Buy and Sell Stock 3

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.

**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.

Solution

Complexity:

• Time complexity: O(n)
• Space complexity: O(1)

function maxProfit(prices) {
    let buy1 = Number.MIN_SAFE_INTEGER;
    let sell1 = 0;
    let buy2 = Number.MIN_SAFE_INTEGER;
    let sell2 = 0;

    for (let i = 0; i < prices.length; i++) {
        buy1 = Math.max(buy1, -prices[i]);
        sell1 = Math.max(sell1, buy1 + prices[i]);
        buy2 = Math.max(buy2, sell1 - prices[i]);
        sell2 = Math.max(sell2, buy2 + prices[i]);
    }
    return sell2;
}