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Best Time to Buy and Sell Stock III

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15
Problem 27: Best Time to Buy and Sell Stock III

Write a C program to find the maximum profit you can achieve from buying and selling stocks. You are given an array prices where prices[i] is the price of a given stock on the ith day. Find the maximum profit you can achieve. You may complete at most two transactions. Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).

Example 1
    
      
  • Input: prices = [3,3,5,0,0,3,1,4]
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  • Output: 6
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  • Explanation: 
    • Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3. 
    • Buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3. 
    • Total profit = 3 + 3 = 6. 
    • This uses exactly 2 transactions and gives maximum profit.
    •
Example 2
    
      
  • Input: prices = [1,2,3,4,5]
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  • Output: 4
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  • Explanation: 
    • Buy on day 1 (price = 1) and sell on day 2 (price = 2), profit = 2-1 = 1. 
    • Buy on day 2 (price = 2) and sell on day 5 (price = 5), profit = 5-2 = 3. 
    • Total profit = 1 + 3 = 4. 
    • You can also buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 4.
    •
Constraints
    
      
  • 1 ≤ prices.length ≤ 10^5
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  • 0 ≤ prices[i] ≤ 10^5
    • 
      
  • You can complete at most 2 transactions
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  • Time Complexity: O(n)
    • 
      
  • Space Complexity: O(1)
    •
ArraysNumberWalmartD. E. Shaw
Editorial

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Hint
Solution

Solution Hints

    
      
  • Use state machine approach with four states for two transactions
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  • Track buy1, sell1, buy2, sell2 for maximum profit at each state
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  • buy1: maximum profit after first buy
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  • sell1: maximum profit after first sell
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  • buy2: maximum profit after second buy
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  • sell2: maximum profit after second sell
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  • Update states in single pass through prices array
    •

Steps to solve by this approach:

 Step 1: Initialize four state variables for tracking profit at each transaction state
 Step 2: buy1 represents maximum profit after first purchase (negative value initially)
 Step 3: sell1 represents maximum profit after first sale
 Step 4: buy2 represents maximum profit after second purchase
 Step 5: sell2 represents maximum profit after second sale (final answer)
 Step 6: For each day, update all states considering current stock price
 Step 7: Return sell2 as it represents maximum profit after completing at most 2 transactions

Submitted Code :