Implement a Simple Banking Ledger

Design and implement a banking ledger for n accounts labeled 1..n with initial balances. Provide an API: deposit(id, amount) -> bool, withdraw(id, amount) -> bool, transfer(fromId, toId, amount) -> bool. Rules: return false for invalid account IDs or insufficient funds; otherwise apply updates and return true. Constraints: up to 200,000 operations, amounts up to 10^12, target O( 1) per operation and O(n) space; assume single-threaded execution. Sub-questions: write unit tests for edge cases (invalid IDs, zero/negative amounts, overflow), extend to support atomic batches of operations with rollback on partial failure, and analyze time/space complexity and common pitfalls (e.g., integer overflow).