<p>You are given an integer array <code>prices</code> where <code>prices[i]</code> is the price of a given stock on the <code>i<sup>th</sup></code> day, and an integer <code>k</code>.</p>

<p>Find the maximum profit you can achieve. You may complete at most <code>k</code> transactions: i.e. you may buy at most <code>k</code> times and sell at most <code>k</code> times.</p>

<p><strong>Note:</strong> You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> k = 2, prices = [2,4,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> k = 2, prices = [3,2,6,5,0,3]
<strong>Output:</strong> 7
<strong>Explanation:</strong> 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.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= 100</code></li>
	<li><code>1 &lt;= prices.length &lt;= 1000</code></li>
	<li><code>0 &lt;= prices[i] &lt;= 1000</code></li>
</ul>

class Solution {
      int solve(vector<int>&prices,int d,bool ans,int k,vector<vector<vector<int>>>&v){
if(d==prices.size()){
    return 0;
}
if(v[d][ans][k]!=-1){
    return v[d][ans][k];
}
int g=0;
int h=0;
if(ans==false and k>0){
g=max(-prices[d]+solve(prices,d+1,true,k-1,v),solve(prices,d+1,false,k,v));


}
if(ans==true ){
h=max(prices[d]+solve(prices,d+1,false,k,v),solve(prices,d+1,true,k,v));


}
return v[d][ans][k]=g+h;

    }
public:
    int maxProfit(int k, vector<int>& prices) {
         int d=0;
        bool ans=false;
     
        vector<vector<vector<int>>>v(prices.size()+1,(vector<vector<int>>(3,vector<int>(k+1,-1))));
       return  solve(prices,d,ans,k,v);
    }
};
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