【Best Time to Buy and Sell Stock IV】

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

Example 1:

Input: k = 2, prices = [2,4,1]
Output: 2
Explanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.

Example 2:

Input: k = 2, prices = [3,2,6,5,0,3]
Output: 7
Explanation: 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.

Constraints:

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

Java Completion:

class Solution {
    public int maxProfit(int k, int[] prices) {
        if (prices.length == 0) return 0;
        int[] buy = new int[k + 1];
        int[] sell = new int[k + 1];
        Arrays.fill(buy, Integer.MIN_VALUE);
        for (int i = 0; i < prices.length; i++) {
            for (int j = 1; j <= k; j++) {
                buy[j] = Math.max(buy[j], sell[j - 1] - prices[i]);
                sell[j] = Math.max(sell[j], buy[j] + prices[i]);
            }
        }
        return sell[k];
    }
}