<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.</p>

<p>Find the maximum profit you can achieve. You may complete <strong>at most two transactions</strong>.</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> prices = [3,3,5,0,0,3,1,4]
<strong>Output:</strong> 6
<strong>Explanation:</strong> Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
Then buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.</pre>

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

<pre>
<strong>Input:</strong> prices = [1,2,3,4,5]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.
Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> prices = [7,6,4,3,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong> In this case, no transaction is done, i.e. max profit = 0.
</pre>

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

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

class Solution {
public:
    int maxProfit(vector<int>& prices) {
        
        
        
        map<int,int>mapp;
        
        int so_far_maxx=0;
        
        int hey=0;
        
        for(int i=prices.size()-1;i>=0;i--)
        {
            int temp=so_far_maxx-prices[i];
            hey=max(hey,temp);
            mapp[i]=hey;
            so_far_maxx=max(so_far_maxx,prices[i]);
            
            
        }
        
        int so_far_minn=1000000;
        
        int ans=0;
        
        
        for(int i=0;i<prices.size();i++)
        {
            int temp=prices[i]-so_far_minn;
            
            int o;
            
            if((i+1)>=prices.size())
                o=0;
            else 
                o=mapp[i];
            
            int ke=temp+o;
            
            ans=max(ans,ke);
            so_far_minn=min(prices[i],so_far_minn);
            
            
            
        }
        
       return ans;
        
//         int l=0;
//         int r=prices.size()-1;
        
//         int ans1=0;
//         int ans2=0;
        
//         int so_far_small1=1000000;
//         // int so_far_big1=-1;
        
//          // int so_far_small2=-1;
//         int so_far_big1=0;
        
        
//        while(true)
//        {
//            if(l>r)
//                break;
           
//            if(l==r)
//            {
//                int temp1=(prices[l]-so_far_small1)-ans1;
//                int temp2=(so_far_big1-prices[r])-ans2;
               
//                if(temp1>=temp2)
//                {
//                    if(temp1>0)
//                    {
//                        ans1+=temp1;
//                    }
//                }
//                else if(temp1<temp2)
//                {
//                    if(temp2>0)
//                    {
//                        ans2+=temp2;
//                    }
//                }
               
//                break;
               
               
//            }
//             ans1=max(ans1,(prices[l]-so_far_small1));
           
//            if(prices[l]<so_far_small1)
//            {
              
//                so_far_small1=prices[l];
//            }
           
//            ans2=max(ans2,(so_far_big1-prices[r]));
           
//            if(prices[r]>so_far_big1)
//            {
//                so_far_big1=prices[r];
//            }
           
//            l++;
//            r--;
           

           
//        }
        
        
//         int ans=ans1+ans2;
        
        
//         int p=0;
        
//         int minn=1000000;
        
//         for(int i=0;i<prices.size();i++)
//         {
//             int hello=prices[i]-minn;
//             p=max(p,hello);
//             minn=min(minn,prices[i]);
//         }
        
        
//         int bye=max(p,ans);
        
        
        
        //return bye;
    }
};
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