```ts
/** Fixed-point money helpers: parse, format, and allocate integer cents. */

export function parseAmount(text: string): number {
  if (typeof text !== "string") {
    throw new Error("amount must be a string");
  }
  const match = /^(\d{1,})(?:\.(\d{2}))?$/.exec(text);
  if (match === null) {
    throw new Error(`malformed amount: ${text}`);
  }
  const whole = Number(match[1]);
  const cents = match[2] === undefined ? 0 : Number(match[2]);
  return whole * 100 + cents;
}

export function formatAmount(cents: number): string {
  if (!Number.isInteger(cents) || cents < 0) {
    throw new Error("cents must be a non-negative integer");
  }
  const whole = Math.floor(cents / 100);
  const rest = String(cents % 100).padStart(2, "0");
  return `${whole}.${rest}`;
}

export function allocateCents(totalCents: number, weights: number[]): number[] {
  if (!Number.isInteger(totalCents) || totalCents < 0) {
    throw new Error("totalCents must be a non-negative integer");
  }
  if (weights.length === 0) {
    throw new Error("weights list cannot be empty");
  }
  const sum = weights.reduce((acc, weight) => acc + weight, 0);
  if (sum === 0) {
    throw new Error("weights must sum to a non-zero integer");
  }

  const baseShares = weights.map((weight) => Math.floor((totalCents * weight) / sum));
  let remainingCents = totalCents - baseShares.reduce((acc, share) => acc + share, 0);

  for (let i = 0; i < remainingCents; i++) {
    let maxRemainder = -1;
    let indexToIncrement = -1;
    for (let j = 0; j < weights.length; j++) {
      if (weights[j] === 0) continue;
      const remainder = baseShares[j] % weights[j];
      if (remainder > maxRemainder) {
        maxRemainder = remainder;
        indexToIncrement = j;
      }
    }
    if (indexToIncrement !== -1) {
      baseShares[indexToIncrement]++;
    } else {
      throw new Error("internal error: unable to allocate remaining cents");
    }
  }

  return baseShares;
}
```