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## [LeetCode]123. Best Time to Buy and Sell Stock III

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 {
public int maxProfit(int[] prices) {
int dp_i10 = 0, dp_i11 = Integer.MIN_VALUE;
int dp_i20 = 0, dp_i21 = Integer.MIN_VALUE;

for(int price:prices){
dp_i20 = Math.max(dp_i20,dp_i21+price);
dp_i21 = Math.max(dp_i21,dp_i10-price);
dp_i10 = Math.max(dp_i10,dp_i11+price);
dp_i11 = Math.max(dp_i11,-price);
}
return dp_i20;
}
}```

Success

Runtime: 1 ms, faster than 99.83% of Java online submissions for Best Time to Buy and Sell Stock III.

Memory Usage: 37.3 MB, less than 100.00% of Java online submissions for Best Time to Buy and Sell Stock III.