"""
Title:  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.

"""


from typing import List


class Solution:

    def maxProfit(self, prices: List[int]) -> int:
        n = len(prices)
        if n < 2:
            return 0

        p1, p2 = prices[0], prices[n - 1]
        profit1, profit2 = [0] * n, [0] * n

        for i in range(1, n):
            profit1[i] = max(profit1[i - 1], prices[i] - p1)
            p1 = min(p1, prices[i])

            j = n - 1 - i
            profit2[j] = max(profit2[j + 1], p2 - prices[j])
            p2 = max(p2, prices[j])

        profit = 0

        for i in range(n):
            profit = max(profit, profit1[i] + profit2[i])
        return profit


def test(got, expected):
    if got == expected:
        prefix = ' OK '
    else:
        prefix = '  X '
    print('{} got: {} expected: {}'.format(prefix, repr(got), repr(expected)))


if __name__ == "__main__":
    solution = Solution()

    test(solution.maxProfit([3,3,5,0,0,3,1,4]), 6)
    test(solution.maxProfit([1,2,3,4,5]), 4)
    test(solution.maxProfit([7,6,4,3,1]), 0)

b64d5df1de219b11025083411608ed20af44821a
<mask token>


class Solution:

    def maxProfit(self, prices: List[int]) ->int:
        n = len(prices)
        if n < 2:
            return 0
        p1, p2 = prices[0], prices[n - 1]
        profit1, profit2 = [0] * n, [0] * n
        for i in range(1, n):
            profit1[i] = max(profit1[i - 1], prices[i] - p1)
            p1 = min(p1, prices[i])
            j = n - 1 - i
            profit2[j] = max(profit2[j + 1], p2 - prices[j])
            p2 = max(p2, prices[j])
        profit = 0
        for i in range(n):
            profit = max(profit, profit1[i] + profit2[i])
        return profit


<mask token>

<mask token>


class Solution:

    def maxProfit(self, prices: List[int]) ->int:
        n = len(prices)
        if n < 2:
            return 0
        p1, p2 = prices[0], prices[n - 1]
        profit1, profit2 = [0] * n, [0] * n
        for i in range(1, n):
            profit1[i] = max(profit1[i - 1], prices[i] - p1)
            p1 = min(p1, prices[i])
            j = n - 1 - i
            profit2[j] = max(profit2[j + 1], p2 - prices[j])
            p2 = max(p2, prices[j])
        profit = 0
        for i in range(n):
            profit = max(profit, profit1[i] + profit2[i])
        return profit


def test(got, expected):
    if got == expected:
        prefix = ' OK '
    else:
        prefix = '  X '
    print('{} got: {} expected: {}'.format(prefix, repr(got), repr(expected)))


<mask token>

<mask token>


class Solution:

    def maxProfit(self, prices: List[int]) ->int:
        n = len(prices)
        if n < 2:
            return 0
        p1, p2 = prices[0], prices[n - 1]
        profit1, profit2 = [0] * n, [0] * n
        for i in range(1, n):
            profit1[i] = max(profit1[i - 1], prices[i] - p1)
            p1 = min(p1, prices[i])
            j = n - 1 - i
            profit2[j] = max(profit2[j + 1], p2 - prices[j])
            p2 = max(p2, prices[j])
        profit = 0
        for i in range(n):
            profit = max(profit, profit1[i] + profit2[i])
        return profit


def test(got, expected):
    if got == expected:
        prefix = ' OK '
    else:
        prefix = '  X '
    print('{} got: {} expected: {}'.format(prefix, repr(got), repr(expected)))


if __name__ == '__main__':
    solution = Solution()
    test(solution.maxProfit([3, 3, 5, 0, 0, 3, 1, 4]), 6)
    test(solution.maxProfit([1, 2, 3, 4, 5]), 4)
    test(solution.maxProfit([7, 6, 4, 3, 1]), 0)

<mask token>
from typing import List


class Solution:

    def maxProfit(self, prices: List[int]) ->int:
        n = len(prices)
        if n < 2:
            return 0
        p1, p2 = prices[0], prices[n - 1]
        profit1, profit2 = [0] * n, [0] * n
        for i in range(1, n):
            profit1[i] = max(profit1[i - 1], prices[i] - p1)
            p1 = min(p1, prices[i])
            j = n - 1 - i
            profit2[j] = max(profit2[j + 1], p2 - prices[j])
            p2 = max(p2, prices[j])
        profit = 0
        for i in range(n):
            profit = max(profit, profit1[i] + profit2[i])
        return profit


def test(got, expected):
    if got == expected:
        prefix = ' OK '
    else:
        prefix = '  X '
    print('{} got: {} expected: {}'.format(prefix, repr(got), repr(expected)))


if __name__ == '__main__':
    solution = Solution()
    test(solution.maxProfit([3, 3, 5, 0, 0, 3, 1, 4]), 6)
    test(solution.maxProfit([1, 2, 3, 4, 5]), 4)
    test(solution.maxProfit([7, 6, 4, 3, 1]), 0)

"""
Title:  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.

"""


from typing import List


class Solution:

    def maxProfit(self, prices: List[int]) -> int:
        n = len(prices)
        if n < 2:
            return 0

        p1, p2 = prices[0], prices[n - 1]
        profit1, profit2 = [0] * n, [0] * n

        for i in range(1, n):
            profit1[i] = max(profit1[i - 1], prices[i] - p1)
            p1 = min(p1, prices[i])

            j = n - 1 - i
            profit2[j] = max(profit2[j + 1], p2 - prices[j])
            p2 = max(p2, prices[j])

        profit = 0

        for i in range(n):
            profit = max(profit, profit1[i] + profit2[i])
        return profit


def test(got, expected):
    if got == expected:
        prefix = ' OK '
    else:
        prefix = '  X '
    print('{} got: {} expected: {}'.format(prefix, repr(got), repr(expected)))


if __name__ == "__main__":
    solution = Solution()

    test(solution.maxProfit([3,3,5,0,0,3,1,4]), 6)
    test(solution.maxProfit([1,2,3,4,5]), 4)
    test(solution.maxProfit([7,6,4,3,1]), 0)
