<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:
    struct CompItem{
        bool operator()(const vector<int>& a,const vector<int>& b) const{
            return a[0] < b[0];
        }
    };
    int f(vector<vector<int>>& eList,int idx,int chance){
        if(chance == 0){
            return 0;
        }
        if(idx>= eList.size()){
            return 0;
        }
        if(dp[idx][chance] != -1){
            return dp[idx][chance];
        }
        int op1 = f(eList,idx+1,chance);
        int op2 = eList[idx][2] ;
        int next = nextIdxList[idx];
        if(next < eList.size()){
            op2 += f(eList,next,chance-1);
        }
        int ret = max(op1,op2);
        dp[idx][chance] = ret;
        return ret;
    }
    vector<vector<int>> dp;
    vector<int> nextIdxList;
    int maxValue(vector<vector<int>>& eList, int k) {
        sort(eList.begin() , eList.end() , [](const vector<int>& a , const vector<int>& b){
            if(a[0] == b[0]){
                return a[1] < b[1];
            }
            return a[0] < b[0];
        });
        int N = eList.size();
        dp.resize(N,vector<int>(k+1,-1));
        nextIdxList.resize(N,N);
        for(int i = 0;i < N;++i){
            auto next = std::upper_bound(eList.begin() , eList.end() ,
                                         std::vector<int>{eList[i][1],0,0} , CompItem());
            if(next == eList.end()){
                continue;
            }
            nextIdxList[i] = next - eList.begin();
        }
        return f(eList,0,k);
    }
};
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