Decimal Expansion (JS)

decimalExpansion.js

function decimalExpansion(numerator, denominator) {
  // Special case for 0
  if (denominator === 0) {
    return null;
  } else if (numerator === 0) {
    return { whole: 0, nonRecurring: "", recurring: null };
  }

  const whole = Math.floor(numerator / denominator);
  let remainder = numerator % denominator;
  let nonRecurring = '';  // The non-recurring part of the decimal
  let recurring = null;   // The recurring part of the decimal
  const remainderHistory = {};  // Track positions of each remainder

  // Process the decimal part
  while (remainder !== 0) {
    // If this remainder has been seen before, we have a repeating decimal
    if (remainderHistory[remainder] !== undefined) {
      recurring = nonRecurring.slice(remainderHistory[remainder]);
      nonRecurring = nonRecurring.slice(0, remainderHistory[remainder]);
      break;
    }

    // Store the position of this remainder
    remainderHistory[remainder] = nonRecurring.length;

    // Get the next digit in the decimal expansion
    remainder *= 10;
    nonRecurring += Math.floor(remainder / denominator);
    remainder %= denominator;
  }

  return {
    whole,
    nonRecurring,  // Non-recurring part of the decimal
    recurring,     // Recurring part of the decimal (or null if none)
  };
}

function fractionFromDecimalExpansion({ whole, nonRecurring, recurring }) {
  // Base case: if everything is zero
  if (whole === 0 && nonRecurring === "" && recurring === null) {
    return { numerator: 0, denominator: 1 };
  }

  // Parse the non-recurring part
  const nonRecurringLength = nonRecurring.length;
  const recurringLength = recurring ? recurring.length : 0;

  // Convert whole and non-recurring part into a fraction
  const wholeNumerator = whole;
  const wholeDenominator = 1;

  const nonRecurringNumerator = nonRecurring ? parseInt(nonRecurring, 10) : 0;
  const nonRecurringDenominator = Math.pow(10, nonRecurringLength);

  // If there is no recurring part
  if (!recurring) {
    const numerator = wholeNumerator * nonRecurringDenominator + nonRecurringNumerator;
    const denominator = nonRecurringDenominator;
    return simplifyFraction(numerator, denominator);
  }

  // Handle the recurring part
  const recurringNumerator = parseInt(recurring, 10);
  const recurringDenominator = Math.pow(10, recurringLength) - 1;

  // Combined denominator for the recurring part
  const totalRecurringDenominator = recurringDenominator * nonRecurringDenominator;
  const totalRecurringNumerator =
    recurringNumerator +
    nonRecurringNumerator * recurringDenominator;

  const totalNumerator = wholeNumerator * totalRecurringDenominator + totalRecurringNumerator;
  const totalDenominator = totalRecurringDenominator;

  return simplifyFraction(totalNumerator, totalDenominator);
}

// Helper function to simplify fractions
function simplifyFraction(numerator, denominator) {
  const gcd = (a, b) => (b === 0 ? a : gcd(b, a % b));
  const divisor = gcd(numerator, denominator);
  return {
    numerator: numerator / divisor,
    denominator: denominator / divisor,
  };
}

for (let numerator = 1; numerator < 10; numerator++) {
  for (let denominator = 1; denominator < 10; denominator++) {
    const expansion = decimalExpansion(numerator, denominator);
    const suffix = expansion.recurring ? expansion.recurring : '';
    const prefix = (expansion.nonRecurring || suffix) ? `${expansion.whole}.${expansion.nonRecurring}` : expansion.whole;

    const firstLine = ' '.repeat(prefix.length) + '_'.repeat(suffix.length);
    const secondLine = prefix + suffix;

    const fraction = fractionFromDecimalExpansion(expansion);

    console.log('------------------------------------------------------------');
    console.log(`${numerator}/${denominator}`);
    console.log(`${fraction.numerator}/${fraction.denominator}`);
    console.log(firstLine);
    console.log(secondLine);
    console.log('');
    console.log(JSON.stringify(expansion))
    console.log('------------------------------------------------------------');
    console.log('');
  }
}