What is the time complexity of Lemonade Change?

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

What data structures are used to solve Lemonade Change?

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

What are the key insights for solving Lemonade Change?

Insight 1: The order of bills matters significantly. You must process them in the order given. Insight 2: You only need to keep track of the number of $5 and $10 bills you have, as you can always use them to make change.

Which companies ask LeetCode 860. Lemonade Change in interviews?

This problem is frequently asked at Zalando.

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Lemonade Change - LeetCode 860 Solution

Lemonade Change - Complete Solution Guide

Lemonade Change is LeetCode problem 860, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

At a lemonade stand, each lemonade costs $5 . Customers are standing in a queue to buy from you and order one at a time (in the order specified by bills). Each customer will only buy one lemonade and pay with either a $5 , $10 , or $20 bill. You must provide the correct change to each customer so that the net transaction is that the customer pays $5 . Note that you do not have any change in hand at first. Given an integer array bills where bills[i] is the bill the i th customer pays, return true

Detailed Explanation

The problem simulates a lemonade stand where each lemonade costs $5. Customers pay with $5, $10, or $20 bills. The goal is to determine if you can always provide the correct change to each customer, given the order of their payments. You start with no change in hand. If at any point you cannot give the correct change, you return `false`; otherwise, you return `true`.

Solution Approach

The provided code uses a greedy approach. It iterates through the `bills` array and keeps track of the number of $5 and $10 bills you have. For each customer, it checks if you have sufficient change to give back. If a customer pays with a $5 bill, you increment the count of $5 bills. If they pay with a $10 bill, you check if you have a $5 bill to give as change. If they pay with a $20 bill, you first try to use a $10 bill and a $5 bill. If that's not possible, you check if you have at least three $5 bills. If neither condition is met, you cannot provide the correct change and return `false`. If you can serve all customers, you return `true`.

Step-by-Step Algorithm

Step 1: Initialize variables `five` and `ten` to 0 to represent the count of $5 and $10 bills, respectively.
Step 2: Iterate through the `bills` array.
Step 3: If the current bill is $5, increment `five`.
Step 4: If the current bill is $10, check if `five > 0`. If so, decrement `five` and increment `ten`. Otherwise, return `false`.
Step 5: If the current bill is $20, first check if both `ten > 0` and `five > 0`. If so, decrement both `ten` and `five`. Otherwise, check if `five >= 3`. If so, decrement `five` by 3. Otherwise, return `false`.
Step 6: After iterating through all the bills, if no `false` has been returned, return `true`.

Key Insights

Insight 1: The order of bills matters significantly. You must process them in the order given.
Insight 2: You only need to keep track of the number of $5 and $10 bills you have, as you can always use them to make change.
Insight 3: Prioritize using a $10 bill and a $5 bill to give change before using three $5 bills, as this maximizes your chances of having enough $5 bills for future transactions.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Greedy.

Companies

Asked at: Zalando.

Lemonade Change | LeetCode 860

Easy

Array Greedy

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

Solution Code

Available in:

class Solution {
    public boolean lemonadeChange(int[] bills) {
        int five = 0;
        int ten = 0;
        for (int bill : bills) {
            if (bill == 5) {
                five++;
            } else if (bill == 10) {
                if (five > 0) {
                    five--;
                    ten++;
                } else {
                    return false;
                }
            } else {
                if (ten > 0 && five > 0) {
                    ten--;
                    five--;
                } else if (five >= 3) {
                    five -= 3;
                } else {
                    return false;
                }
            }
        }
        return true;
    }
}

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Problem Info

Description

Problem 860: Lemonade Change - Detailed explanation and solution approaches.

Topics

Array Greedy

Companies

Zalando

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:860

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

6 steps

1
Step 1: Initialize variables `five` and `ten` to 0 to represent the count of $5 and $10 bills, respectively.
2
Step 2: Iterate through the `bills` array.
3
Step 3: If the current bill is $5, increment `five`.
4
Step 4: If the current bill is $10, check if `five > 0`. If so, decrement `five` and increment `ten`. Otherwise, return `false`.
5
Step 5: If the current bill is $20, first check if both `ten > 0` and `five > 0`. If so, decrement both `ten` and `five`. Otherwise, check if `five >= 3`. If so, decrement `five` by 3. Otherwise, return `false`.
6
Step 6: After iterating through all the bills, if no `false` has been returned, return `true`.

💡

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(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is linear because the algorithm processes each bill in the `bills` array exactly once. The space complexity is constant because the algorithm uses a fixed number of variables, regardless of the input size.

📖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

Using a Dictionary to Store Bill Counts

Instead of using separate variables for $5 and $10 bills, you could use a dictionary (or hash map) to store the counts. The logic would remain similar.

Time: O(n)Space: O(1) since dictionary stores max two types of bills.

Trade-offs: This approach adds a small overhead due to dictionary operations and may be slightly less readable than using separate variables, but could be useful for more bill denominations.

✨

Key Insights

1Insight 1: The order of bills matters significantly. You must process them in the order given.
2Insight 2: You only need to keep track of the number of $5 and $10 bills you have, as you can always use them to make change.
3Insight 3: Prioritize using a $10 bill and a $5 bill to give change before using three $5 bills, as this maximizes your chances of having enough $5 bills for future transactions.

📚

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: The first customer pays with a $10 or $20 bill. In this case, you cannot give change because you start with no bills, and the algorithm correctly returns `false`.
Edge case 2: A long sequence of $20 bills. The algorithm correctly prioritizes using a $10 and $5 bill before using three $5 bills. This is essential for minimizing the chance of running out of $5 bills.
Edge case 3: Only $5 bills are presented. The algorithm will return True since no change is needed.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not prioritizing using a $10 and $5 bill when giving change for a $20 bill. This can lead to running out of $5 bills unnecessarily.

✗Common mistake 2: Not handling the case where you need to give change for a $20 bill but only have three $5 bills.

✗Common mistake 3: Incorrectly assuming that the bills are sorted and that you can calculate the required change beforehand. The order of bills matters, and the change must be calculated iteratively.

✅

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: Simulating cash transactions in a point-of-sale system. Determining if a cashier has sufficient change to handle a series of customer purchases.

🏦Real-world scenario 2: Resource allocation problems. Allocating limited resources (like different denominations of currency) to fulfill a sequence of requests, with the constraint of minimizing waste or running out of resources.

🎮Real-world scenario 3: Inventory Management: Determining if a retailer has enough inventory to satisfy a series of orders.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

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

👨‍💻 From Experience

This is one of the first problems I solved when learning Array. It's a great foundation for more complex problems.

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: October 19, 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

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 14

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

@AlgoMasterJul 7

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How do I verify if a greedy approach is correct?

Prove the greedy choice property: the locally optimal choice leads to globally optimal solution. Use exchange argument: show that swapping any element with the greedy choice doesn't improve the solution. If you can't prove it, test extensively or consider DP.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Lemonade Change"?

For this easy-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.

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