Best Time to Buy and Sell Stock with Transaction Fee

Your are given an array of integers prices, for which the i-th element is the price of a given stock on day i; and a non-negative integer fee representing a transaction fee.

You may complete as many transactions as you like, but you need to pay the transaction fee for each transaction. You may not buy more than 1 share of a stock at a time (ie. you must sell the stock share before you buy again.)

Return the maximum profit you can make.

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] = 1Selling at prices[3] = 8Buying at prices[4] = 4Selling at prices[5] = 9The total profit is ((8 - 1) - 2) + ((9 - 4) - 2) = 8.


Note:

0 < prices.length <= 50000.
0 < prices[i] < 50000.
0 <= fee < 50000.

Solution:

class Solution {
    public int maxProfit(int[] prices, int fee) {
        int n = prices.length;
        if (n == 0) return 0;
        // (i, j) = max profit on day i with or w/ stock
        int[][] dp = new int[n][2];
        dp[0][0] = 0;
        dp[0][1] = -prices[0] - fee;
        int max = 0;
        for (int i = 1; i < n; i ++) {
            dp[i][0] = Math.max(dp[i - 1][0], dp[i - 1][1] + prices[i]);
            dp[i][1] = Math.max(dp[i - 1][1], dp[i - 1][0] - prices[i] - fee);
            max = Math.max(max, dp[i][0]);
        }
        return max;
    }
}