What is the time complexity of Design an ATM Machine?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Design an ATM Machine?

This problem uses Array, Greedy, Design. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Design an ATM Machine?

Insight 1: The problem emphasizes a greedy approach for the withdraw operation, prioritizing larger denominations first. Insight 2: The ATM's state (number of banknotes of each denomination) needs to be maintained consistently after each operation.

Which companies ask LeetCode 2241. Design an ATM Machine in interviews?

This problem is frequently asked at Yandex.

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Design an ATM Machine - LeetCode 2241 Solution

Design an ATM Machine - Complete Solution Guide

Design an ATM Machine is LeetCode problem 2241, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

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

Detailed Explanation

The problem asks us to design an ATM machine with deposit and withdraw functionalities. The ATM stores banknotes of denominations $20, $50, $100, $200, and $500. The `deposit` function adds banknotes to the ATM's inventory. The `withdraw` function aims to dispense the requested amount using the largest possible denominations first, updating the ATM's inventory accordingly. If the ATM cannot dispense the exact amount, it should return `[-1]` and leave the inventory unchanged. The key is to prioritize larger denominations during withdrawal and ensure we have enough of each denomination to fulfill the request.

Solution Approach

The solution implements the ATM class with `deposit` and `withdraw` methods. The `deposit` method simply adds the deposited banknotes to the ATM's existing counts. The `withdraw` method uses a greedy approach. It iterates through the denominations from largest to smallest, determining the maximum number of banknotes of each denomination that can be used without exceeding the remaining amount. If, after iterating through all denominations, the remaining amount is zero, the withdrawal is successful, and the ATM's inventory is updated. Otherwise, the withdrawal fails, and `[-1]` is returned.

Step-by-Step Algorithm

Step 1: Initialize the ATM with the denominations [20, 50, 100, 200, 500] and an array to store the count of each denomination, initially set to 0.
Step 2: Implement the `deposit` function. For each denomination, add the deposited amount to the corresponding count in the `counts` array.
Step 3: Implement the `withdraw` function. Create an array `withdraw_counts` to track the banknotes to dispense.
Step 4: Iterate through the denominations array from largest to smallest (500 to 20).
Step 5: For each denomination, calculate how many banknotes can be dispensed without exceeding the `remaining_amount` and without exceeding the available number of banknotes of that denomination.
Step 6: Update `withdraw_counts` with the number of banknotes to dispense for the current denomination and reduce the `remaining_amount`.
Step 7: After iterating through all denominations, check if `remaining_amount` is 0. If it is, update the ATM's `counts` array by subtracting the dispensed banknotes.
Step 8: If `remaining_amount` is 0, return the `withdraw_counts` array. Otherwise, return `[-1]`.

Key Insights

Insight 1: The problem emphasizes a greedy approach for the withdraw operation, prioritizing larger denominations first.
Insight 2: The ATM's state (number of banknotes of each denomination) needs to be maintained consistently after each operation.
Insight 3: Careful handling of edge cases is crucial to avoid errors and ensure correct operation, particularly when the exact amount cannot be withdrawn.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Array, Greedy, Design.

Companies

Asked at: Yandex.

Design an ATM Machine | LeetCode 2241

Medium

Array Greedy Design

Time: O(1)Space: O(1)

Solution Code

Available in:

class ATM {

    private int[] denominations;
    private int[] counts;

    public ATM() {
        this.denominations = new int[]{20, 50, 100, 200, 500};
        this.counts = new int[5];
    }
    
    public void deposit(int[] banknotesCount) {
        for (int i = 0; i < 5; i++) {
            this.counts[i] += banknotesCount[i];
        }
    }
    
    public int[] withdraw(int amount) {
        int[] withdraw_counts = new int[5];
        int remaining_amount = amount;

        for (int i = 4; i >= 0; i--) {
            int value = this.denominations[i];
            int available_notes = this.counts[i];

            if (remaining_amount == 0) {
                break;
            }
            
            if (available_notes > 0 && remaining_amount >= value) {
                int notes_to_take = Math.min(remaining_amount / value, available_notes);
                
                withdraw_counts[i] = notes_to_take;
                remaining_amount -= notes_to_take * value;
            }
        }

        if (remaining_amount == 0) {
            for (int i = 0; i < 5; i++) {
                this.counts[i] -= withdraw_counts[i];
            }
            return withdraw_counts;
        } else {
            return new int[]{-1};
        }
    }
}

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

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Problem Info

Description

Problem 2241: Design an ATM Machine - Detailed explanation and solution approaches.

