<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:
    int eraseOverlapIntervals(const std::vector<std::vector<int>>& intervals) 
    {
        if(intervals.size() < 2)
        {
            return 0;
        }

        std::vector<std::vector<int>> intervalsCopy(intervals);
        std::sort(intervalsCopy.begin(), intervalsCopy.end());
        int count = 0;
        int start = intervalsCopy[0][0];
        int end = intervalsCopy[0][1];

        for(int index = 1; index < intervalsCopy.size(); ++index)
        {   
            if(end > intervalsCopy[index][0])
            {
                ++count;
                start = std::max(start, intervalsCopy[index][0]);
                end = std::min(end, intervalsCopy[index][1]);
            }
            else
            {
                start = intervalsCopy[index][0];
                end = intervalsCopy[index][1];
            }
        } 

        return count;  
    }
};
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