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Best Time to Buy and Sell Stock III

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 15

Write a Java program to find the maximum profit that can be achieved by performing at most two transactions (buying and selling a stock). You are given an array prices where prices[i] is the price of a given stock on the ith day. You may complete at most two transactions, i.e., you may buy and sell the stock twice. You cannot engage in multiple transactions simultaneously (you must sell the stock before you buy again). Return the maximum profit.

Example 1
    
  
  • Input: prices = [3,3,5,0,0,3,1,4]
    • 
  
  • Output: 6
    • 
  
  • Explanation: Buy on day 3 (price = 0) and sell on day 5 (price = 3), profit = 3
Buy on day 6 (price = 1) and sell on day 7 (price = 4), profit = 3
Total profit = 3 + 3 = 6
    •
Example 2
    
  
  • Input: prices = [1,2,3,4,5]
    • 
  
  • Output: 4
    • 
  
  • Explanation: Buy on day 0 (price = 1) and sell on day 4 (price = 5), profit = 4
No second transaction is performed.
Total profit = 4
    •
Constraints
    
  
  • 1 <= prices.length <= 10^5
    • 
  
  • 0 <= prices[i] <= 10^5
    • 
  
  • You can make at most two transactions
    • 
  
  • Time Complexity: O(n)
    • 
  
  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Use a dynamic programming approach to track the maximum profit after different buy/sell operations
    • 
  
  • Track four variables representing different states: first buy, first sell, second buy, second sell
    • 
  
  • Update each state based on the previous state and the current price
    • 
  
  • Initialize first buy and second buy as -∞ (or a very negative number) as we start with no stock
    • 
  
  • The maximum profit will be the value of the second sell state at the end
    •

Steps to solve by this approach:

 Step 1: Define four variables to represent four states: firstBuy, firstSell, secondBuy, secondSell.

 Step 2: Initialize firstBuy and secondBuy to Integer.MIN_VALUE (since we start with no stock).

 Step 3: Initialize firstSell and secondSell to 0 (since we cannot sell without buying first).

 Step 4: Iterate through each price in the array.

 Step 5: Update firstBuy as the maximum of current firstBuy and negative of current price (representing the lowest cost to buy first stock).

 Step 6: Update firstSell as the maximum of current firstSell and firstBuy plus current price (representing the maximum profit after first sale).

 Step 7: Update secondBuy as the maximum of current secondBuy and firstSell minus current price (representing the lowest net cost after first transaction and second buy).

 Step 8: Update secondSell as the maximum of current secondSell and secondBuy plus current price (representing the maximum profit after both transactions).

 Step 9: Return secondSell as the final answer, which represents the maximum profit.

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