```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+)(?:\.(\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 (weights.length === 0) {
    throw new Error("Cannot allocate with an empty weight list.");
  }
  const sum = weights.reduce((acc, weight) => acc + weight, 0);
  if (sum <= 0) {
    throw new Error("Weights must sum to a positive number.");
  }
  if (!Number.isInteger(totalCents) || totalCents < 0) {
    throw new Error("totalCents must be a non-negative integer");
  }

  // Calculate the exact share size for each weight
  const shares = weights.map((weight, index) => Math.floor((totalCents * weight) / sum));

  // Determine how many cents are left over
  let leftover = totalCents;
  const result: number[] = Array(weights.length).fill(0);

  // Distribute the leftover cents to the shares with the largest remainders first
  for (let i = weights.length - 1; i >= 0 && leftover > 0; i--) {
    const remainder = leftover % 1;
    if (remainder !== 0) {
      result[i] += 1;
      leftover -= 1;
    }
  }

  return result.map((share, index) => share + shares[index]);
}
```