[leetcode] 714. 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] = 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.

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用maxProfit[i]记录前i个数据的最大收益。

用cashWhenHoldOne[i]表示对于前i个数据，在手中有且只有一个stock的情况下，手中现金的最大值。

则：

maxProfit[i] = max(maxProfit[i-1], cashWhenHoldOne[i-1] + prices[i] - fee);
cashWhenHoldOne[i] = max(cashWhenHoldOne[i-1], maxProfit[i-1] - prices[i]);

我的代码如下：

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