Best Time to Buy and Sell Stock III.py

'''
Say you have an array for which the ith element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete at most two transactions.

Note: You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).

Example 1:

Input: [3,3,5,0,0,3,1,4]
Output: 6
Explanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
             Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.

Example 2:

Input: [1,2,3,4,5]
Output: 4
Explanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
             Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are
             engaging multiple transactions at the same time. You must sell before buying again.

Example 3:

Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.


'''

class Solution(object):
    def maxProfit(self, prices):
        """
        :type prices: List[int]
        :rtype: int
        """
        if len(prices) < 2:
            return 0
        
        k = 2
        buy = [float('-inf') for i in xrange(k)]
        sell = [0 for i in xrange(k)]
        
        for x in prices:
            buy[0] = max(buy[0], -x)
            sell[0] = max(sell[0], x + buy[0])
            for i in xrange(1, k):
                buy[i] = max(buy[i], sell[i-1] - x)
                sell[i] = max(sell[i], x + buy[i])
                
        return sell[-1]