Topics

Array Greedy Design

Companies

Yandex

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2241

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Initialize the ATM with the denominations [20, 50, 100, 200, 500] and an array to store the count of each denomination, initially set to 0.
2
Step 2: Implement the `deposit` function. For each denomination, add the deposited amount to the corresponding count in the `counts` array.
3
Step 3: Implement the `withdraw` function. Create an array `withdraw_counts` to track the banknotes to dispense.
4
Step 4: Iterate through the denominations array from largest to smallest (500 to 20).
5
Step 5: For each denomination, calculate how many banknotes can be dispensed without exceeding the `remaining_amount` and without exceeding the available number of banknotes of that denomination.
6
Step 6: Update `withdraw_counts` with the number of banknotes to dispense for the current denomination and reduce the `remaining_amount`.
7
Step 7: After iterating through all denominations, check if `remaining_amount` is 0. If it is, update the ATM's `counts` array by subtracting the dispensed banknotes.
8
Step 8: If `remaining_amount` is 0, return the `withdraw_counts` array. Otherwise, return `[-1]`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(1) because the loop iterates a fixed number of times (5 denominations). The space complexity is O(1) as the algorithm uses a fixed amount of extra space regardless of the input amount. The number of denominations is fixed, and the counts array always has a size of 5.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Dynamic Programming

A dynamic programming approach could be used to find the optimal combination of banknotes to withdraw. However, it is less efficient due to increased time and space complexity.

Time: O(amount * number of denominations)Space: O(amount)

Trade-offs: This approach is overkill for this problem, as the greedy approach is sufficient and more efficient. DP would be suitable if minimizing the *number* of banknotes was desired, but the problem statement prioritizes larger bills.

✨

Key Insights

1Insight 1: The problem emphasizes a greedy approach for the withdraw operation, prioritizing larger denominations first.
2Insight 2: The ATM's state (number of banknotes of each denomination) needs to be maintained consistently after each operation.
3Insight 3: Careful handling of edge cases is crucial to avoid errors and ensure correct operation, particularly when the exact amount cannot be withdrawn.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Greedy Algorithm

Making the best choice at each step without looking ahead.

Edge Cases

Edge case 1: Attempting to withdraw an amount larger than the ATM's total value. The algorithm correctly returns [-1] as the remaining amount will not be zero.
Edge case 2: The ATM does not have the exact denominations to fulfill the request. The algorithm prioritizes larger denominations, and if it can't make up the difference, it returns [-1].
Edge case 3: Withdrawing zero amount, the withdraw function returns an empty array and doesn't modify any counts, which in effect is the same as the amount not being withdrawable and returning [-1].
Edge case 4: The amount can only be satisfied using smaller denominations when larger ones are available but are needed to use. The Greedy approach used correctly prioritizes the larger denominations making sure that the ATM utilizes them as much as possible.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Failing to update the ATM's inventory after a successful withdrawal, leading to incorrect counts for subsequent operations.

✗Common mistake 2: Not prioritizing larger denominations during the withdrawal process, which can result in incorrect or impossible withdrawals.

✗Common mistake 3: Integer overflow. Using 'int' type may not be sufficient if banknotesCount[i] has large values or amount is very large. The problem mentions sum of `banknotesCount[i]` in all deposits doesn't exceed 10^9, so an int is fine. However, in C, it is very important to check for malloc failure.

✗Common mistake 4: Not handling the case where the remaining amount is not zero after attempting to withdraw, leading to incorrect results.

✗Common mistake 5: Using division instead of floor division when determining the number of bills to withdraw from a particular denomination, leading to overestimation of bills needed.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Implementing cash withdrawal logic in ATM machines, where the system needs to efficiently dispense cash using available denominations.

🏦Real-world scenario 2: Optimizing inventory management in banks or retail stores, where minimizing the number of banknotes or coins held is desirable while still meeting customer demand.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: August 21, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What are common greedy problem patterns?

Activity selection (sort by end time), interval scheduling (sort by start/end), Huffman coding (always combine smallest), fractional knapsack (sort by value/weight ratio), and minimum spanning tree. Look for problems where local decisions don't affect future options.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Design an ATM Machine"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether greedy techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?