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## Problem

You are given an array prices where prices[i] is the price of a given stock on the ith day.

Find the maximum profit you can achieve. You may complete at most two transactions.

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

Example 1:

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


## Code

class Solution {
public int maxProfit(int[] prices) {
int t1Cost = Integer.MAX_VALUE,
t2Cost = Integer.MAX_VALUE;
int t1Profit = 0,
t2Profit = 0;

for (int price : prices) {
// the maximum profit if only one transaction is allowed
t1Cost = Math.min(t1Cost, price);
t1Profit = Math.max(t1Profit, price - t1Cost);
// reinvest the gained profit in the second transaction
t2Cost = Math.min(t2Cost, price - t1Profit);
t2Profit = Math.max(t2Profit, price - t2Cost);
}

return t2Profit;
}
}