Final Answer: The algorithm to find the group members with the smallest negative balance involves calculating the total balances for each member based on the debt records, identifying members with negative balances, and returning those with the smallest amount. If no negative balances exist, it returns a specific message. Finally, it sorts the names alphabetically before outputting them. ; Explanation: To find the group member with the smallest negative balance, you can follow this algorithm: Initialize a dictionary to store the balances of each member. Iterate through the debts list of records: For each record (borrower, lender, amount): Deduct the amount from the borrower 's balance (subtracts the debt). Add the amount to the lender 's balance (this lender's balance increases). After processing all records, filter the balances to find members with negative balances. Determine the smallest negative balance among those members. Gather the names of members who have this smallest negative balance. Sort the names alphabetically and return them. If no members have a negative balance, return a list containing "Nobody has a negative balance.". Here is a sample implementation in Python: def smallest_negative_balance(numRows, numCols, debts): balance = {} for borrower, lender, amount in debts: balance[borrower] = balance.get(borrower, 0) - amount balance[lender] = balance.get(lender, 0) + amount negative_balances = {name: bal for name, bal in balance.items() if bal < 0} if not negative_balances: return ["Nobody has a negative balance."] smallest_negative = min(negative_balances.values()) members_with_smallest_balance = [name for name, bal in negative_balances.items() if bal == smallest_negative] return sorted(members_with_smallest_balance) This algorithm efficiently handles large inputs due to the use of dictionaries and only requires two passes through the debts list: once for balance calculations and once for filtering. In the first pass, you collect all changes in balances, and in the second pass, you filter and find the members with the smallest negative balance and sort their names. This approach meets the computational efficiency required for the constraints provided. ; Examples & Evidence: For a given debts list such as [('Alice', 'Bob', 100), ('Bob', 'Alice', 50), ('Alice', 'Charlie', 200)], the balances would be calculated as: Alice: -300, Bob: +50, Charlie: 0. The output will identify 'Alice' as having the smallest negative balance and return ['Alice']. The algorithm uses dictionary structures to efficiently calculate and store balances, ensuring it can scale to the upper limit of inputs without performance issues.

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