LeetCode:Best Time to Buy and Sell Stock with Transaction Fee
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题目:
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.Note:
0 < prices.length <= 50000.
0 < prices[i] < 50000.
0 <= fee < 50000
Example:
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.
思路:
这次的题目的不同之处是每一次卖出股票时需要交一定的交易费用,交易次数没有限制。
和之前一样,这次还是用动态规划的思想:维护两个变量,buy[i](第 i+1 天为买进的最大利润)和 sell[i](第 i+1 天为卖出股票的最大利润)。显然,第一天不可能卖出股票,所以buy[0] = -prices[0],sell[0] = 0。它们的状态转移方程为:
buy[i] = max(sell[i-1] - prices[i], buy[i-1]);
sell[i] = max(buy[i-1] + prices[i] - fee, sell[i-1]);
代码:
class Solution {public: int maxProfit(vector<int>& prices, int fee) { int len = prices.size(); if (len == 0) return 0; int buy[len+1] = {0}; int sell[len+1] = {0}; buy[0] = -prices[0]; sell[0] = 0; for (int i = 1; i < len; i++) { buy[i] = max(sell[i-1] - prices[i], buy[i-1]); sell[i] = max(buy[i-1] + prices[i] - fee, sell[i-1]); } return sell[len-1]; }};
复杂度分析:
时间复杂度:O(n)
空间复杂度:O(n)
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