<p>You are given an 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>fee</code> representing a transaction fee.</p>

<p>Find the maximum profit you can achieve. You may complete as many transactions as you like, but you need to pay the transaction fee for each transaction.</p>

<p><strong>Note:</strong></p>

<ul>
	<li>You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).</li>
	<li>The transaction fee is only charged once for each stock purchase and sale.</li>
</ul>

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

<pre>
<strong>Input:</strong> prices = [1,3,2,8,4,9], fee = 2
<strong>Output:</strong> 8
<strong>Explanation:</strong> The maximum profit can be achieved by:
- Buying at prices[0] = 1
- Selling at prices[3] = 8
- Buying at prices[4] = 4
- Selling at prices[5] = 9
The total profit is ((8 - 1) - 2) + ((9 - 4) - 2) = 8.
</pre>

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

<pre>
<strong>Input:</strong> prices = [1,3,7,5,10,3], fee = 3
<strong>Output:</strong> 6
</pre>

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

<ul>
	<li><code>1 &lt;= prices.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= prices[i] &lt; 5 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= fee &lt; 5 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int maxProfit(vector<int>& prices, int fee) {
         //lest cobvert int memo
        vector<vector<int>>dp(prices.size()+1,vector<int>(2,0));
        int n=prices.size();
     
        for(int index=n-1;index>=0;index--)
        {
            for(int buy=0;buy<2;buy++)
            {
         int profit=0;
        
        if(buy)
        {
           
            int not_buy= dp[index+1][1];
            int buy= -prices[index]+ dp[index+1][0];
            profit=max(buy,not_buy);
        }
        else
        {
            
            int sell=prices[index]-fee+dp[index+1][1];
            int not_sell=dp[index+1][0];
            profit=max(sell,not_sell);
        }
       dp[index][buy]=profit;
            }
        }

        return dp[0][1];
    }
};
80840