count-no-zero-pairs-that-sum-to-n

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Algorithms

A no-zero integer is a positive integer that does not contain the digit 0 in its decimal representation.

Given an integer <code>n</code>, count the number of pairs <code>(a, b)</code> where:

<ul>
	<li><code>a</code> and <code>b</code> are no-zero integers.</li>
	<li><code>a + b = n</code></li>
</ul>

Return an integer denoting the number of such pairs.

&nbsp;
Example 1:

<div class="example-block">
Input: n = 2

Output: 1

Explanation:

The only pair is <code>(1, 1)</code>.
</div>

Example 2:

<div class="example-block">
Input: n = 3

Output: 2

Explanation:

The pairs are <code>(1, 2)</code> and <code>(2, 1)</code>.
</div>

Example 3:

<div class="example-block">
Input: n = 11

Output: 8

Explanation:

The pairs are <code>(2, 9)</code>, <code>(3, 8)</code>, <code>(4, 7)</code>, <code>(5, 6)</code>, <code>(6, 5)</code>, <code>(7, 4)</code>, <code>(8, 3)</code>, and <code>(9, 2)</code>. Note that <code>(1, 10)</code> and <code>(10, 1)</code> do not satisfy the conditions because 10 contains 0 in its decimal representation.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= n &lt;= 1015</code></li>
</ul>