714. Best Time to Buy and Sell Stock with Transaction Fee

1. Description

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 (i.e., you must sell the stock before you buy again).
• The transaction fee is only charged once for each stock purchase and sale.

2. Example

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

3. Constraints

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

4. Solutions

Dynamic Programming

n = prices.size()
Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    int maxProfit(const vector<int> &prices, int fee) {
        const int n = prices.size();
        array<array<int, 2>, 2> profits{{-prices[0], 0}};

        for (int i = 1; i < n; ++i) {
            profits[1][0] = max(profits[0][0], profits[0][1] - prices[i]);
            profits[1][1] = max(profits[0][1], prices[i] + profits[0][0] - fee);

            swap(profits[0], profits[1]);
        }

        return profits[0][1];
    }
};