188. Best Time to Buy and Sell Stock IV

Problem Statement

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: i.e. you may buy at most k times and sell at most k times.

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

Intuition

Exactly same as III Problem just tries=2 is changed to k

Links

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

Video Links

https://www.youtube.com/watch?v=IV1dHbk5CDc&ab_channel=takeUforward

Approach 1:

Memoization

C++

class Solution {
public:
    int find_ans(vector<int>& prices, int index, bool buy, int tries, 
    vector<vector<vector<int>>> &dp){
        if(index == prices.size() or tries == 0)
            return 0;

        if(dp[index][buy][tries] != -1)
            return dp[index][buy][tries];

        int profit;

        if(buy){
            profit = max( -prices[index] + find_ans(prices, index+1, false, tries, dp),
                            find_ans(prices, index+1, true, tries, dp) );
        }

        else{
            profit = max( +prices[index] + find_ans(prices, index+1, true, tries-1, dp),
                            find_ans(prices, index+1, false, tries, dp) );
        }

        return dp[index][buy][tries] = profit;
    }

    int maxProfit(int k, vector<int>& prices) {
        int n = prices.size();
        int tries = k;
        vector<vector<vector<int>>> dp(n, vector<vector<int>> (2, vector<int>(k+1,-1)));

        return find_ans(prices, 0, true, tries, dp);
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++