"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "var resultList = List(1, 2, 3)\n",
+ "val elt = 42\n",
+ "\n",
+ "resultList = resultList :+ elt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5143c58d-3849-4d7c-ad58-7021e92a1a92",
+ "metadata": {},
+ "source": [
+ "- Or, append an element to the end of a list using list concatenation\n",
+ " and update a `var`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 66,
+ "id": "6b76748c",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div class=\"jp-RenderedText\">\n",
+ "<pre><code><span style=\"color: rgb(0, 187, 187)\"><span class=\"ansi-cyan-fg\">resultList</span></span>: <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">List</span></span>[<span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">Int</span></span>] = <span style=\"color: yellow\"><span class=\"ansi-yellow-fg\">List</span></span>(<span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">1</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">2</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">3</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">42</span></span>)\n",
+ "<span style=\"color: rgb(0, 187, 187)\"><span class=\"ansi-cyan-fg\">elt</span></span>: <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">Int</span></span> = <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">42</span></span></code></pre>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ "\u001b[36mresultList\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m, \u001b[32m42\u001b[39m)\n",
+ "\u001b[36melt\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m42\u001b[39m"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "var resultList = List(1, 2, 3)\n",
+ "val elt = 42\n",
+ "\n",
+ "resultList = resultList ::: List(elt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0cf8d689-25e9-4899-b369-228fb4a60c06",
+ "metadata": {},
+ "source": [
+ "- Prepend an element and update a `var`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 67,
+ "id": "a223964a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div class=\"jp-RenderedText\">\n",
+ "<pre><code><span style=\"color: rgb(0, 187, 187)\"><span class=\"ansi-cyan-fg\">resultList</span></span>: <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">List</span></span>[<span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">Int</span></span>] = <span style=\"color: yellow\"><span class=\"ansi-yellow-fg\">List</span></span>(<span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">42</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">1</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">2</span></span>, <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">3</span></span>)\n",
+ "<span style=\"color: rgb(0, 187, 187)\"><span class=\"ansi-cyan-fg\">elt</span></span>: <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">Int</span></span> = <span style=\"color: rgb(0, 187, 0)\"><span class=\"ansi-green-fg\">42</span></span></code></pre>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ "\u001b[36mresultList\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m42\u001b[39m, \u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m3\u001b[39m)\n",
+ "\u001b[36melt\u001b[39m: \u001b[32mInt\u001b[39m = \u001b[32m42\u001b[39m"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "var resultList = List(1, 2, 3)\n",
+ "val elt = 42\n",
+ "\n",
+ "resultList = elt :: resultList"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7cadcb01-c735-4b13-8c34-ed06fefe0e39",
+ "metadata": {},
+ "source": [
+ "- *Warning*: The `:+`, `:::`, or other operations appending operations\n",
+ " take linear $O(n)$ time where $n$ is the length of the (left) list.\n",
+ " Thus, we will often try to avoid using these operations, but it is\n",
+ " ok to use it for this particular part.\n",
+ "\n",
+ "#### Tests"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "id": "40a6d538",
