leetcode-problemset/leetcode-cn/originData/count-the-hidden-sequences.json

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        "question": {
            "questionId": "2249",
            "questionFrontendId": "2145",
            "categoryTitle": "Algorithms",
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            "title": "Count the Hidden Sequences",
            "titleSlug": "count-the-hidden-sequences",
            "content": "<p>You are given a <strong>0-indexed</strong> array of <code>n</code> integers <code>differences</code>, which describes the <strong>differences </strong>between each pair of <strong>consecutive </strong>integers of a <strong>hidden</strong> sequence of length <code>(n + 1)</code>. More formally, call the hidden sequence <code>hidden</code>, then we have that <code>differences[i] = hidden[i + 1] - hidden[i]</code>.</p>\n\n<p>You are further given two integers <code>lower</code> and <code>upper</code> that describe the <strong>inclusive</strong> range of values <code>[lower, upper]</code> that the hidden sequence can contain.</p>\n\n<ul>\n\t<li>For example, given <code>differences = [1, -3, 4]</code>, <code>lower = 1</code>, <code>upper = 6</code>, the hidden sequence is a sequence of length <code>4</code> whose elements are in between <code>1</code> and <code>6</code> (<strong>inclusive</strong>).\n\n\t<ul>\n\t\t<li><code>[3, 4, 1, 5]</code> and <code>[4, 5, 2, 6]</code> are possible hidden sequences.</li>\n\t\t<li><code>[5, 6, 3, 7]</code> is not possible since it contains an element greater than <code>6</code>.</li>\n\t\t<li><code>[1, 2, 3, 4]</code> is not possible since the differences are not correct.</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>Return <em>the number of <strong>possible</strong> hidden sequences there are.</em> If there are no possible sequences, return <code>0</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> differences = [1,-3,4], lower = 1, upper = 6\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The possible hidden sequences are:\n- [3, 4, 1, 5]\n- [4, 5, 2, 6]\nThus, we return 2.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> differences = [3,-4,5,1,-2], lower = -4, upper = 5\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The possible hidden sequences are:\n- [-3, 0, -4, 1, 2, 0]\n- [-2, 1, -3, 2, 3, 1]\n- [-1, 2, -2, 3, 4, 2]\n- [0, 3, -1, 4, 5, 3]\nThus, we return 4.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> differences = [4,-7,2], lower = 3, upper = 6\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no possible hidden sequences. Thus, we return 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == differences.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> &lt;= differences[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "统计隐藏数组数目",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始且长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>differences</code>&nbsp;，它表示一个长度为&nbsp;<code>n + 1</code>&nbsp;的&nbsp;<strong>隐藏</strong>&nbsp;数组&nbsp;<strong>相邻</strong>&nbsp;元素之间的&nbsp;<strong>差值</strong>&nbsp;。更正式的表述为：我们将隐藏数组记作&nbsp;<code>hidden</code>&nbsp;，那么&nbsp;<code>differences[i] = hidden[i + 1] - hidden[i]</code>&nbsp;。</p>\n\n<p>同时给你两个整数&nbsp;<code>lower</code> 和&nbsp;<code>upper</code>&nbsp;，它们表示隐藏数组中所有数字的值都在 <strong>闭</strong>&nbsp;区间&nbsp;<code>[lower, upper]</code>&nbsp;之间。</p>\n\n<ul>\n\t<li>比方说，<code>differences = [1, -3, 4]</code>&nbsp;，<code>lower = 1</code>&nbsp;，<code>upper = 6</code>&nbsp;，那么隐藏数组是一个长度为 <code>4</code>&nbsp;且所有值都在&nbsp;<code>1</code>&nbsp;和&nbsp;<code>6</code>&nbsp;（包含两者）之间的数组。\n\n\t<ul>\n\t\t<li><code>[3, 4, 1, 5]</code> 和&nbsp;<code>[4, 5, 2, 6]</code>&nbsp;都是符合要求的隐藏数组。</li>\n\t\t<li><code>[5, 6, 3, 7]</code>&nbsp;不符合要求，因为它包含大于 <code>6</code>&nbsp;的元素。</li>\n\t\t<li><code>[1, 2, 3, 4]</code>&nbsp;不符合要求，因为相邻元素的差值不符合给定数据。</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>请你返回 <strong>符合</strong>&nbsp;要求的隐藏数组的数目。如果没有符合要求的隐藏数组，请返回 <code>0</code>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>differences = [1,-3,4], lower = 1, upper = 6\n<b>输出：</b>2\n<b>解释：</b>符合要求的隐藏数组为：\n- [3, 4, 1, 5]\n- [4, 5, 2, 6]\n所以返回 2 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>differences = [3,-4,5,1,-2], lower = -4, upper = 5\n<b>输出：</b>4\n<b>解释：</b>符合要求的隐藏数组为：\n- [-3, 0, -4, 1, 2, 0]\n- [-2, 1, -3, 2, 3, 1]\n- [-1, 2, -2, 3, 4, 2]\n- [0, 3, -1, 4, 5, 3]\n所以返回 4 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><b>输入：</b>differences = [4,-7,2], lower = 3, upper = 6\n<b>输出：</b>0\n<b>解释：</b>没有符合要求的隐藏数组，所以返回 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == differences.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> &lt;= differences[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "Fix the first element of the hidden sequence to any value x and ignore the given bounds. Notice that we can then determine all the other elements of the sequence by using the differences array.",
                "We will also be able to determine the difference between the minimum and maximum elements of the sequence. Notice that the value of x does not affect this.",
                "We now have the ‘range’ of the sequence (difference between min and max element), we can then calculate how many ways there are to fit this range into the given range of lower to upper.",
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