16. Best Time to Buy and Sell Stock with Transaction Fee.cpp

/*
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 ith 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 (i.e., you must sell the stock before you buy again).

Example 1:
Input: prices = [1,3,2,8,4,9], fee = 2
Output: 8
Explanation: The maximum profit can be achieved by:
- Buying at prices[0] = 1
- Selling at prices[3] = 8
- Buying at prices[4] = 4
- Selling at prices[5] = 9
The total profit is ((8 - 1) - 2) + ((9 - 4) - 2) = 8.

Example 2:
Input: prices = [1,3,7,5,10,3], fee = 3
Output: 6

Constraints:
1 < prices.length <= 5 * 104
0 < prices[i], fee < 5 * 104

Hint #1  
Consider the first K stock prices. At the end, the only legal states are that you don't own a share of stock, or that you do. Calculate the most profit you could have under each of these two cases.
*/

class Solution
{
public:
  int maxProfit(vector<int> &prices, int fee)
  {
    if (prices.size() <= 1)
      return 0;
    vector<vector<int>> dp(2, vector<int>(prices.size(), 0));
    dp[0][0] = 0;
    dp[1][0] = -prices[0] - fee;
    for (int i = 1; i < prices.size(); ++i)
    {
      dp[0][i] = max(dp[0][i - 1], dp[1][i - 1] + prices[i]);
      dp[1][i] = max(dp[1][i - 1], dp[0][i - 1] - prices[i] - fee);
    }
    return dp[0][prices.size() - 1];
  }
};