What is the time complexity of Best Time to Buy and Sell Stock II?

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

What data structures are used to solve Best Time to Buy and Sell Stock II?

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

What are the key insights for solving Best Time to Buy and Sell Stock II?

Insight 1: The greedy approach works here because we can make independent decisions on each day. If the price tomorrow is higher than today, we buy today and sell tomorrow to make a profit. Insight 2: We don't need to keep track of buy and sell days specifically. We just need to accumulate the profit whenever there's an increase in price from one day to the next.

Which companies ask LeetCode 122. Best Time to Buy and Sell Stock II in interviews?

This problem is frequently asked at Agoda, CTC, Capital One, Citadel, DE Shaw and 23 more companies.

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Best Time to Buy and Sell Stock II - LeetCode 122 Solution

Best Time to Buy and Sell Stock II - Complete Solution Guide

Best Time to Buy and Sell Stock II is LeetCode problem 122, 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

You are given an integer array prices where prices[i] is the price of a given stock on the i th day. On each day, you may decide to buy and/or sell the stock. You can only hold at most one share of the stock at any time. However, you can sell and buy the stock multiple times on the same day , ensuring you never hold than one share of the stock. Find and return the maximum profit you can achieve . Example 1: Input: prices = [7,1,5,3,6,4] Output: 7 Explanation: Buy on day 2 (price = 1) and sell on

Detailed Explanation

The problem requires you to find the maximum profit you can make by buying and selling a stock multiple times, given an array `prices` where `prices[i]` is the price of the stock on day `i`. You can buy and sell on the same day, but you can only hold one share of the stock at a time. The goal is to maximize the total profit from these transactions.

Solution Approach

The solution uses a greedy approach. It iterates through the `prices` array and checks if the current day's price is higher than the previous day's price. If it is, it adds the difference between the two prices to the `total_profit`. This approach is based on the principle that we should buy when the price is low and sell when the price is high, and we can repeat this process as many times as possible.

Step-by-Step Algorithm

Step 1: Initialize `total_profit` to 0.
Step 2: Iterate through the `prices` array starting from the second day (index 1).
Step 3: For each day, compare the price with the previous day's price.
Step 4: If the current day's price is greater than the previous day's price, calculate the difference and add it to `total_profit`.
Step 5: After iterating through all the days, return `total_profit`.

Key Insights

Insight 1: The greedy approach works here because we can make independent decisions on each day. If the price tomorrow is higher than today, we buy today and sell tomorrow to make a profit.
Insight 2: We don't need to keep track of buy and sell days specifically. We just need to accumulate the profit whenever there's an increase in price from one day to the next.
Insight 3: The problem allows for multiple transactions within the same day, which simplifies the logic to only consider increasing price differences.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Dynamic Programming, Greedy.

Companies

Asked at: Agoda, CTC, Capital One, Citadel, DE Shaw, Deutsche Bank, Geico, Goldman Sachs, Groww, Infosys, Intel, J.P. Morgan, Media.net, Nike, Paytm, PhonePe, Qualcomm, Rakuten, Salesforce, TikTok, Uber, Walmart Labs, Wells Fargo, Yahoo, Yandex, Zoho, eBay, tcs.

Best Time to Buy and Sell Stock II | LeetCode 122

Medium

Array Dynamic Programming Greedy

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

Solution Code

Available in:

class Solution {
    public int maxProfit(int[] prices) {
        int total_profit = 0;
        for (int i = 1; i < prices.length; i++) {
            if (prices[i] > prices[i-1]) {
                total_profit += prices[i] - prices[i-1];
            }
        }
        return total_profit;
    }
}

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Problem Info

Description

Problem 122: Best Time to Buy and Sell Stock II - Detailed explanation and solution approaches.

Topics

Array Dynamic Programming Greedy

Companies

AgodaCTCCapital OneCitadelDE ShawDeutsche BankGeicoGoldman Sachs

Stats

Difficulty:Medium

Languages:4

Companies:28

Problem #:122

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

5 steps

1
Step 1: Initialize `total_profit` to 0.
2
Step 2: Iterate through the `prices` array starting from the second day (index 1).
3
Step 3: For each day, compare the price with the previous day's price.
4
Step 4: If the current day's price is greater than the previous day's price, calculate the difference and add it to `total_profit`.
5
Step 5: After iterating through all the days, return `total_profit`.

💡

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 we iterate through the input array once. The space complexity is constant because we only use a few variables that do not depend on 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

Dynamic Programming

This can be solved using Dynamic Programming. We can maintain two states: `holding` (whether we are holding a stock) and `not_holding`. We transition between these states based on the prices.

Time: O(n)Space: O(n) or O(1) with optimization.

Trade-offs: While DP also has O(n) time complexity, it can be less intuitive and requires more code than the greedy approach. The O(n) space complexity can be reduced to O(1) but the code becomes harder to read. The greedy approach is therefore generally preferred for this problem due to its simplicity and efficiency.

✨

Key Insights

1Insight 1: The greedy approach works here because we can make independent decisions on each day. If the price tomorrow is higher than today, we buy today and sell tomorrow to make a profit.
2Insight 2: We don't need to keep track of buy and sell days specifically. We just need to accumulate the profit whenever there's an increase in price from one day to the next.
3Insight 3: The problem allows for multiple transactions within the same day, which simplifies the logic to only consider increasing price differences.

📚

Key Terms Explained

For Students

Array

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

Dynamic Programming

Breaking complex problems into smaller subproblems and storing results.

Greedy Algorithm

Making the best choice at each step without looking ahead.

Edge Cases

Edge case 1: `prices` array is empty or has only one element. In this case, the loop will not execute, and the initial `total_profit` of 0 will be returned, which is the correct answer.
Edge case 2: `prices` array is strictly decreasing (e.g., [7, 6, 5, 4, 3, 1]). The condition `prices[i] > prices[i-1]` will never be true, so `total_profit` will remain 0, which is the correct answer.
Edge case 3: `prices` array is strictly increasing (e.g., [1, 2, 3, 4, 5]). The algorithm correctly adds the difference between consecutive elements to the `total_profit`, resulting in the maximum possible profit (5-1 = 4).
Edge case 4: `prices` array has fluctuating prices (e.g., [7, 1, 5, 3, 6, 4]). The algorithm correctly identifies all the increasing trends (1->5 and 3->6) and sums their profits (5-1 + 6-3 = 7).

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Trying to find the global minimum and maximum and subtracting them. This won't work if there are multiple buy/sell opportunities.

✗Common mistake 2: Using a brute-force approach to try all possible buy/sell combinations, which would result in an exponential time complexity and exceed the time limit.

✗Common mistake 3: Forgetting to handle edge cases like an empty or decreasing `prices` array.

✅

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: Algorithmic trading - This algorithm can be used as a simplified model for identifying short-term profit opportunities in stock trading.

🏦Real-world scenario 2: Resource management - Similar logic can be applied to optimize the usage of resources (e.g., electricity) based on fluctuating costs, buying when cheap and selling/using when expensive.

💡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

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ 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: October 1, 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

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

@InterviewProJul 14

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

@CodeNinjaJul 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 identify if a problem needs dynamic programming?

DP problems typically have: 1) Overlapping subproblems (same calculation repeated), 2) Optimal substructure (optimal solution uses optimal solutions to subproblems). Look for keywords like "minimum/maximum," "count ways," "is it possible," or "longest/shortest."

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

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 "Best Time to Buy and Sell Stock II"?

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 dynamic programming techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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