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:
0 <= k <= 100
0 <= prices.length <= 1000
0 <= prices[i] <= 1000
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;
}
}