<p>You are given a 2D integer array <code>intervals</code> where <code>intervals[i] = [start<sub>i</sub>, end<sub>i</sub>]</code> represents all the integers from <code>start<sub>i</sub></code> to <code>end<sub>i</sub></code> inclusively.</p>

<p>A <strong>containing set</strong> is an array <code>nums</code> where each interval from <code>intervals</code> has <strong>at least two</strong> integers in <code>nums</code>.</p>

<ul>
	<li>For example, if <code>intervals = [[1,3], [3,7], [8,9]]</code>, then <code>[1,2,4,7,8,9]</code> and <code>[2,3,4,8,9]</code> are <strong>containing sets</strong>.</li>
</ul>

<p>Return <em>the minimum possible size of a containing set</em>.</p>

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

<pre>
<strong>Input:</strong> intervals = [[1,3],[3,7],[8,9]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> let nums = [2, 3, 4, 8, 9].
It can be shown that there cannot be any containing array of size 4.
</pre>

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

<pre>
<strong>Input:</strong> intervals = [[1,3],[1,4],[2,5],[3,5]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> let nums = [2, 3, 4].
It can be shown that there cannot be any containing array of size 2.
</pre>

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

<pre>
<strong>Input:</strong> intervals = [[1,2],[2,3],[2,4],[4,5]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> let nums = [1, 2, 3, 4, 5].
It can be shown that there cannot be any containing array of size 4.
</pre>

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

<ul>
	<li><code>1 &lt;= intervals.length &lt;= 3000</code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>0 &lt;= start<sub>i</sub> &lt; end<sub>i</sub> &lt;= 10<sup>8</sup></code></li>
</ul>

class Solution {
public:
    int intersectionSizeTwo(vector<vector<int>>& intervals) {
        sort(begin(intervals), end(intervals), [](const vector<int>& v1, const vector<int>& v2){
            return v1[1] < v2[1] || (v2[1] == v1[1] && v2[0] < v1[0]);
        });

        vector<int> largest{intervals.front()[1]-1, intervals.front()[1]};
        int setsize = 2;
        for(int i=1;i<intervals.size();++i) {
            //  check how many of largest / second largest overlap with the new set
            int overlapCount = getOverlap(intervals[i], largest);

            switch(overlapCount) {
                case 0:
                    largest[1] = intervals[i][1];
                    largest[0] = intervals[i][1]-1;
                    setsize +=2;
                    break;

                case 1:
                    largest[0] = largest[1];
                    largest[1] = intervals[i][1];
                    setsize += 1;
                    break;
                case 2:
                default:
                    break;
            }
        }
        return setsize;
    }

    int getOverlap(const vector<int>& interval,const vector<int>& largest) {
        if(largest[1] < interval[0])
            return 0;

        if(largest[0] < interval[0])
            return 1;
        return 2;
    }
};
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