```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]) || 0;
  const cents = match[2] ? Number(match[2]) : 0;
  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("weight list cannot be empty");
  }
  const sum = weights.reduce((acc, weight) => acc + (Number.isInteger(weight) && weight >= 0 ? weight : -1), 0);
  if (sum <= 0) {
    throw new Error("weights must sum to a non-negative integer");
  }

  const shares = weights.map((weight) => Math.floor((totalCents * weight) / sum));
  const leftover = totalCents % sum;
  let remainingLeftover = leftover;

  for (let i = 0; remainingLeftover > 0; i++) {
    shares[i] += 1;
    remainingLeftover -= 1;
  }

  return shares;
}
```