123. Best Time to Buy and Sell Stock III

Leetcode Array Dynamic Programming

Say you have an array for which the $i^{th}$ 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.

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