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 ith day.

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

Notice that 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:


Solution:

class Solution {
    public int maxProfit(int k, int[] prices) {
        int n = prices.length;
        if (n == 0) return 0;
        // (i, j, k) = max profit on day i with or w/ stock, with at most k txns
        int[][][] dp = new int[n][2][k + 1];
        dp[0][1][0] = Integer.MIN_VALUE;
        for (int i = 1; i <= k; i ++) {
            dp[0][1][i] = -prices[0];
        }
        int max = 0;
        for (int i = 1; i < n; i ++) {
            for (int j = k; j > 0; j --) {
                dp[i][0][j] = Math.max(dp[i - 1][0][j], dp[i - 1][1][j] + prices[i]);
                dp[i][1][j] = Math.max(dp[i - 1][1][j], dp[i - 1][0][j - 1] - prices[i]);
                max = Math.max(max, dp[i][0][j]);
            }
        }

        return max;
    }
}