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.

 public int maxProfit(int k, int[] prices) {
        int len = prices.length;
        if (k >= len / 2) return quickSolve(prices);

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


    private int quickSolve(int[] prices) {
        int len = prices.length, profit = 0;
        for (int i = 1; i < len; i++)
            // as long as there is a price gap, we gain a profit.
            if (prices[i] > prices[i - 1]) profit += prices[i] - prices[i - 1];
        return profit;
    }