<p>We have <code>n</code> jobs, where every job is scheduled to be done from <code>startTime[i]</code> to <code>endTime[i]</code>, obtaining a profit of <code>profit[i]</code>.</p>

<p>You&#39;re given the <code>startTime</code>, <code>endTime</code> and <code>profit</code> arrays, return the maximum profit you can take such that there are no two jobs in the subset with overlapping time range.</p>

<p>If you choose a job that ends at time <code>X</code> you will be able to start another job that starts at time <code>X</code>.</p>

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

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/10/10/sample1_1584.png" style="width: 380px; height: 154px;" /></strong></p>

<pre>
<strong>Input:</strong> startTime = [1,2,3,3], endTime = [3,4,5,6], profit = [50,10,40,70]
<strong>Output:</strong> 120
<strong>Explanation:</strong> The subset chosen is the first and fourth job. 
Time range [1-3]+[3-6] , we get profit of 120 = 50 + 70.
</pre>

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

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/10/10/sample22_1584.png" style="width: 600px; height: 112px;" /> </strong></p>

<pre>
<strong>Input:</strong> startTime = [1,2,3,4,6], endTime = [3,5,10,6,9], profit = [20,20,100,70,60]
<strong>Output:</strong> 150
<strong>Explanation:</strong> The subset chosen is the first, fourth and fifth job. 
Profit obtained 150 = 20 + 70 + 60.
</pre>

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

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/10/10/sample3_1584.png" style="width: 400px; height: 112px;" /></strong></p>

<pre>
<strong>Input:</strong> startTime = [1,1,1], endTime = [2,3,4], profit = [5,6,4]
<strong>Output:</strong> 6
</pre>

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

<ul>
	<li><code>1 &lt;= startTime.length == endTime.length == profit.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= startTime[i] &lt; endTime[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= profit[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int n, dp[50001];
    int nextJobFind(vector<vector<int>>& vec, int start, int currJobEnd) {
        int end = n - 1;

        int result = n;
        while (start <= end) {
            int mid = start + (end - start) / 2;

            if (vec[mid][0] >= currJobEnd) { // take this task
                result = mid;
                end = mid - 1;
            } else {
                start = mid + 1;
            }
        }
        return result;
    }
    int helper(vector<vector<int>>& vec, int i) {

        if (i >= n) {
            return 0;
        }
        int nextJob = nextJobFind(vec, i + 1, vec[i][1]);

        if (dp[i] != -1) {
            return dp[i];
        }
        
        int taken = vec[i][2] + helper(vec, nextJob);
        int skip = 0 + helper(vec, i + 1);

        return dp[i] = max(taken, skip);
    }
    int jobScheduling(vector<int>& startTime, vector<int>& endTime,
                      vector<int>& profit) {
        n = profit.size();
        memset(dp, -1, sizeof(dp));
        vector<vector<int>> vec(n, vector<int>(3, 0));

        for (int i = 0; i < n; i++) {
            vec[i][0] = startTime[i];
            vec[i][1] = endTime[i];
            vec[i][2] = profit[i];
        }

        sort(vec.begin(), vec.end());

        return helper(vec, 0);
    }
};
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