In-Memory Banking System — Design and Implementation

You are to design and implement an in-memory banking system that supports account management and transactions, and can report the top-k accounts by their cumulative outgoing transfers.

Operations

1. createAccount(accountId, initialBalance = 0)
   • Creates a new account with the given ID and initial balance (default 0).
2. deposit(accountId, amount)
   • Adds funds to an existing account.
3. transfer(fromId, toId, amount)
   • Debits the sender (fromId) and credits the receiver (toId).
   • Reject the transfer if the sender has insufficient funds.
   • Maintain, for each account, the cumulative outgoing transaction amount (sum of all successful debits initiated by that account).

Reporting

• topNAccountsByOutgoing(n)
  • Returns the top n accounts by total outgoing amount, breaking ties by accountId ascending.
  • Output format: a list of strings formatted as "{outgoingAmount}:{accountId}".

Requirements

• Describe the data structures you will use.
• Specify error handling for cases such as unknown account, invalid amounts, and insufficient funds.
• Provide pseudocode for both:
  • a full-sort solution, and
  • a heap-based top-k solution.
• Analyze time and space complexity for each operation and for both top-k approaches.