123. Best Time to Buy and Sell Stock III

Description

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

 

Solutions

Solution: Dynamic Programming

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

 

JavaScript

/**
 * @param {number[]} prices
 * @return {number}
 */
const maxProfit = function (prices) {
  const first = { sell: 0, buy: Number.MIN_SAFE_INTEGER };
  const second = { sell: 0, buy: Number.MIN_SAFE_INTEGER };

  for (const price of prices) {
    second.sell = Math.max(second.sell, second.buy + price);
    second.buy = Math.max(second.buy, first.sell - price);
    first.sell = Math.max(first.sell, first.buy + price);
    first.buy = Math.max(first.buy, -price);
  }
  return second.sell;
};