Description
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.
Solutions
1. DP
# Time: O(n)
# Space: O(n)
class Solution:
def maxProfit(self, prices: List[int], fee: int) -> int:
if not prices or len(prices) <= 1:
return 0
n = len(prices)
buy = [0 for _ in range(n)]
sell = [0 for _ in range(n)]
buy[0] = -prices[0] - fee
for i in range(1, n):
buy[i] = max(buy[i - 1], sell[i - 1] - prices[i] - fee) # keep the same as day i-1, or buy from sell status at day i-1
sell[i] = max(sell[i - 1], buy[i - 1] + prices[i]) # keep the same as day i-1, or sell from buy status at day i-1
return sell[n - 1]
# 44/44 cases passed (920 ms)
# Your runtime beats 17.06 % of python3 submissions
# Your memory usage beats 12.5 % of python3 submissions (19.3 MB)