<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 util(int k, vector<int>& prices, int i, int t, bool flag, vector<vector<vector<int>>>& dp) {
        if (i == prices.size()) {
            return 0;
        }
        if (t == k) {
            return 0;
        }
        if (dp[i][t][flag] != -1) return dp[i][t][flag];
        if (flag) {
            return dp[i][t][flag] = max(util(k, prices, i + 1, t, flag, dp), prices[i] + util(k, prices, i + 1, t + 1, !flag, dp));
        } else {
            return dp[i][t][flag] = max(util(k, prices, i + 1, t, flag, dp), -prices[i] + util(k, prices, i + 1, t, !flag, dp));
        }
    }
    int maxProfit(int k, vector<int>& prices) {
        int n = prices.size();
        vector<vector<vector<int>>> dp(n, vector<vector<int>>(k, vector<int>(2, -1)));
        return util(k, prices, 0, 0, false, dp);
    }
};
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