+ "metadata": {
+ "deletable": false,
+ "editable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "c9601d100de72d011a23f82aa2e58a37",
+ "grade": true,
+ "grade_id": "q4_1",
+ "locked": true,
+ "points": 5,
+ "schema_version": 3,
+ "solution": false,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[36mRun starting. Expected test count is: 6\u001b[0m\n",
+ "\u001b[32mcmd68$Helper$$anon$1:\u001b[0m\n",
+ "\u001b[32mfilterPairsByBound\u001b[0m\n",
+ "\u001b[32m- should test1\u001b[0m\n",
+ "\u001b[32m- should test2\u001b[0m\n",
+ "\u001b[32m- should test3\u001b[0m\n",
+ "\u001b[32m- should test4\u001b[0m\n",
+ "\u001b[32m- should test5\u001b[0m\n",
+ "\u001b[32m- should test6\u001b[0m\n",
+ "\u001b[36mRun completed in 9 milliseconds.\u001b[0m\n",
+ "\u001b[36mTotal number of tests run: 6\u001b[0m\n",
+ "\u001b[36mSuites: completed 1, aborted 0\u001b[0m\n",
+ "\u001b[36mTests: succeeded 6, failed 0, canceled 0, ignored 0, pending 0\u001b[0m\n",
+ "\u001b[32mAll tests passed.\u001b[0m\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mres68\u001b[39m: \u001b[32mStatus\u001b[39m = org.scalatest.CompositeStatus@d75bc07"
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "test(new AnyFlatSpec {\n",
+ " \"filterPairsByBound\" should \"test1\" in {\n",
+ " val lst1 = List((1,1), (-1,1), (1,-1))\n",
+ " assertResult( List((1,1)) ){ filterPairsByBound(lst1,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test2\" in {\n",
+ " val lst2 = List((1,2), (2,1), (1,0), (0,1), (1,1))\n",
+ " assertResult( lst2 ){ filterPairsByBound(lst2,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test3\" in {\n",
+ " val lst3 = List((1,5), (5,1))\n",
+ " assertResult( Nil ){ filterPairsByBound(lst3,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test4\" in {\n",
+ " val lst4 = List((2,5), (1,2), (-5,-4), (4,1))\n",
+ " assertResult( List((1,2), (-5,-4)) ){ filterPairsByBound(lst4,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test5\" in {\n",
+ " val lst5 = List( (1, 5), (2, 7), (15, 14), (18, 19), (14, 28), (0,0), (35, 24) )\n",
+ " assertResult( List((1, 5), (15, 14), (18, 19), (0,0)) ){ filterPairsByBound(lst5,4) }\n",
+ " }\n",
+ "\n",
+ " it should \"test6\" in {\n",
+ " val lst6 = List((1, 2), (2, 1), (1,0), (0,1), (1,1))\n",
+ " assertResult( List((1,1)) ){ filterPairsByBound(lst6,0) }\n",
+ " }\n",
+ "})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5712b57c-1bd3-41a8-9c55-722b85829805",
+ "metadata": {},
+ "source": [
+ "### Q4.2: Write a function `filterPairsByBoundLinearTime`\n",
+ "\n",
+ "**Edit this cell:**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 69,
+ "id": "fadb020d",
+ "metadata": {
+ "deletable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "8725d2da34598302b7ff7ab5876da03b",
+ "grade": false,
+ "grade_id": "q4_2_code",
+ "locked": false,
+ "schema_version": 3,
+ "solution": true,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "defined \u001b[32mfunction\u001b[39m \u001b[36mfilterPairsByBoundLinearTime\u001b[39m"
+ ]
+ },
+ "execution_count": 69,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def filterPairsByBoundLinearTime(list: List[(Int, Int)], k: Int): List[(Int, Int)] = {\n",
+ " // helper function to recursively process appropriate elements in list\n",
+ " def filterHelper(remaining: List[(Int, Int)], result: List[(Int, Int)]): List[(Int, Int)] = remaining match {\n",
+ " case Nil => // Nil represents empty set - do nothing\n",
+ " result\n",
+ " // iterate through list beginning at start (or rather current) element\n",
+ " case (n1, n2) :: tail =>\n",
+ " if (abs(n1 - n2) <= k)\n",
+ " // if necessary condition is met, prepend to result\n",
+ " filterHelper(tail, (n1, n2) :: result)\n",
+ " else\n",
+ " // otherwise continue to next element\n",
+ " filterHelper(tail, result)\n",
+ " }\n",
+ " filterHelper(list, Nil).reverse\n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0fa83488-63be-43d5-9905-3f2b4706318d",
