Problem Description

This problem simulates the operations of a bank with n accounts through a class called Bank. Each account in the bank is numbered from 1 to n, and the initial balance for each account is given in a 0-indexed array; this means that the balance of the i-th account in the array corresponds to account number i + 1 in our bank. The Bank class needs to support three types of transactions: transfers between two accounts, deposits into an account, and withdrawals from an account. A transaction is considered valid if the account numbers are within the valid range (1 to n) and for transfers and withdrawals, there is enough money in the account to cover the transaction. Implementing the required functionality in the Bank class involves creating methods that successfully handle these transactions while maintaining accurate account balances and ensuring all business rules are respected.

Intuition

When designing the Bank class and its methods, we should first consider the constraints around account numbers and balances. To handle transactions, we need to check that the requested operation is valid: the account number(s) must be within the valid range and there must be sufficient funds to complete a withdrawal or transfer.

We start with the constructor __init__, which initializes the Bank with a list of account balances and the total number of accounts. This sets up our initial state.

For the transfer method, we check the validity of the account numbers and the availability of funds in the source account. If these conditions are met, we subtract the transferred money from account1 and add it to account2. If the conditions are not met, we return False.

The deposit method is slightly simpler, as it only requires a check to ensure the account exists (the account number is within range). If it does, we add the money to the account's balance.

The withdraw method involves checking both the account number validity and the availability of funds, much like the transfer method. If the checks pass, we subtract the money from the account.

Each of these methods returns a boolean indicating whether the operation was successful (True) or not (False).

By carefully following the rules stated in the problem description and using basic conditional statements to enforce the rules, we arrive at a straightforward solution that satisfies all the requirements of the Bank class.

Solution Approach

The solution is structured around the Bank class with three key methods: transfer, deposit, and withdraw.

• The __init__ constructor simply assigns the provided balance list and calculates the number of accounts using the len function which is stored in self.n.

• For the transfer method:

  1. It first checks if both the source (account1) and destination (account2) account numbers are within the valid range by comparing them with self.n. It also checks if the source account has enough balance to transfer by comparing money with the balance of account1.
  2. If any condition fails, it returns False.
  3. If the conditions are met, the method subtracts the amount of money from the balance of account1 and adds that amount to the balance of account2.
  4. It finally returns True indicating a successful transaction.

• For the deposit method:

  1. It verifies if the account number is valid.
  2. If the account is invalid, it returns False.
  3. If valid, it adds the money to the balance of the specified account.
  4. It then returns True to signify success.

• The withdraw method:

  1. Checks if the account number is within the valid range and if the account has a balance greater than or equal to the withdrawal money.
  2. Should the account not exist or have insufficient funds, the method returns False.
  3. Otherwise, it subtracts the withdrawal money from the account's balance and returns True.

The design employs basic array indexing to represent individual account balances. This simple data structure is effective in providing efficient direct access to specific elements, which is essential for operations like transfer, deposit, and withdraw that require looking up and modifying values based on account numbers. Conditionals (if-else statements) are used throughout to enforce business rules and validate transactions.

Overall, the solution follows a pragmatic approach, applying core programming constructs like lists, condition checking, arithmetic operations, and boolean return values to fulfill the transaction requirements of a banking system.

Example Walkthrough

Consider a scenario where we have a Bank with 3 accounts. The initial balances for these accounts are [10, 100, 20], which correspond to accounts 1, 2, and 3 respectively. Let's walk through a series of transactions to demonstrate the solution approach.

1. Initialization:

   • We create a Bank object using the initial balances.
   • The __init__ method sets up our internal state with these balances and establishes that we have 3 accounts.

2. Deposit Attempt:

   • We call the deposit method for account number 2 with an amount of 50.
   • The method checks if account number 2 is valid (which is true, as it's within the range of 1 to 3).
   • It adds 50 to account number 2's balance, resulting in the new balances being [10, 150, 20].
   • The method returns True since the transaction was successful.

3. Withdrawal Attempt:

   • Next, we attempt to withdraw 30 from account number 3.
   • The withdraw method checks if account 3 has at least 30. It does, so the money is subtracted.
   • The balance is updated to [10, 150, -10], and the method returns True.
   • Note: This outcome reveals an oversight in the provided approach, as it allows the balance to go negative. A real implementation should check and ensure the withdrawal does not result in a negative balance, so the transaction should instead return False.

4. Transfer Attempt:

   • We now want to transfer 100 from account 1 to account 3. We call the transfer method with account1 = 1, account2 = 3, and money = 100.
   • The transfer method first checks if account 1 exists and has at least 100 to transfer. It doesn't, as the balance is currently 10.
   • Since there are insufficient funds, the method returns False, and no transfer occurs.

Through this example, the essential process of depositing, withdrawing, and transferring money between accounts is illustrated using array indexing, condition statements, and boolean values to handle the business logic of these transactions systematically. However, modifications might be necessary to prevent negative account balances as noted in step 3.

Solution Implementation

Time and Space Complexity

Time Complexity

• __init__(): The time complexity is O(1) because only a reference to the list is created (assuming that the list is passed by reference and not copied).

• transfer(account1, account2, money): The time complexity is O(1) because it performs a constant number of operations: checking whether the accounts are valid, whether the balance is sufficient, and updating the balances.

• deposit(account, money): The time complexity is O(1) as it involves a simple validation of the account existence and an addition operation on the balance.

• withdraw(account, money): The time complexity is O(1) since it includes the checking of whether the account exists and whether the balance is enough, followed by the subtraction from the balance.

Space Complexity

• __init__(): The space complexity is O(n) because it stores a list of balances for n accounts, where n is the length of the initial list. Here, n represents the number of accounts.

• transfer(account1, account2, money): The space complexity is O(1) as it does not use any additional space that scales with the input size.

• deposit(account, money): The space complexity is O(1) given that no extra space proportional to the size of input data is used besides what is already stored in the Bank class.

• withdraw(account, money): The space complexity is also O(1) for the same reason as deposit and transfer; it does not require additional space depending on the input.

Learn more about how to find time and space complexity quickly using problem constraints.