<p>You are given an array of <code>events</code> where <code>events[i] = [startDay<sub>i</sub>, endDay<sub>i</sub>, value<sub>i</sub>]</code>. The <code>i<sup>th</sup></code> event starts at <code>startDay<sub>i</sub></code><sub> </sub>and ends at <code>endDay<sub>i</sub></code>, and if you attend this event, you will receive a value of <code>value<sub>i</sub></code>. You are also given an integer <code>k</code> which represents the maximum number of events you can attend.</p>

<p>You can only attend one event at a time. If you choose to attend an event, you must attend the <strong>entire</strong> event. Note that the end day is <strong>inclusive</strong>: that is, you cannot attend two events where one of them starts and the other ends on the same day.</p>

<p>Return <em>the <strong>maximum sum</strong> of values that you can receive by attending events.</em></p>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2021/01/10/screenshot-2021-01-11-at-60048-pm.png" style="width: 400px; height: 103px;" /></p>

<pre>
<strong>Input:</strong> events = [[1,2,4],[3,4,3],[2,3,1]], k = 2
<strong>Output:</strong> 7
<strong>Explanation: </strong>Choose the green events, 0 and 1 (0-indexed) for a total value of 4 + 3 = 7.</pre>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2021/01/10/screenshot-2021-01-11-at-60150-pm.png" style="width: 400px; height: 103px;" /></p>

<pre>
<strong>Input:</strong> events = [[1,2,4],[3,4,3],[2,3,10]], k = 2
<strong>Output:</strong> 10
<strong>Explanation:</strong> Choose event 2 for a total value of 10.
Notice that you cannot attend any other event as they overlap, and that you do <strong>not</strong> have to attend k events.</pre>

<p><strong class="example">Example 3:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2021/01/10/screenshot-2021-01-11-at-60703-pm.png" style="width: 400px; height: 126px;" /></strong></p>

<pre>
<strong>Input:</strong> events = [[1,1,1],[2,2,2],[3,3,3],[4,4,4]], k = 3
<strong>Output:</strong> 9
<strong>Explanation:</strong> Although the events do not overlap, you can only attend 3 events. Pick the highest valued three.</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= events.length</code></li>
	<li><code>1 &lt;= k * events.length &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= startDay<sub>i</sub> &lt;= endDay<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= value<sub>i</sub> &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution {
public:
vector<vector<int>> dp;
    int solve(int ind, int endTime, int k, vector<vector<int>>& events)
    {
        if(ind == size(events) || k == 0) return 0;

        if(events[ind][0] <= endTime) return solve(ind+1, endTime, k, events);
        if(dp[ind][k] != -1) return dp[ind][k];

        int skip = 0 + solve(ind+1, endTime, k, events);
        int take = events[ind][2] + solve(ind+1, events[ind][1], k-1, events);

        return dp[ind][k] = max(skip, take);
    }
    int maxValue(vector<vector<int>>& events, int k) {
        sort(begin(events), end(events));
        int n = size(events);
        dp.resize(n, vector<int>(k+1, -1));
        return solve(0, 0, k, events);
    }
};
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