Leetcode_BestTimeToBuyAndSellStockIV.cpp

/*

Problem No:-188

You are given an integer array prices where prices[i] is the price of a given stock on the ith day, and an integer k.

Find the maximum profit you can achieve. You may complete at most k transactions.

Note: 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:

1 <= k <= 100
1 <= prices.length <= 1000
0 <= prices[i] <= 1000

*/


class Solution {
public:
    int maxProfit(int k, vector<int>& prices) {
        if (k == 0) return 0;
        if (k >= prices.size()/2) {
            int s = 0;
            for (int i = 1; i < prices.size(); ++i)
                s += max(prices[i] - prices[i-1], 0);
            return s;
        }
        vector<int> v1(k, INT_MIN);
        vector<int> v2(k, 0);
        for (int price : prices)
            for (int i = 0; i < k; ++i) {
                v1[i] = max(v1[i], (i > 0 ? v2[i-1] : 0) - price);
                v2[i] = max(v2[i], v1[i] + price);
            }
        return v2.back();
        
    }
};