<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 greedy(vector<int>& prices) {
        int n = prices.size();
        int profit = 0;

        for (int i = 1; i < n; i++) {

            if (prices[i] > prices[i - 1]) {
                profit += prices[i] - prices[i - 1];
            }
        }

        return profit;
    }
    int memo(int day, int holding, vector<int>& prices, int& n,
             vector<vector<int>>& dp) {
        if (day >= n)
            return 0;
        if (dp[day][holding] != INT_MIN)
            return dp[day][holding];
        int profit = 0;
        if (holding) {
            // holding the stock , currrently
            // choice - sell the holding share or dont sell and hold the share
            // for future,
            profit = max(profit,
                         prices[day] + memo(day + 1, !holding, prices, n, dp));
            profit = max(profit, memo(day + 1, holding, prices, n, dp));
        } else {

            profit = max(profit,
                         -prices[day] + memo(day + 1, !holding, prices, n, dp));
            profit = max(profit, memo(day + 1, holding, prices, n, dp));
        }
        return dp[day][holding] = profit;
    }
    int tabu(vector<int>& prices, int &n) {

        vector<vector<int>> dp(n + 1, vector<int>(2, 0));
        for (int day = n-1 ; day >= 0; day--) {
            for (int holding = 0; holding <= 1; holding++) {
                int profit = 0;
                if (holding) {
                    profit = max(dp[day + 1][holding], prices[day] + dp[day + 1][!holding]);
                } else {
                    profit = max(dp[day + 1][holding], -prices[day] + dp[day + 1][!holding]);
                }
                 dp[day][holding] = profit;
            }
        }
        return dp[0][0];
    }
    int spaceOptimisation(vector<int>& prices, int &n){
        vector<vector<int>> dp(n + 1, vector<int>(2, 0));
        vector<int>prev={0, 0};
        for (int day = n-1 ; day >= 0; day--) {
            vector<int>curr(2, 0);
            for (int holding = 0; holding <= 1; holding++) {
                int profit = 0;
                if (holding) {
                    profit = max(prev[holding], prices[day] + prev[!holding]);
                } else {
                    profit = max(prev[holding], -prices[day] +prev[!holding]);
                }
                curr[holding] = profit;
            }
            prev=curr;
        }
        return prev[0];
    }
    int maxProfit(vector<int>& prices) {
        int n = prices.size();
        // vector<vector<int>> dp(n + 1, vector<int>(2, INT_MIN));
        // return memo(0, 0, prices, n, dp);
        // return tabu(prices, n);
        return spaceOptimisation(prices, n);

    }
};

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