3573 - Best Time to Buy and Sell Stock V.

Medium

You are given an integer array prices where prices[i] is the price of a stock in dollars on the <code>i^th</code> day, and an integer k.

You are allowed to make at most k transactions, where each transaction can be either of the following:

• Normal transaction: Buy on day i, then sell on a later day j where i < j. You profit prices[j] - prices[i].

• Short selling transaction: Sell on day i, then buy back on a later day j where i < j. You profit prices[i] - prices[j].

Note that you must complete each transaction before starting another. Additionally, you can't buy or sell on the same day you are selling or buying back as part of a previous transaction.

Return the maximum total profit you can earn by making at most k transactions.

Example 1:

Input: prices = 1,7,9,8,2, k = 2

Output: 14

Explanation:

We can make $14 of profit through 2 transactions:

• A normal transaction: buy the stock on day 0 for

  $1 then sell it on day 2 for $

  9.

• A short selling transaction: sell the stock on day 3 for

  $8 then buy back on day 4 for $

  2.

Example 2:

Input: prices = 12,16,19,19,8,1,19,13,9, k = 3

Output: 36

Explanation:

We can make $36 of profit through 3 transactions:

• A normal transaction: buy the stock on day 0 for

  $12 then sell it on day 2 for $

  19.

• A short selling transaction: sell the stock on day 3 for

  $19 then buy back on day 4 for $

  8.

• A normal transaction: buy the stock on day 5 for

  $1 then sell it on day 6 for $

  19.

Constraints:

• <code>2 <= prices.length <= 10³</code>

• <code>1 <= pricesi<= 10⁹</code>

• 1 <= k <= prices.length / 2