<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 {

    int calculate(int index, int txns, vector<int>& prices, vector<unordered_map<int, int>>& dp) {

        if(txns == 0 || index >= prices.size())
            return 0;

        if(dp[txns].find(index) != dp[txns].end()) {
            return dp[txns][index];
        }

        int result = 0;
        int min_price = prices[index];
        for(int i = index; i < prices.size(); i++) {
            if(prices[i] > min_price) {
                result = max(result, prices[i] - min_price + calculate(i + 1, txns - 1, prices, dp));
            } else {
                min_price = prices[i];
            }
        }

        return dp[txns][index] = result;
    }

public:
    int maxProfit(int k, vector<int>& prices) {
        // dp[txn][index]
        vector<unordered_map<int, int>> dp(k + 1, unordered_map<int, int>());
        return calculate(0, k, prices, dp);
    }
};
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