2043. Simple Bank System - Detailed Explanation

Problem Statement

The Simple Bank System problem asks us to design a Bank class to manage multiple bank accounts and their transactions. We have n accounts numbered from 1 to n, and an initial balance for each account is provided in an array. We need to support three types of operations on these accounts:

• Transfer money from one account to another.
• Deposit money into an account.
• Withdraw money from an account.

Each transaction must be executed only if it is valid. A transaction is considered valid if:

1. The account number(s) involved are within the range 1 to n (i.e., the accounts exist).
2. For withdrawal or the source account of a transfer, the amount of money to take out does not exceed the current balance of that account.

If a transaction is valid, it should update the account balances accordingly and return true. If not, it should not change any balances and return false.

Constraints:

• 1 ≤ n ≤ 10^5 (number of accounts)
• Account numbers are in the range 1 to n.
• 0 ≤ balance[i], money ≤ 10^12 (balances and transaction amounts can be large).
• At most 10^4 calls to each of the functions (transfer, deposit, withdraw) will be made. This means we could have up to about 30,000 total transactions to process in the worst case.

Example 1:

• Input:
  ["Bank", "withdraw", "transfer", "deposit", "transfer", "withdraw"]
[[[10, 100, 20, 50, 30]], [3, 10], [5, 1, 20], [5, 20], [3, 4, 15], [10, 50]]
• Output:
  [null, true, true, true, false, false]
• Explanation:

  1. Bank([10, 100, 20, 50, 30]) initializes 5 accounts with given balances (account1=10, account2=100, account3=20, account4=50, account5=$30). Output is null for constructor.

  2. withdraw(3, 10) returns true – Account 3 had 20, so withdrawing 10 is valid. New balance of account3 is 20 - 10 = $10.

  3. transfer(5, 1, 20) returns true – Account 5 had 30, so transferring 20 to account1 is valid. New balance of account5 is 30 - 20 = 10**, and account1 becomes 10 + 20 = **30.

  4. deposit(5, 20) returns true – Depositing 20 into account5 is always valid. New balance of account5 is 10 + 20 = **30**.

  5. transfer(3, 4, 15) returns false – Account 3 currently has 10, so it cannot transfer 15 (insufficient funds). Balances remain unchanged (account3 is still $10).

  6. withdraw(10, 50) returns false – Account 10 does not exist (we only have 5 accounts), so the transaction is invalid.

Example 2:

• Input:
  ["Bank", "deposit", "withdraw", "withdraw"]
[[[50]], [1, 20], [1, 30], [1, 50]]
• Output:
  [null, true, true, false]
• Explanation:

  1. Bank([50]) initializes 1 account with balance $50.

  2. deposit(1, 20) returns true – Account 1 receives 20, increasing the balance from 50 to $70.

  3. withdraw(1, 30) returns true – 30 is withdrawn from account1 (had 70), leaving $40.

  4. withdraw(1, 50) returns false – Cannot withdraw 50 because account1 only has 40 now (insufficient funds).

Example 3:

• Input:
  ["Bank", "transfer", "transfer", "deposit", "withdraw"]
[[[20, 5]], [1, 2, 5], [2, 1, 15], [2, 20], [1, 25]]
• Output:
  [null, true, false, true, false]
• Explanation:

  1. Bank([20, 5]) initializes 2 accounts: account1=20, account2=5.

  2. transfer(1, 2, 5) returns true – 5 is moved from account1 to account2. New balances: account1 = **15**, account2 = $10.

  3. transfer(2, 1, 15) returns false – Account 2 has 10, which is not enough to transfer 15. No balances change (account1 still 15, account2 10).

  4. deposit(2, 20) returns true – Account 2 gains 20, new balance = **30**.

  5. withdraw(1, 25) returns false – Account 1 has 15, cannot withdraw 25. Balance remains $15.

These examples demonstrate various scenarios: valid and invalid withdrawals, deposits, and transfers, including edge cases like insufficient funds and non-existent accounts.

Hints

• Think about data representation: Since accounts are numbered 1 through n, a simple array or list can hold the balances. The index of the array can correspond to the account number (with an offset because of 1-indexing). This makes accessing any account's balance very fast.

• Be careful with indexing: If accounts are 1-indexed (i.e., account 1 is at index 0 of the array), make sure to convert between account number and array index correctly. For example, use index = account - 1 when accessing the balance array.

• Validate accounts first: Before performing any operation, always check that the given account number(s) are within the valid range. An account number is valid if 1 <= account <= n (where n is the number of accounts). If an account is out of range, the operation should immediately return false.

• Check balances for withdrawals/transfers: For a withdrawal or a transfer, ensure the source account has enough balance (balance >= money) before deducting anything. If not, the operation fails (returns false) and no balance is changed.

• Reuse logic when possible: The transfer operation can be seen as a withdraw followed by a deposit. Consider calling your withdraw and deposit methods inside transfer to avoid duplicating code, or handle it in a single method with combined checks. Just be careful to only withdraw if both accounts are valid and the source has enough money.

