123. Best Time to Buy and Sell Stock III

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: 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.

Example 4:

Input: prices = [1]
Output: 0

Constraints:

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

# @lc code=start
using LeetCode

function max_profit_iii(prices::Vector{Int})::Int
    sell1 = sell2 = 0
    buy2 = buy1 = -prices[1]
    for i in 2:length(prices)
        sell2 = max(buy2 + prices[i], sell2)
        buy2 = max(sell1 - prices[i], buy2)
        sell1 = max(buy1 + prices[i], sell1)
        buy1 = max(buy1, -prices[i])
    end
    sell2
end
# @lc code=end

max_profit_iii (generic function with 1 method)

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