add 2022 winter final question 1 generator (#32)

* add 2022 winter final question 1 generator

* linting

src/content/questions/comp2804/2022-winter-final/1/generator.test.ts

@@ -0,0 +1,106 @@
+import { describe, expect } from "@jest/globals";
+import Generator from "./generator";
+
+describe("comp2804/2022-winter-final/1", () => {
+  describe("generateValues", () => {
+    it("will return two values", () => {
+      const generator = new Generator();
+
+      const values = generator.generateValues();
+
+      expect(values).toHaveLength(2);
+    });
+
+    it("will return a string length between 50 and 100", () => {
+      const generator = new Generator();
+
+      const [stringLength, _] = generator.generateValues();
+
+      expect(stringLength).toBeGreaterThanOrEqual(50);
+      expect(stringLength).toBeLessThanOrEqual(100);
+    });
+
+    it("will return a positions value between 5 and 20", () => {
+      const generator = new Generator();
+
+      const [_, positions] = generator.generateValues();
+
+      expect(positions).toBeGreaterThanOrEqual(5);
+      expect(positions).toBeLessThanOrEqual(20);
+    });
+  });
+
+  describe("createOptions", () => {
+    it("will return five options", () => {
+      const generator = new Generator();
+
+      const options = generator.createOptions(50, 5);
+
+      expect(options).toHaveLength(5);
+    });
+
+    it("will have exactly one correct option", () => {
+      const generator = new Generator();
+
+      const options = generator.createOptions(50, 5);
+      const correctOptions = options.filter((option) => option.correct);
+
+      expect(correctOptions).toHaveLength(1);
+    });
+  });
+
+  describe("createCorrectOption", () => {
+    it("will return the correct option", () => {
+      const generator = new Generator();
+
+      const option = generator.createCorrectOption(50, 10);
+
+      expect(option.label).toBe("$\\binom{50}{10}\\cdot 4^{40}$");
+      expect(option.correct).toBe(true);
+    });
+  });
+
+  describe("createIncorrectOption1", () => {
+    it("will return an option with the combination being multiplied with 5 ^ value instead of 4 ^ value", () => {
+      const generator = new Generator();
+
+      const option = generator.createIncorrectOption1(50, 10);
+
+      expect(option.label).toBe("$\\binom{50}{10}\\cdot 5^{40}$");
+      expect(option.correct).toBe(false);
+    });
+  });
+
+  describe("createIncorrectOption2", () => {
+    it("will return an option with the combination using the number of letters instead of positions and being multiplied with 5 ^ value instead of 4 ^ value", () => {
+      const generator = new Generator();
+
+      const option = generator.createIncorrectOption2(50, 10);
+
+      expect(option.label).toBe("$\\binom{50}{5}\\cdot 5^{40}$");
+      expect(option.correct).toBe(false);
+    });
+  });
+
+  describe("createIncorrectOption3", () => {
+    it("will return an option with the combination using the number of letters instead of positions", () => {
+      const generator = new Generator();
+
+      const option = generator.createIncorrectOption3(50, 10);
+
+      expect(option.label).toBe("$\\binom{50}{5}\\cdot 4^{40}$");
+      expect(option.correct).toBe(false);
+    });
+  });
+
+  describe("createIncorrectOption4", () => {
+    it("will return an option which does not use combinations", () => {
+      const generator = new Generator();
+
+      const option = generator.createIncorrectOption4(50, 10);
+
+      expect(option.label).toBe("$5^{10}\\cdot 4^{40}$");
+      expect(option.correct).toBe(false);
+    });
+  });
+});

src/content/questions/comp2804/2022-winter-final/1/generator.ts

@@ -0,0 +1,106 @@
+import { MultipleChoiceQuestionGenerator } from "@common/MultipleChoiceQuestionGenerator";
+import type {
+  MultipleChoiceQuestion,
+  MultipleChoiceQuestionOption,
+} from "@common/MultipleChoiceQuestionGenerator";
+
+class Generator extends MultipleChoiceQuestionGenerator {
+  generateQuestion(): MultipleChoiceQuestion {
+    const [stringLength, positions] = this.generateValues();
+    const dynamicQuestionBody = `Consider strings of length $${stringLength}$, in which each character is one of the characters $a,b,c,d,e$.  How many such strings have exactly $${positions}$ letters $e$?`;
+    return {
+      body: dynamicQuestionBody,
+      options: this.createOptions(stringLength, positions),
+    };
+  }
+
+  generateValues(): [number, number] {
+    const stringLength = Math.floor(Math.random() * 51) + 50; //generate a value between 50 and 100
+    const positions = Math.floor(Math.random() * 16) + 5; //generate a value between 5 and 20
+
+    return [stringLength, positions];
+  }
+
+  createOptions(
+    stringLength: number,
+    positions: number,
+  ): MultipleChoiceQuestionOption[] {
+    const correctOption = this.createCorrectOption(stringLength, positions);
+    const incorrectOption1 = this.createIncorrectOption1(
+      stringLength,
+      positions,
+    );
+    const incorrectOption2 = this.createIncorrectOption2(
+      stringLength,
+      positions,
+    );
+    const incorrectOption3 = this.createIncorrectOption3(
+      stringLength,
+      positions,
+    );
+    const incorrectOption4 = this.createIncorrectOption4(
+      stringLength,
+      positions,
+    );
+
+    return this.shuffleOptions([
+      correctOption,
+      incorrectOption1,
+      incorrectOption2,
+      incorrectOption3,
+      incorrectOption4,
+    ]);
+  }
+
+  createCorrectOption(
+    stringLength: number,
+    positions: number,
+  ): MultipleChoiceQuestionOption {
+    return {
+      label: `$\\binom{${stringLength}}{${positions}}\\cdot 4^{${stringLength - positions}}$`,
+      correct: true,
+    };
+  }
+
+  createIncorrectOption1(
+    stringLength: number,
+    positions: number,
+  ): MultipleChoiceQuestionOption {
+    return {
+      label: `$\\binom{${stringLength}}{${positions}}\\cdot 5^{${stringLength - positions}}$`,
+      correct: false,
+    };
+  } //mutliples with 5 ^ value instead of 4
+
+  createIncorrectOption2(
+    stringLength: number,
+    positions: number,
+  ): MultipleChoiceQuestionOption {
+    return {
+      label: `$\\binom{${stringLength}}{5}\\cdot 5^{${stringLength - positions}}$`,
+      correct: false,
+    };
+  } //uses number of letters instead of positions and multiples with 5 ^ value instead of 4
+
+  createIncorrectOption3(
+    stringLength: number,
+    positions: number,
+  ): MultipleChoiceQuestionOption {
+    return {
+      label: `$\\binom{${stringLength}}{5}\\cdot 4^{${stringLength - positions}}$`,
+      correct: false,
+    };
+  } //uses number of letters instead of positions
+
+  createIncorrectOption4(
+    stringLength: number,
+    positions: number,
+  ): MultipleChoiceQuestionOption {
+    return {
+      label: `$5^{${positions}}\\cdot 4^{${stringLength - positions}}$`,
+      correct: false,
+    };
+  } //does not use combinations
+}
+
+export default Generator;

src/content/questions/comp2804/2022-winter-final/1/index.md

@@ -5,6 +5,7 @@ type: multiple-choice
 author: Michiel Smid
 question: comp2804/2022-winter-final/1/question.ts
 solution: comp2804/2022-winter-final/1/solution.md
+generator: comp2804/2022-winter-final/1/generator.ts
 tags:
   - comp2804
   - comp2804-final