<p>Given an array of intervals <code>intervals</code> where <code>intervals[i] = [start<sub>i</sub>, end<sub>i</sub>]</code>, return <em>the minimum number of intervals you need to remove to make the rest of the intervals non-overlapping</em>.</p>

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

<pre>
<strong>Input:</strong> intervals = [[1,2],[2,3],[3,4],[1,3]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> [1,3] can be removed and the rest of the intervals are non-overlapping.
</pre>

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

<pre>
<strong>Input:</strong> intervals = [[1,2],[1,2],[1,2]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> You need to remove two [1,2] to make the rest of the intervals non-overlapping.
</pre>

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

<pre>
<strong>Input:</strong> intervals = [[1,2],[2,3]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> You don&#39;t need to remove any of the intervals since they&#39;re already non-overlapping.
</pre>

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

<ul>
	<li><code>1 &lt;= intervals.length &lt;= 10<sup>5</sup></code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>-5 * 10<sup>4</sup> &lt;= start<sub>i</sub> &lt; end<sub>i</sub> &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    vector<vector<int>> mIntervals;

    std::vector<int> dp;
    int solve(int n) {
        if(n >= mIntervals.size()) return 0;

        auto start = mIntervals[n][0];
        auto end = mIntervals[n][1];

        int & memo = dp[n];

        if(memo != -1) return memo;

        int dont_take = 1+ solve(n+1);

        auto next_non_overlapping = std::lower_bound(mIntervals.begin() + n + 1, mIntervals.end(), std::vector<int>{end, end}) - mIntervals.begin();

        int take = (next_non_overlapping - n -1) + solve(next_non_overlapping);

        memo = std::min(take, dont_take);
        //std::cout << memo << " " << take << " " << dont_take << std::endl;
        return memo;
    }
    int eraseOverlapIntervals(vector<vector<int>>& intervals) {
        
        dp.resize(intervals.size() +1 , -1);
        //memset(dp, -1, sizeof(dp));
        std::sort(intervals.begin(), intervals.end());

        mIntervals = intervals;
    
        
        return solve(0);
    }
};
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