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# 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:**<br>

```
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`.

```java
class Solution {
    public int maxProfit(int[] prices, int fee) {
        int T_ik0 = 0, T_ik1 = Integer.MIN_VALUE;

        for (int price : prices) {
            int T_ik0_old = T_ik0;
            // If we want 0 stocks in our hand at end of ith day
            // Either take ans from 0 stock i-1th day
            // Or take ans from 1 stock i-1th day and sell it
            T_ik0 = Math.max(T_ik0, T_ik1 + price);
            // If we want 1 stock in our hand at end of ith day
            // Either take ans from 1 stock i-1th day
            // Or take ans from 0 stock i-1th day and but 1 stock at ith day
            // Also we are including fees when we buy stock
            T_ik1 = Math.max(T_ik1, T_ik0_old - price - fee);
        }

        return T_ik0;
    }
}
```