math-quiz/lib/engine/parenthesis-sign.ts

import type {
  GradeResult,
  ParenthesisSignProblem,
  UserAnswer,
} from "./types";

const MIN_MULTIPLIER = -9;
const MAX_MULTIPLIER = -1;
const MIN_TERM = 1;
const MAX_TERM = 9;
const MAX_TERM_COUNT = 4;

export type ParenthesisTermCount = 2 | 3 | 4;

interface ProblemSeed {
  multiplier: number;
  terms: number[];
  operators: ("+" | "-")[];
}

function randomInt(min: number, max: number) {
  return Math.floor(Math.random() * (max - min + 1)) + min;
}

function formatLatexTerms(terms: number[]) {
  return terms
    .map((term, index) => {
      if (index === 0) return `${term}`;

      const operator = term < 0 ? "-" : "+";
      return `${operator} ${Math.abs(term)}`;
    })
    .join(" ");
}

function formatParenthesisTerms(
  terms: number[],
  operators: ("+" | "-")[],
) {
  return terms
    .map((term, index) => {
      if (index === 0) return `${term}`;

      return `${operators[index - 1]} ${term}`;
    })
    .join(" ");
}

function createProblem({
  multiplier,
  terms,
  operators,
}: ProblemSeed): ParenthesisSignProblem {
  const signedTerms = terms.map((term, index) => {
    if (index === 0) return term;

    return operators[index - 1] === "-" ? -term : term;
  });
  const distributedTerms = signedTerms.map((term) => multiplier * term);
  const [a, b] = terms;
  const [operator] = operators;
  const [distributedA, distributedB] = distributedTerms;
  const key = [
    multiplier,
    ...terms.flatMap((term, index) =>
      index === 0 ? [`${term}`] : [operators[index - 1], `${term}`],
    ),
  ].join(":");

  return {
    id: `parenthesis-sign:${key}`,
    key,
    multiplier,
    terms,
    operators,
    a,
    operator,
    b,
    distributedTerms,
    distributedA,
    distributedB,
    latexBefore: `${multiplier}\\left(${formatParenthesisTerms(
      terms,
      operators,
    )}\\right)`,
    latexAfter: formatLatexTerms(distributedTerms),
  };
}

function createTermCombinations(termCount: ParenthesisTermCount) {
  const combinations: number[][] = [];

  function addTerms(nextTerms: number[]) {
    if (nextTerms.length === termCount) {
      combinations.push(nextTerms);
      return;
    }

    for (let term = MIN_TERM; term <= MAX_TERM; term += 1) {
      if (nextTerms.includes(term)) continue;

      addTerms([...nextTerms, term]);
    }
  }

  addTerms([]);

  return combinations;
}

function createOperatorCombinations(termCount: ParenthesisTermCount) {
  const combinations: ("+" | "-")[][] = [];
  const operatorCount = termCount - 1;

  function addOperators(nextOperators: ("+" | "-")[]) {
    if (nextOperators.length === operatorCount) {
      combinations.push(nextOperators);
      return;
    }

    addOperators([...nextOperators, "+"]);
    addOperators([...nextOperators, "-"]);
  }

  addOperators([]);

  return combinations;
}

function createAllProblemSeeds(termCount: ParenthesisTermCount) {
  const seeds: ProblemSeed[] = [];
  const termCombinations = createTermCombinations(termCount);
  const operatorCombinations = createOperatorCombinations(termCount);

  for (
    let multiplier = MIN_MULTIPLIER;
    multiplier <= MAX_MULTIPLIER;
    multiplier += 1
  ) {
    for (const terms of termCombinations) {
      for (const operators of operatorCombinations) {
        seeds.push({ multiplier, terms, operators });
      }
    }
  }

  return seeds;
}

const ALL_PROBLEM_SEEDS_BY_TERM_COUNT: Record<
  ParenthesisTermCount,
  ProblemSeed[]
> = {
  2: createAllProblemSeeds(2),
  3: createAllProblemSeeds(3),
  4: createAllProblemSeeds(4),
};

function shuffle<T>(items: T[]) {
  const shuffled = [...items];

  for (let index = shuffled.length - 1; index > 0; index -= 1) {
    const targetIndex = randomInt(0, index);
    const current = shuffled[index];
    shuffled[index] = shuffled[targetIndex];
    shuffled[targetIndex] = current;
  }

  return shuffled;
}

function assertTermCount(termCount: number): asserts termCount is ParenthesisTermCount {
  if (!Number.isInteger(termCount) || termCount < 2 || termCount > MAX_TERM_COUNT) {
    throw new Error("termCount must be 2, 3, or 4.");
  }
}

export function generateProblem(
  termCount: ParenthesisTermCount = 2,
): ParenthesisSignProblem {
  assertTermCount(termCount);

  const terms: number[] = [];

  while (terms.length < termCount) {
    const term = randomInt(MIN_TERM, MAX_TERM);

    if (!terms.includes(term)) {
      terms.push(term);
    }
  }

  return createProblem({
    multiplier: randomInt(MIN_MULTIPLIER, MAX_MULTIPLIER),
    terms,
    operators: Array.from({ length: termCount - 1 }, () =>
      Math.random() < 0.5 ? "+" : "-",
    ),
  });
}

export function generateSession(
  count = 10,
  termCount: ParenthesisTermCount = 2,
): ParenthesisSignProblem[] {
  if (!Number.isInteger(count) || count < 1) {
    throw new Error("count must be a positive integer.");
  }

  assertTermCount(termCount);

  const seeds = ALL_PROBLEM_SEEDS_BY_TERM_COUNT[termCount];

  if (count > seeds.length) {
    throw new Error(`count cannot exceed ${seeds.length}.`);
  }

  return shuffle(seeds).slice(0, count).map(createProblem);
}

export function gradeAnswer(
  problem: ParenthesisSignProblem,
  answer: UserAnswer,
): GradeResult {
  const userAnswer =
    answer.terms ?? (answer.a !== undefined && answer.b !== undefined
      ? [answer.a, answer.b]
      : []);

  return {
    correct:
      userAnswer.length === problem.distributedTerms.length &&
      userAnswer.every((value, index) => value === problem.distributedTerms[index]),
    userAnswer,
    correctAnswer: problem.distributedTerms,
  };
}