188. Best Time to Buy and Sell Stock IV

https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/

Problem

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 <= 109

• 0 <= prices.length <= 1000

• 0 <= prices[i] <= 1000

Solution

class Solution {
public:
    int maxProfit(int k, vector<int>& prices) {
        if (k == 0 || prices.empty()) return 0;
        vector<int> buy(k, INT_MIN);
        vector<int> sell(k, 0);
        for (const auto p: prices) {
            for (int i = 0; i < k; ++i) {
                buy[i] = (i == 0) ? max(buy[i], -p) : max(buy[i], sell[i - 1] - p);
                sell[i] = max(sell[i], buy[i] + p);
            }
        }
        return sell.back();
    }
};

• #dp