cabrits-math/lib/problems/generators/fraction-problems.ts

import type { MathProblem, Difficulty } from "../types";
import { randomInt, randomChoice } from "@/lib/utils";
import * as frac from "@/lib/math/fractions";

let counter = 0;
function nextId() {
  return `fp-${++counter}-${Date.now()}`;
}

export function generateFractionAddSubtract(difficulty: Difficulty): MathProblem {
  const operation = randomChoice(["add", "subtract"] as const);
  const op = operation === "add" ? "+" : "-";

  let n1: number, d1: number, n2: number, d2: number;

  if (difficulty === 1) {
    // Common denominators
    d1 = randomChoice([2, 3, 4, 5, 6, 8, 10, 12]);
    d2 = d1;
    n1 = randomInt(1, d1 - 1);
    n2 = operation === "subtract" ? randomInt(1, n1) : randomInt(1, d1 - n1);
  } else if (difficulty === 2) {
    // One denominator is a multiple of the other
    d1 = randomChoice([2, 3, 4, 5, 6]);
    const multiplier = randomChoice([2, 3]);
    d2 = d1 * multiplier;
    n1 = randomInt(1, d1 - 1);
    n2 = randomInt(1, d2 - 1);
  } else {
    // Unlike denominators
    d1 = randomChoice([3, 4, 5, 7, 8, 9]);
    d2 = randomChoice([3, 4, 5, 7, 8, 9].filter((d) => d !== d1));
    n1 = randomInt(1, d1 - 1);
    n2 = randomInt(1, d2 - 1);
  }

  const [ansNum, ansDen] = operation === "add"
    ? frac.add(n1, d1, n2, d2)
    : frac.subtract(n1, d1, n2, d2);

  const prompt = `\\frac{${n1}}{${d1}} ${op} \\frac{${n2}}{${d2}}`;

  const commonDen = frac.lcm(d1, d2);
  const steps = d1 === d2
    ? [
        { explanation: "Denominators are the same, so just " + (operation === "add" ? "add" : "subtract") + " the numerators" },
        { explanation: `${n1} ${op} ${n2} = ${operation === "add" ? n1 + n2 : n1 - n2}`, math: `\\frac{${operation === "add" ? n1 + n2 : n1 - n2}}{${d1}}` },
      ]
    : [
        { explanation: `Find the common denominator: LCM(${d1}, ${d2}) = ${commonDen}` },
        { explanation: `Convert: ${n1}×${commonDen / d1}/${d1}×${commonDen / d1} and ${n2}×${commonDen / d2}/${d2}×${commonDen / d2}` },
        { explanation: `${op === "+" ? "Add" : "Subtract"} numerators`, math: `\\frac{${ansNum}}{${ansDen}}` },
      ];

  return {
    id: nextId(),
    prompt,
    answer: { kind: "fraction", numerator: ansNum, denominator: ansDen },
    hints: [
      d1 === d2 ? "The denominators are already the same!" : "Find a common denominator first",
      d1 !== d2 ? `Try using the Butterfly Method: cross multiply` : `Just ${operation} the numerators`,
    ],
    steps,
  };
}

export function generateFractionMultiply(difficulty: Difficulty): MathProblem {
  const denChoices = difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [2, 3, 4, 5, 6, 7, 8] : [3, 5, 7, 9, 11, 12, 15];
  const d1 = randomChoice(denChoices);
  const d2 = randomChoice(denChoices);
  const n1 = randomInt(1, d1 - 1);
  const n2 = randomInt(1, d2 - 1);

  const [ansNum, ansDen] = frac.multiply(n1, d1, n2, d2);

  return {
    id: nextId(),
    prompt: `\\frac{${n1}}{${d1}} \\times \\frac{${n2}}{${d2}}`,
    answer: { kind: "fraction", numerator: ansNum, denominator: ansDen },
    hints: [
      "Multiply numerator × numerator",
      "Multiply denominator × denominator",
      "Simplify if possible",
    ],
    steps: [
      { explanation: `Multiply numerators: ${n1} × ${n2} = ${n1 * n2}` },
      { explanation: `Multiply denominators: ${d1} × ${d2} = ${d1 * d2}` },
      { explanation: "Simplify", math: `\\frac{${ansNum}}{${ansDen}}` },
    ],
  };
}

export function generateFractionDivide(difficulty: Difficulty): MathProblem {
  const denChoices = difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [2, 3, 4, 5, 6, 7, 8] : [3, 5, 7, 9, 11, 14, 15];
  const d1 = randomChoice(denChoices);
  const d2 = randomChoice(denChoices);
  const n1 = randomInt(1, d1 - 1);
  const n2 = randomInt(1, d2 - 1);

  const [ansNum, ansDen] = frac.divide(n1, d1, n2, d2);

  return {
    id: nextId(),
    prompt: `\\frac{${n1}}{${d1}} \\div \\frac{${n2}}{${d2}}`,
    answer: { kind: "fraction", numerator: ansNum, denominator: ansDen },
    hints: [
      "Keep the first fraction the same",
      "Flip the second fraction (reciprocal)",
      "Then multiply",
    ],
    steps: [
      { explanation: `Keep ${n1}/${d1}, flip ${n2}/${d2} to ${d2}/${n2}` },
      { explanation: `Multiply: ${n1}×${d2} / ${d1}×${n2}` },
      { explanation: "Simplify", math: `\\frac{${ansNum}}{${ansDen}}` },
    ],
  };
}

export function generateFractionOfQuantity(difficulty: Difficulty): MathProblem {
  const denChoices = difficulty === 1 ? [2, 4, 5, 10] : difficulty === 2 ? [3, 4, 5, 6, 8] : [7, 8, 9, 12, 15];
  const den = randomChoice(denChoices);
  const num = randomInt(1, den - 1);
  const multiplier = randomChoice(difficulty === 1 ? [2, 4, 5, 10] : [3, 6, 7, 8, 9, 12]);
  const quantity = den * multiplier;
  const answer = num * multiplier;

  return {
    id: nextId(),
    prompt: `\\frac{${num}}{${den}} \\text{ of } ${quantity}`,
    answer: { kind: "integer", value: answer },
    hints: [
      `Divide ${quantity} by ${den} first`,
      `Then multiply by ${num}`,
    ],
    steps: [
      { explanation: `Divide the quantity by the denominator: ${quantity} ÷ ${den} = ${quantity / den}` },
      { explanation: `Multiply by the numerator: ${quantity / den} × ${num} = ${answer}` },
    ],
  };
}

export function generateWholeFromFraction(difficulty: Difficulty): MathProblem {
  const denChoices = difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [3, 5, 6, 8] : [7, 8, 9, 12];
  const den = randomChoice(denChoices);
  const num = randomInt(1, den - 1);
  const whole = den * randomChoice(difficulty === 1 ? [2, 3, 4, 5] : [3, 5, 6, 7, 8, 10]);
  const part = (num / den) * whole;

  return {
    id: nextId(),
    prompt: `\\frac{${num}}{${den}} \\text{ of a number is } ${part}\\text{. Find the number.}`,
    answer: { kind: "integer", value: whole },
    hints: [
      `If ${num}/${den} of the number is ${part}...`,
      `Find 1/${den} first by dividing ${part} by ${num}`,
      `Then multiply by ${den} to get the whole`,
    ],
    steps: [
      { explanation: `1/${den} of the number = ${part} ÷ ${num} = ${part / num}` },
      { explanation: `The whole number = ${part / num} × ${den} = ${whole}` },
    ],
  };
}