Best Time to Buy and Sell Stock III 🚀

Welcome to CodeYourCraft! Today, we're going to delve into a fascinating problem known as "Best Time to Buy and Sell Stock III". This problem is a variation of the classic "Buy and Sell Stock" problem, and it's a great way to understand more about Algorithms and Data Structures. Let's get started! 🎯

Understanding the Problem 📝

Imagine you're a stock trader, and you're given an array prices that contains the daily price of a stock for some number of days. Your task is to maximize your profit by buying and selling this stock multiple times. Here's the catch: you can't hold more than two stocks at a time.

That means you can be in one of three states:

0: You have no stocks.
1: You have one stock purchased at a certain price.
2: You have two stocks, one bought at a lower price (first stock) and one bought at a higher price (second stock).

The goal is to calculate the maximum profit you can make from these transactions.

Walkthrough of the Solution 💡

Let's break down the problem into smaller parts and think about how we can approach it.

First, we need to identify the days where we should buy and sell stocks to make a profit.
Then, we need to keep track of the maximum profit we can make when holding either one or two stocks.
Finally, we'll calculate the overall maximum profit by iterating through the prices array.

Pseudocode 💻

let maximum_profit = 0
let first_buy_price = float('inf')
let second_sell_price = 0

for each day in prices:
  if current day price < first_buy_price:
    first_buy_price = current day price
    state = 0 (no stocks)
  elif current day price < second_sell_price:
    second_sell_price = current day price
    state = 1 (one stock)
  else:
    profit = second_sell_price - first_buy_price
    if profit > maximum_profit:
      maximum_profit = profit
      second_sell_price = current day price
      state = 2 (two stocks)
    first_buy_price = current day price
    state = 1 (one stock)

if state == 2:
  profit = second_sell_price - first_buy_price
  maximum_profit = max(maximum_profit, profit)

Coding the Solution 🔧

Now that we've designed the algorithm, let's see how we can implement it in code. We'll use Python as our programming language.

python

def max_profit(prices):
    maximum_profit = 0
    first_buy_price = float('inf')
    second_sell_price = 0

    for price in prices:
        if price < first_buy_price:
            first_buy_price = price
            state = 0
        elif price < second_sell_price:
            second_sell_price = price
            state = 1
        else:
            profit = second_sell_price - first_buy_price
            if profit > maximum_profit:
                maximum_profit = profit
                second_sell_price = price
                state = 2
            first_buy_price = price
            state = 1

    if state == 2:
        profit = second_sell_price - first_buy_price
        maximum_profit = max(maximum_profit, profit)

    return maximum_profit

Putting it all Together 🤝

Now that you understand the problem and the algorithm to solve it, try implementing the code on your own. Once you're done, you can test your solution using the following example:

python

prices = [3, 3, 5, 0, 0, 3, 1, 4]
print(max_profit(prices)) # Expected output: 6

Quiz Time 🧮

That's it for today! We hope you found this lesson informative and enjoyable. If you have any questions or need help with the code, feel free to reach out. Happy coding! 🌟