## Algorithm

Problem Nmae: 123. Best Time to Buy and Sell Stock III

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.
```

Constraints:

• `1 <= prices.length <= 105`
• `0 <= prices[i] <= 105`

## Code Examples

### #1 Code Example with C Programming

```Code - C Programming```

``````
int maxProfit(int* prices, int pricesSize) {
int sell1, sell2;   // max profit if I sell
int i;

sell1 = sell2 = 0;

for (i = 0; i < pricesSize; i ++) {
// possible profit
sell1 = sell1 > buy1  + prices[i] ? sell1 : buy1  + prices[i];
sell2 = sell2 > buy2  + prices[i] ? sell2 : buy2  + prices[i];
}

return sell2;
}
``````
Copy The Code &

Input

cmd
prices = [3,3,5,0,0,3,1,4]

Output

cmd
6

### #2 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const maxProfit = function(prices) {
let maxProfit1 = 0
let maxProfit2 = 0

for (let p of prices) {
maxProfit2 = Math.max(maxProfit2, p - lowestBuyPrice2)
maxProfit1 = Math.max(maxProfit1, p - lowestBuyPrice1)
}
return maxProfit2
}
``````
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Input

cmd
prices = [3,3,5,0,0,3,1,4]

Output

cmd
6

### #3 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def maxProfit(self, prices):
s1 = s2 = 0
b1 = b2 = -float("inf")
for p in prices:
if -p > b1: b1 = -p
if b1 + p > s1: s1 = b1 + p
if s1 - p > b2: b2 = s1 - p
if b2 + p > s2: s2 = b2 + p
return s2
``````
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Input

cmd
prices = [1,2,3,4,5]

Output

cmd
4

### #4 Code Example with C# Programming

```Code - C# Programming```

``````
using System;

namespace LeetCode
{
{
public int MaxProfit(int[] prices)
{
int sell1 = 0, sell2 = 0;

for (int i = 0; i < prices.Length; i++)
{
sell1 = Math.Max(sell1, prices[i] - buy1);
sell2 = Math.Max(sell2, prices[i] - buy2);
}

return sell2;
}
}
}
``````
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Input

cmd
prices = [1,2,3,4,5]