Best Time to Buy and Sell Stock IV.cpp

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:
1. 0 <= k <= 109
2. 0 <= prices.length <= 104
3. 0 <= prices[i] <= 1000





SOLUTION:



class Solution {

public:
    
    int maxProfit(int k, vector<int>& prices) {
        
        int i,j,n,ans;
        n = prices.size();
        
        if(k==0 || n<=1)
            return 0;
        
        if(k>=(n/2))
        {
            ans=0;
            for(i=1;i<n;i++)
            {
                ans+=max(0,prices[i]-prices[i-1]);
            }
            
            return ans;
        }
        
        vector<int> buy(k,INT_MIN),sell(k,INT_MIN);
        
        for(i=0;i<n;i++)
        {
            for(j=0;j<k;j++)
            {
                buy[j] = max(buy[j],(j==0)?0-prices[i]:sell[j-1]-prices[i]);
                sell[j] = max(sell[j],buy[j]+prices[i]);
            }
        }
        
        return sell[k-1];
    }
};