<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:
vector<vector<int>>dp;
    int solve(int idx,int canBuy,vector<int>& prices, int fee)
    {
        if(idx==prices.size())
        return 0;
        int &val=dp[idx][canBuy];
        if(val!=-1)
        return val;
        int op1=0,op2=0;
        if(canBuy==0)
        {
            op1=prices[idx]-fee + solve(idx+1,1,prices,fee);
        }
        else
        {
            op1=-1*prices[idx]+solve(idx+1,0,prices,fee);
        }
        op2=solve(idx+1,canBuy,prices,fee);
        return val=max(op1,op2);
    }
    int maxProfit(vector<int>& prices, int fee) {
        dp.resize(prices.size()+1,vector<int>(2,-1));
        return solve(0,1,prices,fee);
    }
};
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