leetcode-problemset/leetcode-cn/problem (English)/将数字变成二进制回文数的最少操作(English) [minimum-operations-to-make-binary-palindrome].html

<p>You are given an integer array <code>nums</code>.</p>

<p>For each element <code>nums[i]</code>, you may perform the following operations <strong>any</strong> number of times (including zero):</p>

<ul>
	<li>Increase <code>nums[i]</code> by 1, or</li>
	<li>Decrease <code>nums[i]</code> by 1.</li>
</ul>

<p>A number is called a <strong>binary palindrome</strong> if its binary representation without leading zeros reads the same forward and backward.</p>

<p>Your task is to return an integer array <code>ans</code>, where <code>ans[i]</code> represents the <strong>minimum</strong> number of operations required to convert <code>nums[i]</code> into a <strong>binary palindrome</strong>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,4]</span></p>

<p><strong>Output:</strong> <span class="example-io">[0,1,1]</span></p>

<p><strong>Explanation:</strong></p>

<p>One optimal set of operations:</p>

<table style="border: 1px solid black;">
	<thead>
		<tr>
			<th style="border: 1px solid black;"><code>nums[i]</code></th>
			<th style="border: 1px solid black;">Binary(<code>nums[i]</code>)</th>
			<th style="border: 1px solid black;">Nearest<br />
			Palindrome</th>
			<th style="border: 1px solid black;">Binary<br />
			(Palindrome)</th>
			<th style="border: 1px solid black;">Operations Required</th>
			<th style="border: 1px solid black;"><code>ans[i]</code></th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">Already palindrome</td>
			<td style="border: 1px solid black;">0</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;">10</td>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;">11</td>
			<td style="border: 1px solid black;">Increase by 1</td>
			<td style="border: 1px solid black;">1</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">4</td>
			<td style="border: 1px solid black;">100</td>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;">11</td>
			<td style="border: 1px solid black;">Decrease by 1</td>
			<td style="border: 1px solid black;">1</td>
		</tr>
	</tbody>
</table>

<p>Thus, <code>ans = [0, 1, 1]</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [6,7,12]</span></p>

<p><strong>Output:</strong> <span class="example-io">[1,0,3]</span></p>

<p><strong>Explanation:</strong></p>

<p>One optimal set of operations:</p>

<table style="border: 1px solid black;">
	<thead>
		<tr>
			<th style="border: 1px solid black;"><code>nums[i]</code></th>
			<th style="border: 1px solid black;">Binary(<code>nums[i]</code>)</th>
			<th style="border: 1px solid black;">Nearest<br />
			Palindrome</th>
			<th style="border: 1px solid black;">Binary<br />
			(Palindrome)</th>
			<th style="border: 1px solid black;">Operations Required</th>
			<th style="border: 1px solid black;"><code>ans[i]</code></th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 1px solid black;">6</td>
			<td style="border: 1px solid black;">110</td>
			<td style="border: 1px solid black;">5</td>
			<td style="border: 1px solid black;">101</td>
			<td style="border: 1px solid black;">Decrease by 1</td>
			<td style="border: 1px solid black;">1</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">7</td>
			<td style="border: 1px solid black;">111</td>
			<td style="border: 1px solid black;">7</td>
			<td style="border: 1px solid black;">111</td>
			<td style="border: 1px solid black;">Already palindrome</td>
			<td style="border: 1px solid black;">0</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">12</td>
			<td style="border: 1px solid black;">1100</td>
			<td style="border: 1px solid black;">15</td>
			<td style="border: 1px solid black;">1111</td>
			<td style="border: 1px solid black;">Increase by 3</td>
			<td style="border: 1px solid black;">3</td>
		</tr>
	</tbody>
</table>

<p>Thus, <code>ans = [1, 0, 3]</code>.</p>
</div>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5000</code></li>
	<li><code><sup>​​​​​​​</sup>1 &lt;= nums[i] &lt;=<sup> </sup>5000</code></li>
</ul>