LeetCode-Best Time to Buy and Sell Stock IV

Say you have an array for which the i^th element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete at most k transactions.

Note:
You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.

Analysis:

DP formula is

hold[i][j] = Math.max(hold[i][j-1], unhold[i][j-1]-prices[j]);

unhold[i][j] = Math.max(unhold[i][j-1], hold[i-1][j-1]+prices[j]);

Solution:

public class Solution {
    public int maxProfit(int k, int[] prices) {
        if (prices.length<2) return 0;
        int len = prices.length;
        
        // IMPORTANT: you can skip calculation if you are allowed to perform the max times of transactions. 
        if (k>=len/2){
            int profit = 0;
            for (int i=1;i<len;i++)
                if (prices[i] > prices[i-1])
                    profit += (prices[i] - prices[i-1]);
            return profit;
        }
        
        int[] hold = new int[len];
        int[] unhold = new int[len];
        
        hold[0] = -prices[0];
        for (int i=1;i<len;i++)
            hold[i] = Math.max(hold[i-1], -prices[i]);

        
        for (int i=1;i<=k;i++){
            int lastHold = hold[0];
            hold[0] = -prices[0];
            for (int j=1;j<len;j++){
                lastHold = hold[j];
                hold[j] = Math.max(hold[j-1], unhold[j-1]-prices[j]);
                unhold[j] = Math.max(unhold[j-1], lastHold+prices[j]);
            }
        }
            
        return Math.max(hold[len-1],unhold[len-1]);
    }
}