LeetCode #2043 — MEDIUM

Simple Bank System

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

Problem Statement

You have been tasked with writing a program for a popular bank that will automate all its incoming transactions (transfer, deposit, and withdraw). The bank has n accounts numbered from 1 to n. The initial balance of each account is stored in a 0-indexed integer array balance, with the (i + 1)th account having an initial balance of balance[i].

Execute all the valid transactions. A transaction is valid if:

  • The given account number(s) are between 1 and n, and
  • The amount of money withdrawn or transferred from is less than or equal to the balance of the account.

Implement the Bank class:

  • Bank(long[] balance) Initializes the object with the 0-indexed integer array balance.
  • boolean transfer(int account1, int account2, long money) Transfers money dollars from the account numbered account1 to the account numbered account2. Return true if the transaction was successful, false otherwise.
  • boolean deposit(int account, long money) Deposit money dollars into the account numbered account. Return true if the transaction was successful, false otherwise.
  • boolean withdraw(int account, long money) Withdraw money dollars from the account numbered account. Return true if the transaction was successful, false otherwise.

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
Bank bank = new Bank([10, 100, 20, 50, 30]);
bank.withdraw(3, 10);    // return true, account 3 has a balance of $20, so it is valid to withdraw $10.
                         // Account 3 has $20 - $10 = $10.
bank.transfer(5, 1, 20); // return true, account 5 has a balance of $30, so it is valid to transfer $20.
                         // Account 5 has $30 - $20 = $10, and account 1 has $10 + $20 = $30.
bank.deposit(5, 20);     // return true, it is valid to deposit $20 to account 5.
                         // Account 5 has $10 + $20 = $30.
bank.transfer(3, 4, 15); // return false, the current balance of account 3 is $10,
                         // so it is invalid to transfer $15 from it.
bank.withdraw(10, 50);   // return false, it is invalid because account 10 does not exist.

Constraints:

  • n == balance.length
  • 1 <= n, account, account1, account2 <= 105
  • 0 <= balance[i], money <= 1012
  • At most 104 calls will be made to each function transfer, deposit, withdraw.
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You have been tasked with writing a program for a popular bank that will automate all its incoming transactions (transfer, deposit, and withdraw). The bank has n accounts numbered from 1 to n. The initial balance of each account is stored in a 0-indexed integer array balance, with the (i + 1)th account having an initial balance of balance[i]. Execute all the valid transactions. A transaction is valid if: The given account number(s) are between 1 and n, and The amount of money withdrawn or transferred from is less than or equal to the balance of the account. Implement the Bank class: Bank(long[] balance) Initializes the object with the 0-indexed integer array balance. boolean transfer(int account1, int account2, long money) Transfers money dollars from the account numbered account1 to the account numbered account2. Return true if the transaction was successful, false otherwise. boolean

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Hash Map · Design

Example 1

["Bank","withdraw","transfer","deposit","transfer","withdraw"]
[[[10,100,20,50,30]],[3,10],[5,1,20],[5,20],[3,4,15],[10,50]]

Related Problems

  • Design an ATM Machine (design-an-atm-machine)
Step 02

Core Insight

What unlocks the optimal approach

  • How do you determine if a transaction will fail?
  • Simply apply the operations if the transaction is valid.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2043: Simple Bank System
class Bank {
    private long[] balance;
    private int n;

    public Bank(long[] balance) {
        this.balance = balance;
        this.n = balance.length;
    }

    public boolean transfer(int account1, int account2, long money) {
        if (account1 > n || account2 > n || balance[account1 - 1] < money) {
            return false;
        }
        balance[account1 - 1] -= money;
        balance[account2 - 1] += money;
        return true;
    }

    public boolean deposit(int account, long money) {
        if (account > n) {
            return false;
        }
        balance[account - 1] += money;
        return true;
    }

    public boolean withdraw(int account, long money) {
        if (account > n || balance[account - 1] < money) {
            return false;
        }
        balance[account - 1] -= money;
        return true;
    }
}

/**
 * Your Bank object will be instantiated and called as such:
 * Bank obj = new Bank(balance);
 * boolean param_1 = obj.transfer(account1,account2,money);
 * boolean param_2 = obj.deposit(account,money);
 * boolean param_3 = obj.withdraw(account,money);
 */
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(1) per op
Space
O(n)

Approach Breakdown

NAIVE
O(n) per op time
O(n) space

Use a simple list or array for storage. Each operation (get, put, remove) requires a linear scan to find the target element — O(n) per operation. Space is O(n) to store the data. The linear search makes this impractical for frequent operations.

OPTIMIZED DESIGN
O(1) per op time
O(n) space

Design problems target O(1) amortized per operation by combining data structures (hash map + doubly-linked list for LRU, stack + min-tracking for MinStack). Space is always at least O(n) to store the data. The challenge is achieving constant-time operations through clever structure composition.

Shortcut: Combine two data structures to get O(1) for each operation type. Space is always O(n).
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.