best-time-to-buy-and-sell-stock-with-transaction-fee.py

# Time:  O(n)
# Space: O(1)

# 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.

class Solution(object):
    def maxProfit(self, prices, fee):
        """
        :type prices: List[int]
        :type fee: int
        :rtype: int
        """
        cash, hold = 0, -prices[0]
        for i in xrange(1, len(prices)):
            cash = max(cash, hold+prices[i]-fee)
            hold = max(hold, cash-prices[i])
        return cash