<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, and an integer <code>k</code>.</p>

<p>Find the maximum profit you can achieve. You may complete at most <code>k</code> transactions: i.e. you may buy at most <code>k</code> times and sell at most <code>k</code> times.</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> k = 2, prices = [2,4,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
</pre>

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

<pre>
<strong>Input:</strong> k = 2, prices = [3,2,6,5,0,3]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= 100</code></li>
	<li><code>1 &lt;= prices.length &lt;= 1000</code></li>
	<li><code>0 &lt;= prices[i] &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int maxProfit(int k, vector<int>& prices) {
        int n = prices.size() + 1;
        int m = n < 2*k+1 ? n : 2*k+1;
        std::cout << m << '\n';
        std::vector<std::vector<int>> profits(m, std::vector<int> (n, -99));
        std::vector<std::vector<int>> choices(m, std::vector<int> (n, -2));
        
        // Initialize profits vector. Impossible choices are set to -9999
        // Initialize choices vector. Impossible choices are set to -2, unchosen yet are set to 0.
        unsigned i, j;

        for (i=0; i < m; i++)
            for (j=i; j < n; j++)
                if (i <= j) {
                    profits[i][j] = 0;
                    choices[i][j] = 0;
                }

        // Loop through and set the options.
        for (i=1; i<m; i++)
            for (j=i; j<n; j++) {
                int interacted_val = profits[i-1][j-1] + prices[j-1] * (i%2?-1:1);
                if (profits[i][j-1] <= interacted_val){
                    profits[i][j] = interacted_val;
                    choices[i][j] = 1;
                } else {
                    profits[i][j] = profits[i][j-1];
                    choices[i][j] = -1;
                }
            }

        for (auto row : profits){
            for (auto val : row)
                std::cout << val << '\t';
            std::cout << '\n';
        }

        int max = profits[0][n-1];
        for (i=1; i<m; i++)
            if (profits[i][n-1] > max)
                max=profits[i][n-1];
        
        return max;
    }
};
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