<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 dp[500001][2];
int check(int i , int n , vector<int>& prices, bool b , int fee){
    if(i>=n)return 0;
    if(dp[i][b]!=-1)return dp[i][b];
    int maxp=0;
    if(b==true){
        int buy=check(i+1,n,prices,false,fee)-prices[i];
        int not_buy=check(i+1,n,prices,true,fee);
        maxp=max(buy,not_buy);
    }else{
        int sell=prices[i]+check(i+1,n,prices,true,fee)-fee;
        int not_sell=check(i+1,n,prices,false,fee);
        maxp=max(sell,not_sell);
    }
    return dp[i][b]=maxp;
}
    int maxProfit(vector<int>& prices, int fee) {
        int n=prices.size();
        bool b=true;
        memset(dp,-1,sizeof(dp));
        return check(0,n,prices,b,fee);
    }
};
66496