• Use appropriate data types: The balances and transaction amounts can be up to 10^12, which may exceed the limit of a 32-bit integer. In languages like Java, use a 64-bit type (like long) to store money. In Python, the built-in int can handle big numbers, but conceptually it's a large integer.

Multiple Approaches

There are not many drastically different algorithms for this problem since it’s straightforward simulation. However, we can discuss a naive approach versus a more efficient approach, and how careful design can improve clarity and performance.

Approach 1: Brute Force Simulation (Naive)

Idea: Simulate each transaction in a straightforward way by manually checking all conditions every time. A very naive implementation might even search for the account in a list or use if/else logic separately for each operation without reusing code. For example, for a transfer, you could explicitly check both account numbers and then subtract and add balances, writing out all steps.

How it works:

• Use an array or list balance to store account balances.
• For each operation:

  • withdraw(account, money): Check if account is valid by ensuring 1 <= account <= n. If not, return false. If valid, then check if balance[account-1] >= money. If not enough balance, return false. Otherwise, subtract the money from balance[account-1] and return true.

  • deposit(account, money): Check validity of account. If valid, add money to balance[account-1] and return true. If not valid, return false.

  • transfer(account1, account2, money): First check both account1 and account2 are in range. If either is invalid, return false. Then check if balance[account1-1] >= money (the source has enough funds). If not, return false. If all checks pass, subtract money from account1's balance and add money to account2's balance, then return true.

This approach is essentially implementing the logic directly as stated. It works correctly, but if one implemented it very naively, they might do unnecessary work. For instance, a naive approach might linearly search through the list of accounts to verify an account exists (which is not needed because we can calculate the index directly). Such unnecessary looping would make each operation O(n) where n is the number of accounts.

Complexity: In the worst naive scenario, if each transaction involved scanning through n accounts to find the right one, a single operation could take O(n) time. With up to m operations, that could be O(n * m) steps. Given the constraints (n up to 100k, and m up to 30k total calls), this could be on the order of 100k * 30k = 3 billion checks in the worst case, which would be far too slow. Fortunately, we don't need to scan – we can directly index into the array. The space complexity for this approach is O(n) to store the balances array. (If a truly naive approach used extra structures or copies, it could be worse, but that's unnecessary.)

Approach 2: Optimal Direct Access (Efficient Simulation)

Idea: We can optimize by using direct indexing to access accounts in O(1) time, rather than any searching. Since account numbers map directly to indices in the balance array, each operation can be done in constant time by directly checking or updating the corresponding entry. Additionally, we can streamline the code by avoiding repetition – for example, using helper checks or reusing deposit/withdraw logic inside transfer as appropriate.

How it works:

• Initialization: Simply store the given balance array internally (no need to copy element by element, we can just keep a reference in most languages). Also store n = len(balance) for quick access to the number of accounts.

• Validating accounts: Write a small helper (or just inline check) to verify an account number is within 1..n. This is a quick comparison.

• withdraw(account, money): Check account validity. If invalid, return false. If valid, check if balance[account-1] >= money. If not, return false (insufficient funds). If yes, subtract the amount: balance[account-1] -= money and return true.

• deposit(account, money): Check account validity. If valid, add the amount: balance[account-1] += money and return true. If invalid, return false. (Depositing money into a valid account is always allowed since there's no upper limit on balance given in the problem.)

• transfer(account1, account2, money): Check both accounts are valid. If either is invalid, return false immediately (no money moves). If both valid, check that account1 (source) has at least money. If not, return false (cannot transfer more than available). If yes, then perform the transfer: subtract money from balance[account1-1] and add money to balance[account2-1], then return true.

  • Tip: We can implement transfer by simply doing the above steps, or we could call our withdraw(account1, money) and deposit(account2, money) methods internally. If withdraw fails, we return false; if it succeeds, then call deposit on account2 and return that result. This way, we reuse our already tested logic for those operations.

Because we are using direct index access and simple conditional checks, each operation runs in constant time, O(1). We do a fixed amount of work (a few comparisons and arithmetic operations) for each call, regardless of the number of accounts. This meets the performance needs easily – even 30,000 operations will execute quickly when each is O(1). The space complexity remains O(n) for storing the balances. We use only a few extra variables for indices or for the number of accounts, which is negligible compared to the array size.

Complexity: Each transaction (deposit, withdraw, or transfer) completes in O(1) time on average, since it involves just index lookups and arithmetic. Thus, processing m operations is O(m). With m up to ~30,000, this is very efficient. Space complexity is O(n) for the balance storage (proportional to the number of accounts), which is optimal since we must at least store all account balances.

Comparison of Approaches: In this problem, the "brute force" and "optimal" approaches end up being conceptually similar because the straightforward solution is already optimal. The key difference is avoiding any unnecessary loops or overhead:

• A truly naive approach that used linear scans to find accounts would be inefficient (O(n) per operation), but most people will naturally use direct indexing here.
• The optimal approach uses direct indexing and careful checks, making each operation O(1). This is the intended solution and is easy to implement given the direct relationship between account number and array index.

Code Implementation

Below are implementations of the Bank class in both Python and Java. Each provides the required methods (transfer, deposit, withdraw).

Python Implementation