Best Time to Buy and Sell Stock

Understanding how to maximize profit from stock prices is a critical skill in coding interviews and real-world stock trading scenarios. One of the most common problems that test this skill is the Best Time to Buy and Sell Stock problem. This challenge involves determining the best moment to buy low sell high using a single transaction for optimal gains. It also teaches fundamental concepts in financial optimization and basic market analysis.

In this tutorial, you will learn how to approach the problem efficiently by focusing on smart investment strategies and accurate profit calculation.

Problem Statement

Given a price array where each element represents the stock price on a particular day, your task is to find the maximum profit you can achieve by completing exactly one transaction — meaning you must buy low sell high once.

Example:
Input: [7, 1, 5, 3, 6, 4]
Output: 5
Explanation: Buy on day 2 (price = 1) and sell on day 5 (price = 6), maximize profit = 6 - 1 = 5.

The challenge lies in carefully analyzing the stock prices to pick the ideal days for a single transaction.

Brute Force Approach

A simple way to solve the problem is by checking every possible pair of days to buy low sell high and calculating the profit for each. This involves nested loops to scan through the price array.

Algorithm Steps:

• Traverse through the price array.
• For each day, compare it with every following day's stock prices.
• Perform a profit calculation and update the maximum profit accordingly.

Performance:

• Time Complexity: O(n²)
• Space Complexity: O(1)

Although this method works, it is inefficient for larger datasets and does not align with best practices in financial optimization or market analysis.

Optimized One-Pass Solution

To improve efficiency, a one-pass solution can be used where you track the minimum price while scanning the array and calculate the potential profit at each step.

Algorithm Steps:

• Initialize two variables: min_price to a large value and max_profit to zero.
• Traverse the price array once:
  • Update min_price if the current price is lower.
  • Calculate the potential profit calculation by subtracting min_price from the current price.
  • Update max_profit if the potential profit is higher.

Python Code Example:

1
2
3
4
5
6
7
8
9
def maxProfit(prices):
    min_price = float('inf')
    max_profit = 0
    for price in prices:
        if price < min_price:
            min_price = price
        elif price - min_price > max_profit:
            max_profit = price - min_price
    return max_profit

Performance:

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

This optimized method aligns perfectly with smart investment strategies and real-world stock trading approaches by minimizing time while maximizing return.

Key Concepts Behind the Strategy

Mastering this problem means understanding the balance between buy low sell high principles and efficient market analysis. Key points include:

• Always keep track of the minimum stock prices seen so far.
• Continuously perform profit calculation as you traverse the array.
• Stick to a single transaction to meet the problem's constraint.

Applying these principles ensures solid performance both in interviews and real-world financial optimization scenarios.

Variations of the Problem

Once you master the basic version, you can explore advanced variations like:

• Multiple transactions allowed
• Cooldown periods between buys
• Transaction fees included

Each variation requires a deeper look at investment strategy and advanced market analysis.

Interview Tips

When solving the Best Time to Buy and Sell Stock problem during interviews:

• Always explain your investment strategy before coding.
• Mention the importance of financial optimization.
• Discuss why a one-pass solution is preferable for large datasets.

This shows not only coding skills but also an analytical mindset similar to professionals handling real stock trading.

Conclusion

The Best Time to Buy and Sell Stock problem teaches you how to interpret stock prices, perform accurate profit calculations, and apply smart investment strategies. By mastering techniques like buy low sell high and optimizing for a single transaction, you improve both your coding skills and your understanding of essential financial optimization principles.

Practice these strategies, enhance your market analysis skills, and get ready to maximize profit in any coding challenge or real-world financial situation.