leetcode-problemset/leetcode-cn/originData/count-stepping-numbers-in-range.json

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        "question": {
            "questionId": "2921",
            "questionFrontendId": "2801",
            "categoryTitle": "Algorithms",
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            "title": "Count Stepping Numbers in Range",
            "titleSlug": "count-stepping-numbers-in-range",
            "content": "<p>Given two positive integers <code>low</code> and <code>high</code> represented as strings, find the count of <strong>stepping numbers</strong> in the inclusive range <code>[low, high]</code>.</p>\n\n<p>A <strong>stepping number</strong> is an integer such that all of its adjacent digits have an absolute difference of <strong>exactly</strong> <code>1</code>.</p>\n\n<p>Return <em>an integer denoting the count of stepping numbers in the inclusive range</em> <code>[low, high]</code><em>. </em></p>\n\n<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p><strong>Note:</strong> A stepping number should not have a leading zero.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> low = &quot;1&quot;, high = &quot;11&quot;\n<strong>Output:</strong> 10\n<strong>Explanation: </strong>The stepping numbers in the range [1,11] are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. There are a total of 10 stepping numbers in the range. Hence, the output is 10.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> low = &quot;90&quot;, high = &quot;101&quot;\n<strong>Output:</strong> 2\n<strong>Explanation: </strong>The stepping numbers in the range [90,101] are 98 and 101. There are a total of 2 stepping numbers in the range. Hence, the output is 2. </pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= int(low) &lt;= int(high) &lt; 10<sup>100</sup></code></li>\n\t<li><code>1 &lt;= low.length, high.length &lt;= 100</code></li>\n\t<li><code>low</code> and <code>high</code> consist of only digits.</li>\n\t<li><code>low</code> and <code>high</code> don&#39;t have any leading zeros.</li>\n</ul>\n",
            "translatedTitle": "统计范围内的步进数字数目",
            "translatedContent": "<p>给你两个正整数&nbsp;<code>low</code> 和&nbsp;<code>high</code>&nbsp;，都用字符串表示，请你统计闭区间 <code>[low, high]</code>&nbsp;内的 <strong>步进数字</strong>&nbsp;数目。</p>\n\n<p>如果一个整数相邻数位之间差的绝对值都 <strong>恰好</strong>&nbsp;是 <code>1</code>&nbsp;，那么这个数字被称为 <strong>步进数字</strong>&nbsp;。</p>\n\n<p>请你返回一个整数，表示闭区间&nbsp;<code>[low, high]</code>&nbsp;之间步进数字的数目。</p>\n\n<p>由于答案可能很大，请你将它对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;后返回。</p>\n\n<p><b>注意：</b>步进数字不能有前导 0 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>low = \"1\", high = \"11\"\n<b>输出：</b>10\n<strong>解释：</strong>区间 [1,11] 内的步进数字为 1 ，2 ，3 ，4 ，5 ，6 ，7 ，8 ，9 和 10 。总共有 10 个步进数字。所以输出为 10 。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>low = \"90\", high = \"101\"\n<b>输出：</b>2\n<strong>解释：</strong>区间 [90,101] 内的步进数字为 98 和 101 。总共有 2 个步进数字。所以输出为 2 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= int(low) &lt;= int(high) &lt; 10<sup>100</sup></code></li>\n\t<li><code>1 &lt;= low.length, high.length &lt;= 100</code></li>\n\t<li><code>low</code> 和&nbsp;<code>high</code>&nbsp;只包含数字。</li>\n\t<li><code>low</code> 和&nbsp;<code>high</code>&nbsp;都不含前导 0 。</li>\n</ul>\n",
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            "hints": [
                "Calculate the number of stepping numbers in the range [1, high] and subtract the number of stepping numbers in the range [1, low - 1].",
                "The main problem is calculating the number of stepping numbers in the range [1, x].",
                "First, calculate the number of stepping numbers shorter than x in length, which can be done using dynamic programming. (dp[i][j] is the number of i-digit stepping numbers ending with digit j).",
                "Finally, calculate the number of stepping numbers that have the same length as x similarly. However, this time we need to maintain whether the prefix (in string) is smaller than or equal to x in the DP state."
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