<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.</p>

<p>On each day, you may decide to buy and/or sell the stock. You can only hold <strong>at most one</strong> share of the stock at any time. However, you can buy it then immediately sell it on the <strong>same day</strong>.</p>

<p>Find and return <em>the <strong>maximum</strong> profit you can achieve</em>.</p>

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

<pre>
<strong>Input:</strong> prices = [7,1,5,3,6,4]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Buy on day 2 (price = 1) and sell on day 3 (price = 5), profit = 5-1 = 4.
Then buy on day 4 (price = 3) and sell on day 5 (price = 6), profit = 6-3 = 3.
Total profit is 4 + 3 = 7.
</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.
Total profit is 4.
</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> There is no way to make a positive profit, so we never buy the stock to achieve the maximum profit of 0.
</pre>

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

<ul>
	<li><code>1 &lt;= prices.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= prices[i] &lt;= 10<sup>4</sup></code></li>
</ul>

/*
class Solution {
public:
    int maxProfit(vector<int>& prices) {
        int maxprofit = 0;
        for(int i = 1 ; i < prices.size() ; i++){
            if(prices[i-1] < prices[i]){
                maxprofit += prices[i] - prices[i-1];
            }
        }
        return maxprofit;
    }
};

class Solution { ////////// TLE
public:
    int f(int ind , int buy , vector<int>& prices ,vector<vector<int>> dp){
        if(ind == prices.size())return 0;
        if(dp[ind][buy] != -1) return dp[ind][buy];
        int profit = 0;
        if(buy){
            profit = max(-prices[ind] + f(ind+1,0,prices,dp) , 0 + f(ind+1,1,prices,dp));
        }else{
            profit = max(prices[ind] + f(ind+1,1,prices,dp) , f(ind+1,0,prices,dp));
        }
        return dp[ind][buy] = profit;
    }
    int maxProfit(vector<int>& prices) {
        int n = prices.size();
        vector<vector<int>> dp(n,vector<int>(2,-1));
        return f(0,1,prices,dp);
    }
};



class Solution { 
public:
    int maxProfit(vector<int>& prices) {
        int n = prices.size();
        vector<vector<int>> dp(n+1,vector<int>(2,0));
        dp[n][0] = dp[n][1] = 0;
        for(int ind = n-1 ; ind >= 0 ; ind--){
            for(int buy = 0 ; buy <= 1 ; buy++){
                int profit = 0;
                if(buy){
                    profit = max(-prices[ind] + dp[ind+1][0] , 0 + dp[ind+1][1]);
                }else{
                    profit = max(prices[ind] + dp[ind+1][1] , dp[ind+1][0]);
                }
                dp[ind][buy] = profit;
            }
        }
        return dp[0][1];
    }
};

*/

/*

class Solution { 
public:
    int maxProfit(vector<int>& prices) {
        int n = prices.size();
        //vector<vector<int>> dp(n+1,vector<int>(2,0));
        vector<int> prev(2,0) , cur(2,0);
        prev[0] = prev[1] = 0;
        for(int ind = n-1 ; ind >= 0 ; ind--){
            for(int buy = 0 ; buy <= 1 ; buy++){
                int profit = 0;
                if(buy){
                    profit = max(-prices[ind] + prev[0] , 0 + prev[1]);
                }else{
                    profit = max(prices[ind] + prev[1] , prev[0]);
                }
                cur[buy] = profit;
            }
            prev = cur;
        }
        return prev[1];
    }
};

*/
/*

class Solution { 
public:
    int maxProfit(vector<int>& prices) {
        int n = prices.size();
        vector<vector<int>> dp(n+1,vector<int>(2,0));
        dp[n][0] = dp[n][1] = 0;
        for(int ind = n-1 ; ind >= 0 ; ind--){
            for(int buy = 0 ; buy <= 1 ; buy++){
                if(buy){
                    dp[ind][buy] = max(-prices[ind] + dp[ind+1][0] , 0 + dp[ind+1][1]);
                }else{
                    dp[ind][buy] = max(prices[ind] + dp[ind+1][1] , dp[ind+1][0]);
                }
            }
        }
        return dp[0][1];
    }
};
*/

class Solution { 
public:
    int maxProfit(vector<int>& prices) {
        int n = prices.size();
        //vector<vector<int>> dp(n+1,vector<int>(2,0));
        //dp[n][0] = dp[n][1] = 0;
        vector<int> next(2,0);
        for(int ind = n-1 ; ind >= 0 ; ind--){
            vector<int> cur(2,0);
            for(int buy = 0 ; buy <= 1 ; buy++){
                if(buy){
                    cur[buy] = max(-prices[ind] + next[0] , 0 + next[1]);
                }else{
                    cur[buy] = max(prices[ind] + next[1] , next[0]);
                }
            }
            next = cur;
        }
        return next[1];
    }
};
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