Aggregate loans and match repayments

You are building a loan servicing tool.

You are given two datasets.

Part 1: Aggregate raw loan records

Each raw loan record has the following fields:

• loan_id : string
• customer_id : string
• amount : positive integer
• created_at : timestamp

Multiple records may belong to the same loan_id. Write a function that aggregates all records with the same loan_id into a single loan summary containing:

• loan_id
• customer_id
• created_at of the earliest record for that loan
• total_amount : the sum of all amounts for that loan

You may assume all records for the same loan_id belong to the same customer_id.

Part 2: Match repayment transactions to loans

You are then given the aggregated loans from Part 1 and a list of repayment transactions. Each transaction has:

• txn_id : string
• customer_id : string
• amount : positive integer
• timestamp : timestamp

Match transactions to outstanding loans using these rules:

1. A transaction can only be applied to loans for the same customer_id .
2. For each customer, loans must be paid in ascending order of created_at .
3. A transaction may partially pay a loan.
4. A single transaction may be split across multiple loans.
5. A loan may be paid by multiple transactions.

Return:

• a list of matches of the form (txn_id, loan_id, matched_amount)
• the remaining unpaid balance for every loan after all transactions are applied

Discuss the time and space complexity of your approach.