Maximum profit of transactions

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Problem description

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).

Sample Input1:

3 3 5 0 0 3 1 4

Sample Output1:

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.

Sample Input2:

1 2 3 4 5

Sample Output2:

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.