leetcode-problemset/leetcode-cn/originData/count-the-number-of-powerful-integers.json

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            "title": "Count the Number of Powerful Integers",
            "titleSlug": "count-the-number-of-powerful-integers",
            "content": "<p>You are given three integers <code>start</code>, <code>finish</code>, and <code>limit</code>. You are also given a <strong>0-indexed</strong> string <code>s</code> representing a <strong>positive</strong> integer.</p>\n\n<p>A <strong>positive</strong> integer <code>x</code> is called <strong>powerful</strong> if it ends with <code>s</code> (in other words, <code>s</code> is a <strong>suffix</strong> of <code>x</code>) and each digit in <code>x</code> is at most <code>limit</code>.</p>\n\n<p>Return <em>the <strong>total</strong> number of powerful integers in the range</em> <code>[start..finish]</code>.</p>\n\n<p>A string <code>x</code> is a suffix of a string <code>y</code> if and only if <code>x</code> is a substring of <code>y</code> that starts from some index (<strong>including </strong><code>0</code>) in <code>y</code> and extends to the index <code>y.length - 1</code>. For example, <code>25</code> is a suffix of <code>5125</code> whereas <code>512</code> is not.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> start = 1, finish = 6000, limit = 4, s = &quot;124&quot;\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The powerful integers in the range [1..6000] are 124, 1124, 2124, 3124, and, 4124. All these integers have each digit &lt;= 4, and &quot;124&quot; as a suffix. Note that 5124 is not a powerful integer because the first digit is 5 which is greater than 4.\nIt can be shown that there are only 5 powerful integers in this range.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> start = 15, finish = 215, limit = 6, s = &quot;10&quot;\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The powerful integers in the range [15..215] are 110 and 210. All these integers have each digit &lt;= 6, and &quot;10&quot; as a suffix.\nIt can be shown that there are only 2 powerful integers in this range.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> start = 1000, finish = 2000, limit = 4, s = &quot;3000&quot;\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> All integers in the range [1000..2000] are smaller than 3000, hence &quot;3000&quot; cannot be a suffix of any integer in this range.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= start &lt;= finish &lt;= 10<sup>15</sup></code></li>\n\t<li><code>1 &lt;= limit &lt;= 9</code></li>\n\t<li><code>1 &lt;= s.length &lt;= floor(log<sub>10</sub>(finish)) + 1</code></li>\n\t<li><code>s</code> only consists of numeric digits which are at most <code>limit</code>.</li>\n\t<li><code>s</code> does not have leading zeros.</li>\n</ul>\n",
            "translatedTitle": "统计强大整数的数目",
            "translatedContent": "<p>给你三个整数&nbsp;<code>start</code>&nbsp;，<code>finish</code>&nbsp;和&nbsp;<code>limit</code>&nbsp;。同时给你一个下标从&nbsp;<strong>0</strong>&nbsp;开始的字符串&nbsp;<code>s</code>&nbsp;，表示一个 <strong>正</strong>&nbsp;整数。</p>\n\n<p>如果一个 <strong>正</strong>&nbsp;整数&nbsp;<code>x</code> 末尾部分是&nbsp;<code>s</code>&nbsp;（换句话说，<code>s</code>&nbsp;是 <code>x</code>&nbsp;的 <strong>后缀</strong>），且 <code>x</code>&nbsp;中的每个数位至多是 <code>limit</code>&nbsp;，那么我们称 <code>x</code>&nbsp;是 <strong>强大的</strong>&nbsp;。</p>\n\n<p>请你返回区间&nbsp;<code>[start..finish]</code>&nbsp;内强大整数的&nbsp;<strong>总数目</strong>&nbsp;。</p>\n\n<p>如果一个字符串 <code>x</code>&nbsp;是 <code>y</code>&nbsp;中某个下标开始（<strong>包括</strong>&nbsp;<code>0</code>&nbsp;），到下标为&nbsp;<code>y.length - 1</code>&nbsp;结束的子字符串，那么我们称&nbsp;<code>x</code>&nbsp;是&nbsp;<code>y</code>&nbsp;的一个后缀。比方说，<code>25</code>&nbsp;是&nbsp;<code>5125</code>&nbsp;的一个后缀，但不是&nbsp;<code>512</code>&nbsp;的后缀。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>start = 1, finish = 6000, limit = 4, s = \"124\"\n<b>输出：</b>5\n<b>解释：</b>区间 [1..6000] 内的强大数字为 124 ，1124 ，2124 ，3124 和 4124 。这些整数的各个数位都 &lt;= 4 且 \"124\" 是它们的后缀。注意 5124 不是强大整数，因为第一个数位 5 大于 4 。\n这个区间内总共只有这 5 个强大整数。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>start = 15, finish = 215, limit = 6, s = \"10\"\n<b>输出：</b>2\n<b>解释：</b>区间 [15..215] 内的强大整数为 110 和 210 。这些整数的各个数位都 &lt;= 6 且 \"10\" 是它们的后缀。\n这个区间总共只有这 2 个强大整数。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>start = 1000, finish = 2000, limit = 4, s = \"3000\"\n<b>输出：</b>0\n<b>解释：</b>区间 [1000..2000] 内的整数都小于 3000 ，所以 \"3000\" 不可能是这个区间内任何整数的后缀。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= start &lt;= finish &lt;= 10<sup>15</sup></code></li>\n\t<li><code>1 &lt;= limit &lt;= 9</code></li>\n\t<li><code>1 &lt;= s.length &lt;= floor(log<sub>10</sub>(finish)) + 1</code></li>\n\t<li><code>s</code>&nbsp;数位中每个数字都小于等于&nbsp;<code>limit</code>&nbsp;。</li>\n\t<li><code>s</code>&nbsp;不包含任何前导 0 。</li>\n</ul>\n",
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                "We can use digit DP to count powerful integers in the range <code>[1, x]</code>.",
                "Let <code>dp[i][j]</code> be the number of integers that have <code>i</code> digits (with allowed leading 0s) and <code>j</code> refers to the comparison between the current number and the prefix of <code>x</code>, <code>j == 0</code> if the i-digit number formed currently is identical to the leftmost <code>i</code> digits of <code>x</code>, else if <code>j ==1</code> it means the i-digit number is smaller than the leftmost <code>i</code> digits of <code>x</code>.",
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