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] = 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.

  Note:

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

DP求解，程式如下所示：

class Solution {
    public int maxProfit(int[] prices, int fee) {
        int pre = prices[0], sum = 0;
        int profit = 0;
        for (int i = 1; i < prices.length; ++ i){
            sum += prices[i] - pre;
            if (sum > fee){
                profit += sum - fee;
                sum = fee;
            }
            else {
                if (sum < 0){
                    sum = 0;
                }
            }
            pre = prices[i];
        }
        return profit;
    }
}