LeetCode #2241 — MEDIUM

Design an ATM Machine

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

Solve on LeetCode
The Problem

Problem Statement

There is an ATM machine that stores banknotes of 5 denominations: 20, 50, 100, 200, and 500 dollars. Initially the ATM is empty. The user can use the machine to deposit or withdraw any amount of money.

When withdrawing, the machine prioritizes using banknotes of larger values.

  • For example, if you want to withdraw $300 and there are 2 $50 banknotes, 1 $100 banknote, and 1 $200 banknote, then the machine will use the $100 and $200 banknotes.
  • However, if you try to withdraw $600 and there are 3 $200 banknotes and 1 $500 banknote, then the withdraw request will be rejected because the machine will first try to use the $500 banknote and then be unable to use banknotes to complete the remaining $100. Note that the machine is not allowed to use the $200 banknotes instead of the $500 banknote.

Implement the ATM class:

  • ATM() Initializes the ATM object.
  • void deposit(int[] banknotesCount) Deposits new banknotes in the order $20, $50, $100, $200, and $500.
  • int[] withdraw(int amount) Returns an array of length 5 of the number of banknotes that will be handed to the user in the order $20, $50, $100, $200, and $500, and update the number of banknotes in the ATM after withdrawing. Returns [-1] if it is not possible (do not withdraw any banknotes in this case).

Example 1:

Input
["ATM", "deposit", "withdraw", "deposit", "withdraw", "withdraw"]
[[], [[0,0,1,2,1]], [600], [[0,1,0,1,1]], [600], [550]]
Output
[null, null, [0,0,1,0,1], null, [-1], [0,1,0,0,1]]

Explanation
ATM atm = new ATM();
atm.deposit([0,0,1,2,1]); // Deposits 1 $100 banknote, 2 $200 banknotes,
                          // and 1 $500 banknote.
atm.withdraw(600);        // Returns [0,0,1,0,1]. The machine uses 1 $100 banknote
                          // and 1 $500 banknote. The banknotes left over in the
                          // machine are [0,0,0,2,0].
atm.deposit([0,1,0,1,1]); // Deposits 1 $50, $200, and $500 banknote.
                          // The banknotes in the machine are now [0,1,0,3,1].
atm.withdraw(600);        // Returns [-1]. The machine will try to use a $500 banknote
                          // and then be unable to complete the remaining $100,
                          // so the withdraw request will be rejected.
                          // Since the request is rejected, the number of banknotes
                          // in the machine is not modified.
atm.withdraw(550);        // Returns [0,1,0,0,1]. The machine uses 1 $50 banknote
                          // and 1 $500 banknote.

Constraints:

  • banknotesCount.length == 5
  • 0 <= banknotesCount[i] <= 109
  • 1 <= amount <= 109
  • At most 5000 calls in total will be made to withdraw and deposit.
  • At least one call will be made to each function withdraw and deposit.
  • Sum of banknotesCount[i] in all deposits doesn't exceed 109
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: There is an ATM machine that stores banknotes of 5 denominations: 20, 50, 100, 200, and 500 dollars. Initially the ATM is empty. The user can use the machine to deposit or withdraw any amount of money. When withdrawing, the machine prioritizes using banknotes of larger values. For example, if you want to withdraw $300 and there are 2 $50 banknotes, 1 $100 banknote, and 1 $200 banknote, then the machine will use the $100 and $200 banknotes. However, if you try to withdraw $600 and there are 3 $200 banknotes and 1 $500 banknote, then the withdraw request will be rejected because the machine will first try to use the $500 banknote and then be unable to use banknotes to complete the remaining $100. Note that the machine is not allowed to use the $200 banknotes instead of the $500 banknote. Implement the ATM class: ATM() Initializes the ATM object. void deposit(int[] banknotesCount) Deposits

Baseline thinking

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

Pattern signal: Array · Greedy · Design

Example 1

["ATM","deposit","withdraw","deposit","withdraw","withdraw"]
[[],[[0,0,1,2,1]],[600],[[0,1,0,1,1]],[600],[550]]

Related Problems

  • Simple Bank System (simple-bank-system)
  • Minimum Number of Operations to Convert Time (minimum-number-of-operations-to-convert-time)
Step 02

Core Insight

What unlocks the optimal approach

  • Store the number of banknotes of each denomination.
  • Can you use math to quickly evaluate a withdrawal request?
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 #2241: Design an ATM Machine
class ATM {
    private int[] d = {20, 50, 100, 200, 500};
    private int m = d.length;
    private long[] cnt = new long[5];

    public ATM() {
    }

    public void deposit(int[] banknotesCount) {
        for (int i = 0; i < banknotesCount.length; ++i) {
            cnt[i] += banknotesCount[i];
        }
    }

    public int[] withdraw(int amount) {
        int[] ans = new int[m];
        for (int i = m - 1; i >= 0; --i) {
            ans[i] = (int) Math.min(amount / d[i], cnt[i]);
            amount -= ans[i] * d[i];
        }
        if (amount > 0) {
            return new int[] {-1};
        }
        for (int i = 0; i < m; ++i) {
            cnt[i] -= ans[i];
        }
        return ans;
    }
}

/**
 * Your ATM object will be instantiated and called as such:
 * ATM obj = new ATM();
 * obj.deposit(banknotesCount);
 * int[] param_2 = obj.withdraw(amount);
 */
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(n log n)
Space
O(1)

Approach Breakdown

EXHAUSTIVE
O(2ⁿ) time
O(n) space

Try every possible combination of choices. With n items each having two states (include/exclude), the search space is 2ⁿ. Evaluating each combination takes O(n), giving O(n × 2ⁿ). The recursion stack or subset storage uses O(n) space.

GREEDY
O(n log n) time
O(1) space

Greedy algorithms typically sort the input (O(n log n)) then make a single pass (O(n)). The sort dominates. If the input is already sorted or the greedy choice can be computed without sorting, time drops to O(n). Proving greedy correctness (exchange argument) is harder than the implementation.

Shortcut: Sort + single pass → O(n log n). If no sort needed → O(n). The hard part is proving it works.
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.

Using greedy without proof

Wrong move: Locally optimal choices may fail globally.

Usually fails on: Counterexamples appear on crafted input orderings.

Fix: Verify with exchange argument or monotonic objective before committing.