count-of-integers

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Algorithms

You are given two numeric strings <code>num1</code> and <code>num2</code> and two integers <code>max_sum</code> and <code>min_sum</code>. We denote an integer <code>x</code> to be good if:

<ul>
	<li><code>num1 &lt;= x &lt;= num2</code></li>
	<li><code>min_sum &lt;= digit_sum(x) &lt;= max_sum</code>.</li>
</ul>

Return the number of good integers. Since the answer may be large, return it modulo <code>109 + 7</code>.

Note that <code>digit_sum(x)</code> denotes the sum of the digits of <code>x</code>.

&nbsp;
Example 1:

<pre>
Input: num1 = &quot;1&quot;, num2 = &quot;12&quot;, <code>min_sum</code> = 1, max_sum = 8
Output: 11
Explanation: There are 11 integers whose sum of digits lies between 1 and 8 are 1,2,3,4,5,6,7,8,10,11, and 12. Thus, we return 11.
</pre>

Example 2:

<pre>
Input: num1 = &quot;1&quot;, num2 = &quot;5&quot;, <code>min_sum</code> = 1, max_sum = 5
Output: 5
Explanation: The 5 integers whose sum of digits lies between 1 and 5 are 1,2,3,4, and 5. Thus, we return 5.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= num1 &lt;= num2 &lt;= 1022</code></li>
	<li><code>1 &lt;= min_sum &lt;= max_sum &lt;= 400</code></li>
</ul>

count

Count of Integers

Math

String

Dynamic Programming

给你两个数字字符串&nbsp;<code>num1</code>&nbsp;和&nbsp;<code>num2</code>&nbsp;，以及两个整数&nbsp;<code>max_sum</code> 和&nbsp;<code>min_sum</code>&nbsp;。如果一个整数&nbsp;<code>x</code>&nbsp;满足以下条件，我们称它是一个好整数：

<ul>
	<li><code>num1 &lt;= x &lt;= num2</code></li>
	<li><code>min_sum &lt;= digit_sum(x) &lt;= max_sum</code>.</li>
</ul>

请你返回好整数的数目。答案可能很大，请返回答案对&nbsp;<code>109 + 7</code>&nbsp;取余后的结果。

注意，<code>digit_sum(x)</code>&nbsp;表示&nbsp;<code>x</code>&nbsp;各位数字之和。

&nbsp;

示例 1：

<pre>
输入：num1 = "1", num2 = "12", min_num = 1, max_num = 8
输出：11
解释：总共有 11 个整数的数位和在 1 到 8 之间，分别是 1,2,3,4,5,6,7,8,10,11 和 12 。所以我们返回 11 。
</pre>

示例 2：

<pre>
输入：num1 = "1", num2 = "5", min_num = 1, max_num = 5
输出：5
解释：数位和在 1 到 5 之间的 5 个整数分别为 1,2,3,4 和 5 。所以我们返回 5 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= num1 &lt;= num2 &lt;= 1022</code></li>
	<li><code>1 &lt;= min_sum &lt;= max_sum &lt;= 400</code></li>
</ul>