added best time to buy sell stock IV in leetcode folder

LeetCode/Best time to buy and sell stocks IV/best time to buy and sell stock IV.cpp

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+/*
+Question Link:
+https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/
+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).
+*/
+/*
+Input: k = 2, prices = [2,4,1]
+Output: 2
+*/
+
+class Solution {
+public:
+    int dp[1001][2][101];
+    int solve(int i,int own,int k,vector<int>& prices)
+    {
+        // if i becomes greater than prices array length then there are no more stocks left . hence we return.
+        if(i>=prices.size())
+        {
+            return 0;
+        }
+        // if the number of transactions performed become greater than k then also we return since you can perform max k transactions.
+        if(k<=0)
+        {
+            return 0;
+        }
+        // memoize ... check if the situation already exist then we just take that value.
+        if(dp[i][own][k]!=-1)
+        {
+            return dp[i][own][k];
+        }
+        // if you own a stock at that paticular day then you two options either to sell it or dont sell that stock.
+        // we call solve function for both the options.
+        if(own)
+        {
+            // if we decide to sell the stock then we add the price of stock at that day
+            // then we go to next day that is increment i , and make variable own to 0 , and reduce the number of transaction available to us by 1
+            int opt1=prices[i]+solve(i+1,0,k-1,prices);
+
+             // if we do not sell the stock then 
+            //  we go to next day that is increment i , do not change the own variable cause we still own the stock , and pass k unchanged
+            int opt2=solve(i+1,1,k,prices);
+
+            // we store the max of the two in the dp array cause we have to maximize the profit
+            dp[i][1][k]=max(opt1,opt2);
+            // hence we return this value.
+            return dp[i][1][k];
+        }
+        // if you do not own a stock at that paticular day then you two options either to buy the stock on that day or dont buy.
+        // we call solve function for both the options.
+        else
+        {
+            // if we decide to buy the stock then we subtract the price of stock at that day
+            // then we go to next day that is increment i , and make variable own to 1 , and pass k unchanged
+            int opt1=-(prices[i])+solve(i+1,1,k,prices);
+
+             // if we do not buy the stock then 
+            //  we go to next day that is increment i , do not change the own variable cause we still dont own the stock , and pass k unchanged
+            int opt2=solve(i+1,0,k,prices);
+
+            // we store the max of the two in the dp array cause we have to maximize the profit
+            dp[i][0][k]=max(opt1,opt2);
+            // hence we return this value.
+            return dp[i][0][k];
+        }
+    }
+    int maxProfit(int k,vector<int>& prices) {
+        // set the dp array to -1 initially
+        memset(dp,-1,sizeof(dp));
+
+        // call the solve function 
+        // pass 0 in i cause we start with the 0th element in the prices array
+        // then we pass 0 in own variable cause we do not own a stock at the starting
+        return solve(0,0,k,prices);
+    }
+};