+ "metadata": {},
+ "source": [
+ "If you followed the hint and ignored the linear-time warning in the\n",
+ "previous part\n",
+ "<a href=\"#sec-filterPairsByBound\" class=\"quarto-xref\">Section 4.1</a>,\n",
+ "then you would have used the `:+` or `:::` operation to append an\n",
+ "element to the end of a list at each step.\n",
+ "\n",
+ "``` scala\n",
+ "for (... <- list) {\n",
+ " // iterate over a loop\n",
+ " ...\n",
+ " newList = newList :+ newElement // This takes O(length of newList).\n",
+ "}\n",
+ "```\n",
+ "\n",
+ "Each `:+` or `:::` operation requires a full list traversal to find the\n",
+ "end of `newList` and then append to it. The overall algorithm thus\n",
+ "requires $O(n^2)$ time where is the length of the original `list` (also\n",
+ "the number of loop iterations).\n",
+ "\n",
+ "To illustrate, cut-and-paste and then run this code in a new test cell.\n",
+ "Just remember to delete that cell before you submit. It will take a long\n",
+ "time to run.\n",
+ "\n",
+ "``` scala\n",
+ "// Create a list of 1,000,000 pairs\n",
+ "val longTestList = (1 to 1000000).map(x => (x, x - 1)).toList\n",
+ "// Run the function you wrote\n",
+ "filterPairsByBound(longTestList, 1)\n",
+ "// This will take a long time to finish.\n",
+ "```\n",
+ "\n",
+ "In this problem, we wish to implement a function\n",
+ "`filterPairsByBoundLinearTime` that solves the exact same problem as the\n",
+ "previous part\n",
+ "<a href=\"#sec-filterPairsByBound\" class=\"quarto-xref\">Section 4.1</a>\n",
+ "but takes time linear in the size of the input list.\n",
+ "\n",
+ "To do so, we would like you to use the `::` (read “cons”) operator on a\n",
+ "list that prepends an element to the front of a list, instead of `:+` or\n",
+ "`:::` that appends to the back of a list.\n",
+ "\n",
+ "You will want to use the `List` `reverse` API method:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 70,
+ "id": "e3731008",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mlist\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m7\u001b[39m, \u001b[32m8\u001b[39m)\n",
+ "\u001b[36mr\u001b[39m: \u001b[32mList\u001b[39m[\u001b[32mInt\u001b[39m] = \u001b[33mList\u001b[39m(\u001b[32m8\u001b[39m, \u001b[32m7\u001b[39m, \u001b[32m6\u001b[39m, \u001b[32m5\u001b[39m, \u001b[32m2\u001b[39m, \u001b[32m1\u001b[39m)"
+ ]
+ },
+ "execution_count": 70,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "val list = List(1, 2, 5, 6, 7, 8)\n",
+ "val r = list.reverse"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6f9f4725-99b1-41e4-88a5-174ad8818a50",
+ "metadata": {},
+ "source": [
+ "The `r` has the reverse of `list`, and it works in linear time in the\n",
+ "length of `list`.\n",
+ "\n",
+ "The restrictions remain the same as the previous part\n",
+ "<a href=\"#sec-filterPairsByBound\" class=\"quarto-xref\">Section 4.1</a>,\n",
+ "but we would like you to focus on ensuring that your solution runs in\n",
+ "linear time.\n",
+ "\n",
+ "#### Tests"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 71,
+ "id": "90d2d800",
+ "metadata": {
+ "deletable": false,
+ "editable": false,
+ "nbgrader": {
+ "cell_type": "code",
+ "checksum": "c1afc073bb37fd79685ece1caf82e854",
+ "grade": true,
+ "grade_id": "q4_2",
+ "locked": true,
+ "points": 7,
+ "schema_version": 3,
+ "solution": false,
+ "task": false
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\u001b[36mRun starting. Expected test count is: 6\u001b[0m\n",
+ "\u001b[32mcmd71$Helper$$anon$1:\u001b[0m\n",
+ "\u001b[32mfilterPairsByBoundLinearTime\u001b[0m\n",
+ "\u001b[32m- should test1\u001b[0m\n",
+ "\u001b[32m- should test2\u001b[0m\n",
+ "\u001b[32m- should test3\u001b[0m\n",
+ "\u001b[32m- should test4\u001b[0m\n",
+ "\u001b[32m- should test5\u001b[0m\n",
+ "\u001b[32m- should test6\u001b[0m\n",
+ "\u001b[36mRun completed in 4 milliseconds.\u001b[0m\n",
+ "\u001b[36mTotal number of tests run: 6\u001b[0m\n",
+ "\u001b[36mSuites: completed 1, aborted 0\u001b[0m\n",
