<p>You are given two lists of closed intervals, <code>firstList</code> and <code>secondList</code>, where <code>firstList[i] = [start<sub>i</sub>, end<sub>i</sub>]</code> and <code>secondList[j] = [start<sub>j</sub>, end<sub>j</sub>]</code>. Each list of intervals is pairwise <strong>disjoint</strong> and in <strong>sorted order</strong>.</p>

<p>Return <em>the intersection of these two interval lists</em>.</p>

<p>A <strong>closed interval</strong> <code>[a, b]</code> (with <code>a &lt;= b</code>) denotes the set of real numbers <code>x</code> with <code>a &lt;= x &lt;= b</code>.</p>

<p>The <strong>intersection</strong> of two closed intervals is a set of real numbers that are either empty or represented as a closed interval. For example, the intersection of <code>[1, 3]</code> and <code>[2, 4]</code> is <code>[2, 3]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/01/30/interval1.png" style="width: 700px; height: 194px;" />
<pre>
<strong>Input:</strong> firstList = [[0,2],[5,10],[13,23],[24,25]], secondList = [[1,5],[8,12],[15,24],[25,26]]
<strong>Output:</strong> [[1,2],[5,5],[8,10],[15,23],[24,24],[25,25]]
</pre>

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

<pre>
<strong>Input:</strong> firstList = [[1,3],[5,9]], secondList = []
<strong>Output:</strong> []
</pre>

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

<ul>
	<li><code>0 &lt;= firstList.length, secondList.length &lt;= 1000</code></li>
	<li><code>firstList.length + secondList.length &gt;= 1</code></li>
	<li><code>0 &lt;= start<sub>i</sub> &lt; end<sub>i</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>end<sub>i</sub> &lt; start<sub>i+1</sub></code></li>
	<li><code>0 &lt;= start<sub>j</sub> &lt; end<sub>j</sub> &lt;= 10<sup>9</sup> </code></li>
	<li><code>end<sub>j</sub> &lt; start<sub>j+1</sub></code></li>
</ul>

class Solution {
public:
    vector<vector<int>> intervalIntersection(vector<vector<int>>& firstList, vector<vector<int>>& secondList) {
        vector<vector<int>> res;
        
        int i = 0, j = 0;
        while (i < firstList.size() && j < secondList.size()) {
            vector<int> intersection = intersects(firstList[i], secondList[j]);
            if (intersection.size() > 0){
                res.push_back(intersection);
            }
            if (firstList[i][1] < secondList[j][1]) {
                i++;
            } else {
                j++;
            }
        }
        
        return res;
    }
    
    vector<int> intersects(vector<int>& interval1, vector<int>& interval2) {
        int a = interval1[0], b = interval1[1];
        int c = interval2[0], d = interval2[1];
        
        int x = max(a, c), y = min(b, d);
        
        if (x <= y) return {x, y};
        return {};
    }
};
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