leetcode-problemset/leetcode-cn/problem (English)/删除数对后的最小数组长度(English) [minimum-array-length-after-pair-removals].html

<p>You are given a <strong>0-indexed</strong> <strong>sorted</strong> array of integers <code>nums</code>.</p>

<p>You can perform the following operation any number of times:</p>

<ul>
	<li>Choose <strong>two</strong> indices, <code>i</code> and <code>j</code>, where <code>i &lt; j</code>, such that <code>nums[i] &lt; nums[j]</code>.</li>
	<li>Then, remove the elements at indices <code>i</code> and <code>j</code> from <code>nums</code>. The remaining elements retain their original order, and the array is re-indexed.</li>
</ul>

<p>Return <em>an integer that denotes the <strong>minimum</strong> length of </em><code>nums</code><em> after performing the operation any number of times (<strong>including zero</strong>).</em></p>

<p>Note that <code>nums</code> is sorted in <strong>non-decreasing</strong> order.</p>

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

<pre>
<strong>Input:</strong> nums = [1,3,4,9]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Initially, nums = [1, 3, 4, 9].
In the first operation, we can choose index 0 and 1 because nums[0] &lt; nums[1] &lt;=&gt; 1 &lt; 3.
Remove indices 0 and 1, and nums becomes [4, 9].
For the next operation, we can choose index 0 and 1 because nums[0] &lt; nums[1] &lt;=&gt; 4 &lt; 9.
Remove indices 0 and 1, and nums becomes an empty array [].
Hence, the minimum length achievable is 0.</pre>

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

<pre>
<strong>Input:</strong> nums = [2,3,6,9]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Initially, nums = [2, 3, 6, 9]. 
In the first operation, we can choose index 0 and 2 because nums[0] &lt; nums[2] &lt;=&gt; 2 &lt; 6. 
Remove indices 0 and 2, and nums becomes [3, 9]. 
For the next operation, we can choose index 0 and 1 because nums[0] &lt; nums[1] &lt;=&gt; 3 &lt; 9. 
Remove indices 0 and 1, and nums becomes an empty array []. 
Hence, the minimum length achievable is 0.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,1,2]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Initially, nums = [1, 1, 2].
In an operation, we can choose index 0 and 2 because nums[0] &lt; nums[2] &lt;=&gt; 1 &lt; 2. 
Remove indices 0 and 2, and nums becomes [1]. 
It is no longer possible to perform an operation on the array. 
Hence, the minimum achievable length is 1. 
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>nums</code> is sorted in <strong>non-decreasing</strong> order.</li>
</ul>