+ "\u001b[36mTests: succeeded 6, failed 0, canceled 0, ignored 0, pending 0\u001b[0m\n",
+ "\u001b[32mAll tests passed.\u001b[0m\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\u001b[36mres71\u001b[39m: \u001b[32mStatus\u001b[39m = org.scalatest.CompositeStatus@41a47f32"
+ ]
+ },
+ "execution_count": 71,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "test(new AnyFlatSpec {\n",
+ " \"filterPairsByBoundLinearTime\" should \"test1\" in {\n",
+ " val lst1 = List((1,1), (-1,1), (1,-1))\n",
+ " assertResult( List((1,1)) ){ filterPairsByBoundLinearTime(lst1,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test2\" in {\n",
+ " val lst2 = List((1,2), (2,1), (1,0), (0,1), (1,1))\n",
+ " assertResult( lst2 ){ filterPairsByBoundLinearTime(lst2,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test3\" in {\n",
+ " val lst3 = List((1,5), (5,1))\n",
+ " assertResult( Nil ){ filterPairsByBoundLinearTime(lst3,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test4\" in {\n",
+ " val lst4 = List((2,5), (1,2), (-5,-4), (4,1))\n",
+ " assertResult( List((1,2), (-5,-4)) ){ filterPairsByBoundLinearTime(lst4,1) }\n",
+ " }\n",
+ "\n",
+ " it should \"test5\" in {\n",
+ " val lst5 = List( (1, 5), (2, 7), (15, 14), (18, 19), (14, 28), (0,0), (35, 24) )\n",
+ " assertResult( List((1, 5), (15, 14), (18, 19), (0,0)) ){ filterPairsByBoundLinearTime(lst5,4) }\n",
+ " }\n",
+ "\n",
+ " it should \"test6\" in {\n",
+ " val lst6 = List((1, 2), (2, 1), (1,0), (0,1), (1,1))\n",
+ " assertResult( List((1,1)) ){ filterPairsByBoundLinearTime(lst6,0) }\n",
+ " }\n",
+ "})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9c75c291-9711-4901-92f6-ef093fb92a6a",
+ "metadata": {},
+ "source": [
+ "## Submission\n",
+ "\n",
+ "#### Submission Instructions\n",
+ "\n",
+ "If you are a University of Colorado Boulder student, we use Gradescope\n",
+ "for assignment submission. In summary,\n",
+ "\n",
+ "- [ ] Work on a copy of this Jupyter notebook.\n",
+ "- [ ] Submit it to the corresponding Gradescope assignment entry for\n",
+ " grading.\n",
+ "\n",
+ "#### GitHub and Gradescope\n",
+ "\n",
+ "We use GitHub Classroom for assignment distribution, which gives you a\n",
+ "private GitHub repository to work on your assignment. While using GitHub\n",
+ "is perhaps overkill for this assignment, it does give you the ability to\n",
+ "version and save incremental progress on GitHub (lest your laptop fails)\n",
+ "and makes it easier to get help from the course staff. It will also\n",
+ "become particularly useful when more files are involved, and it is never\n",
+ "too early to get used to the workflow professional software engineers\n",
+ "use with Git.\n",
+ "\n",
+ "To use use GitHub and Gradescope,\n",
+ "\n",
+ "- [ ] Create a private GitHub repository by clicking on a GitHub\n",
+ " Classroom link from the corresponding Canvas assignment entry.\n",
+ "- [ ] Clone your private GitHub repository to your development\n",
+ " environment (using the `<> Code` button on GitHub to get the\n",
+ " repository URL).\n",
+ "- [ ] Work on the copy of this Jupyter notebook from your cloned\n",
+ " repository. Use Git to save versions on GitHub (e.g., `git add`,\n",
+ " `git commit`, `git push` on the command line, via JupyterLab, or via\n",
+ " VSCode).\n",
+ "- [ ] Submit to the corresponding Gradescope assignment entry for\n",
+ " grading by choosing GitHub as the submission method.\n",
+ "\n",
+ "You need to have a GitHub identity and must have your full name in your\n",
+ "GitHub profile in case we need to associate you with your submissions."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Scala",
+ "language": "scala",
+ "name": "scala"
+ },
+ "language_info": {
+ "codemirror_mode": "text/x-scala",
+ "file_extension": ".sc",
+ "mimetype": "text/x-scala",
+ "name": "scala",
+ "nbconvert_exporter": "script",
+ "version": "2.13.14"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}