best-time-to-buy-and-sell-stock-iii.cpp

// 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(vector<int>& prices) {
        int s1 = 0,
            s2 = 0,
            b1 = -1<<31,
            b2 = -1<<31;
        for (auto i : prices) {
            b1 = std::max(b1, -i);
            s1 = std::max(s1, b1+i);
            b2 = std::max(b2, s1-i);
            s2 = std::max(s2, b2+i);
        }
        return s2;
    }
};