Best Time to Buy and Sell Stock with Transaction Fee

You are given an array prices where prices[i] is the price of a given stock on the i^th day, and an integer fee representing a transaction fee.

Find the maximum profit you can achieve. You may complete as many transactions as you like, but you need to pay the transaction fee for each transaction.

Note:

  • You may not engage in multiple transactions simultaneously; you must sell the stock before you buy again.
  • The transaction fee is only charged once for each stock purchase and sale.
Example 1
Inputprices = [1,3,2,8,4,9], fee = 2
Output8
The maximum profit is achieved by buying at prices[0] = 1, selling at prices[3] = 8, buying at prices[4] = 4, and selling at prices[5] = 9, for a total profit of ((8 - 1) - 2) + ((9 - 4) - 2) = 8.
Example 2
Inputprices = [1,3,7,5,10,3], fee = 3
Output6
The maximum profit achievable with a transaction fee of 3 is 6.

Constraints

  • 1 <= prices.length <= 5 * 10^4
  • 1 <= prices[i] < 5 * 10^4
  • 0 <= fee < 5 * 10^4

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