```typescript
/** 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("weight list must not be empty");
  }
  const sum = weights.reduce((acc, weight) => acc + weight, 0);
  if (sum === 0) {
    throw new Error("total cannot be zero when allocating cents");
  }
  if (!Number.isInteger(totalCents) || totalCents < 0) {
    throw new Error("total must be a non-negative integer");
  }

  const allocate = (total: number, weights: number[]): number[] => {
    const totalWeight = weights.reduce((acc, weight) => acc + weight, 0);
    if (totalWeight === 0) return [];
    const shares = weights.map(weight => Math.floor(total * (weight / totalWeight)));
    const remainder = total - shares.reduce((acc, share) => acc + share, 0);
    let nextShareIndex = 0;
    for (let i = 0; i < shares.length && remainder > 0; i++) {
      if (shares[i] === Math.min(...shares)) {
        shares[i]++;
        remainder--;
        nextShareIndex = i;
      }
    }
    return shares;
  };

  return allocate(totalCents, weights);
}
```