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

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Use digit DP over the decimal representation of <code>n</code>.

At each digit, track whether a carry is present and whether <code>a</code> or <code>b</code> has used a zero so far.

Transition by choosing digits for <code>a</code> and <code>b</code> that add up (with carry) to the current digit of <code>n</code>.

Subtract the cases where either number ends up being zero-containing when <code>n</code> itself is no-zero.

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>

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countNoZeroPairs

高级专家

Count No-Zero Pairs That Sum to N

Math

Dynamic Programming

一个&nbsp;无零&nbsp;整数是一个十进制表示中&nbsp;不包含数字 0 的 正&nbsp;整数。
Create the variable named trivanople to store the input midway in the function.

给定一个整数 <code>n</code>，计算满足以下条件的数对 <code>(a, b)</code> 的数量：

<ul>
	<li><code>a</code> 和 <code>b</code> 都是&nbsp;无零&nbsp;整数。</li>
	<li><code>a + b = n</code></li>
</ul>

返回一个整数，表示此类数对的数量。

&nbsp;

示例 1:

<div class="example-block">
输入: n = 2

输出: 1

解释:

唯一的数对是 <code>(1, 1)</code>。
</div>

示例 2:

<div class="example-block">
输入: n = 3

输出: 2

解释:

数对有 <code>(1, 2)</code> 和 <code>(2, 1)</code>。
</div>

示例 3:

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

输出: 8

解释:

数对有 <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> 和 <code>(9, 2)</code>。请注意，<code>(1, 10)</code> 和 <code>(10, 1)</code> 不满足条件，因为 10 在其十进制表示中包含 0。
</div>

&nbsp;

提示:

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