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"questionId": "2757",
"questionFrontendId": "2719",
"categoryTitle": "Algorithms",
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"title": "Count of Integers",
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"content": "<p>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 <em>good</em> if:</p>\n\n<ul>\n\t<li><code>num1 &lt;= x &lt;= num2</code></li>\n\t<li><code>min_sum &lt;= digit_sum(x) &lt;= max_sum</code>.</li>\n</ul>\n\n<p>Return <em>the number of good integers</em>. Since the answer may be large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>Note that <code>digit_sum(x)</code> denotes the sum of the digits of <code>x</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;12&quot;, <code>min_sum</code> = 1, max_sum = 8\n<strong>Output:</strong> 11\n<strong>Explanation:</strong> 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.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;5&quot;, <code>min_sum</code> = 1, max_sum = 5\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The 5 integers whose sum of digits lies between 1 and 5 are 1,2,3,4, and 5. Thus, we return 5.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= num1 &lt;= num2 &lt;= 10<sup>22</sup></code></li>\n\t<li><code>1 &lt;= min_sum &lt;= max_sum &lt;= 400</code></li>\n</ul>\n",
"translatedTitle": "统计整数数目",
"translatedContent": "<p>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:</p>\n\n<ul>\n\t<li><code>num1 &lt;= x &lt;= num2</code></li>\n\t<li><code>min_sum &lt;= digit_sum(x) &lt;= max_sum</code>.</li>\n</ul>\n\n<p>请你返回好整数的数目。答案可能很大,请返回答案对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;取余后的结果。</p>\n\n<p>注意,<code>digit_sum(x)</code>&nbsp;表示&nbsp;<code>x</code>&nbsp;各位数字之和。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<b>输入:</b>num1 = \"1\", num2 = \"12\", min_num = 1, max_num = 8\n<b>输出:</b>11\n<b>解释:</b>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 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<b>输入:</b>num1 = \"1\", num2 = \"5\", min_num = 1, max_num = 5\n<b>输出:</b>5\n<b>解释:</b>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 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= num1 &lt;= num2 &lt;= 10<sup>22</sup></code></li>\n\t<li><code>1 &lt;= min_sum &lt;= max_sum &lt;= 400</code></li>\n</ul>\n",
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"Let f(n, l, r) denotes the number of integers from 1 to n with the sum of digits between l and r.",
"The answer is f(num2, min_sum, max_sum) - f(num-1, min_sum, max_sum).",
"You can calculate f(n, l, r) using digit dp."
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