Best Time to Buy and Sell Stock IV

Hard

Arrays Dynamic Programming Dynamic Programming

Problem

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

Find the maximum profit you can achieve. You may complete at most k transactions: i.e., you may buy at most k times and sell at most k times.

Note: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).

Constraints

1 <= k <= 100
1 <= prices.length <= 1000
0 <= prices[i] <= 1000

Examples

Input: k = 2, prices = [2,4,1]

Output: 2

Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4 - 2 = 2.

Input: k = 2, prices = [3,2,6,5,0,3]

Output: 7

Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6 - 2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3 - 0 = 3. Total profit = 4 + 3 = 7.

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