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leetcode/problem/set-intersection-size-at-least-two.html
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@@ -1,24 +1,39 @@
<p>An integer interval <code>[a, b]</code> (for integers <code>a &lt; b</code>) is a set of all consecutive integers from <code>a</code> to <code>b</code>, including <code>a</code> and <code>b</code>.</p>
<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>Find the minimum size of a set S such that for every integer interval A in <code>intervals</code>, the intersection of S with A has a size of at least two.</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>Example 1:</strong></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> Consider the set S = {2, 3, 4}. For each interval, there are at least 2 elements from S in the interval.
Also, there isn&#39;t a smaller size set that fulfills the above condition.
Thus, we output the size of this set, which is 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>Example 2:</strong></p>
<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> An example of a minimum sized set is {1, 2, 3, 4, 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>
@@ -27,5 +42,5 @@ Thus, we output the size of this set, which is 3.
<ul>
<li><code>1 &lt;= intervals.length &lt;= 3000</code></li>
<li><code>intervals[i].length == 2</code></li>
<li><code>0 &lt;= a<sub>i</sub> &lt;&nbsp;b<sub>i</sub> &lt;= 10<sup>8</sup></code></li>
<li><code>0 &lt;= start<sub>i</sub> &lt; end<sub>i</sub> &lt;= 10<sup>8</sup></code></li>
</ul>