两次交易最大利润

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Estoy viendo el código Python maxProfit(prices) para calcular ganancias máximas en trading, asegurándome de que realice al menos dos transacciones.

Análisis de beneficios en transacciones

The confusion arises from interpreting the loop iterations as multiple transactions. However, the loop is not performing transactions but rather updating the potential profits of up to two transactions as it iterates through the prices.

Here's how the code works:

1. Variables Initialization:

   • buy1: Maximum profit after buying the first stock (initialized to negative infinity to represent the maximum loss).
   • sell1: Maximum profit after selling the first stock.
   • buy2: Maximum profit after buying the second stock (taking into account the profit from the first sale).
   • sell2: Maximum profit after selling the second stock.

2. Loop Execution:

   • The loop iterates over each price in the prices list.
   • At each price point, the algorithm updates the four variables to reflect the best possible outcomes so far.

3. Understanding the Updates:

   • buy1 = max(buy1, -price):
     • Determines the maximum profit after buying the first stock at the lowest price seen so far.
   • sell1 = max(sell1, buy1 + price):
     • Calculates the maximum profit after selling the first stock at the highest price after the lowest buy price.
   • buy2 = max(buy2, sell1 - price):
     • Determines the maximum profit after buying the second stock, considering the profit from the first sale.
   • sell2 = max(sell2, buy2 + price):
     • Calculates the maximum profit after selling the second stock.

4. Why It Doesn't Exceed Two Transactions:

   • Single Transactions: The variables buy1 and sell1 keep track of the first transaction (buying and selling once).
   • Second Transaction: The variables buy2 and sell2 handle the second transaction (buying and selling again).
   • At Most Two Transactions: Even though the loop runs for all price points, it only updates the maximum possible profits for up to two transactions. It does not execute more than two buys or sells.
   • State Tracking: The algorithm maintains the best possible state at each point without performing actual transactions.

5. Analogy:

   • Think of buy1, sell1, buy2, and sell2 as placeholders for the best possible outcomes rather than actions.
   • The loop evaluates all possibilities to update these placeholders but doesn't represent actual transactions being made in each iteration.

6. Example:

   • Suppose you have prices [3, 8, 5, 1, 7, 8].
   • The algorithm will find the best day to execute the first buy and sell (buy1 and sell1) and then the best day to execute the second buy and sell (buy2 and sell2).
   • It ensures that the second transaction happens after the first sale, adhering to the rules of stock trading (you can't sell stock you don't own).

7. Conclusion:

   • The loop's purpose is to explore all price points to find the optimal moments to perform up to two transactions.
   • It does not violate the "at most two transactions" constraint because it only tracks two buys and two sells throughout the entire process.

Additional Insight:

• Dynamic Programming Approach: This algorithm is a form of dynamic programming where we update the best possible profits based on previous computations.
• Time Complexity: The algorithm runs in O(n) time, making it efficient for large datasets.
• Constraint Adherence: By only using four variables to represent two transactions, it inherently limits the number of transactions regardless of the number of loop iterations.

Visual Representation:

Imagine plotting the stock prices on a graph. The algorithm scans through this graph once, updating the best opportunities to buy low and sell high twice. It doesn't jump back in time or perform more than two buy/sell actions. It simply keeps track of the optimal points as it moves forward.

Key Takeaway:

• The loop's iterations are not transactions themselves but opportunities to update the best possible outcomes for up to two transactions.
• The algorithm effectively finds the maximum profit achievable with at most two transactions by the end of the loop.

I hope this clarifies how the code works and why it doesn't exceed the two-transaction limit specified in the problem.