leetcode-problemset/leetcode-cn/originData/find-the-sum-of-subsequence-powers.json

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        "question": {
            "questionId": "3316",
            "questionFrontendId": "3098",
            "categoryTitle": "Algorithms",
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            "title": "Find the Sum of Subsequence Powers",
            "titleSlug": "find-the-sum-of-subsequence-powers",
            "content": "<p>You are given an integer array <code>nums</code> of length <code>n</code>, and a <strong>positive</strong> integer <code>k</code>.</p>\n\n<p>The <strong>power</strong> of a <span data-keyword=\"subsequence-array\">subsequence</span> is defined as the <strong>minimum</strong> absolute difference between <strong>any</strong> two elements in the subsequence.</p>\n\n<p>Return <em>the <strong>sum</strong> of <strong>powers</strong> of <strong>all</strong> subsequences of </em><code>nums</code><em> which have length</em> <strong><em>equal to</em></strong> <code>k</code>.</p>\n\n<p>Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,2,3,4], k = 3</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There are 4 subsequences in <code>nums</code> which have length 3: <code>[1,2,3]</code>, <code>[1,3,4]</code>, <code>[1,2,4]</code>, and <code>[2,3,4]</code>. The sum of powers is <code>|2 - 3| + |3 - 4| + |2 - 1| + |3 - 4| = 4</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [2,2], k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The only subsequence in <code>nums</code> which has length 2 is&nbsp;<code>[2,2]</code>. The sum of powers is <code>|2 - 2| = 0</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [4,3,-1], k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">10</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There are 3 subsequences in <code>nums</code> which have length 2: <code>[4,3]</code>, <code>[4,-1]</code>, and <code>[3,-1]</code>. The sum of powers is <code>|4 - 3| + |4 - (-1)| + |3 - (-1)| = 10</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == nums.length &lt;= 50</code></li>\n\t<li><code>-10<sup>8</sup> &lt;= nums[i] &lt;= 10<sup>8</sup> </code></li>\n\t<li><code>2 &lt;= k &lt;= n</code></li>\n</ul>\n",
            "translatedTitle": "求出所有子序列的能量和",
            "translatedContent": "<p>给你一个长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>nums</code>&nbsp;和一个 <strong>正</strong>&nbsp;整数&nbsp;<code>k</code>&nbsp;。</p>\n\n<p>一个子序列的 <strong>能量</strong>&nbsp;定义为子序列中&nbsp;<strong>任意</strong>&nbsp;两个元素的差值绝对值的 <strong>最小值</strong>&nbsp;。</p>\n\n<p>请你返回 <code>nums</code>&nbsp;中长度 <strong>等于</strong>&nbsp;<code>k</code>&nbsp;的 <strong>所有</strong>&nbsp;子序列的 <strong>能量和</strong>&nbsp;。</p>\n\n<p>由于答案可能会很大，将答案对&nbsp;<code>10<sup>9 </sup>+ 7</code>&nbsp;<strong>取余</strong>&nbsp;后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [1,2,3,4], k = 3</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><code>nums</code>&nbsp;中总共有 4 个长度为 3 的子序列：<code>[1,2,3]</code>&nbsp;，<code>[1,3,4]</code>&nbsp;，<code>[1,2,4]</code>&nbsp;和&nbsp;<code>[2,3,4]</code>&nbsp;。能量和为 <code>|2 - 3| + |3 - 4| + |2 - 1| + |3 - 4| = 4</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [2,2], k = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>0</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><code>nums</code>&nbsp;中唯一一个长度为 2 的子序列是&nbsp;<code>[2,2]</code>&nbsp;。能量和为&nbsp;<code>|2 - 2| = 0</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">nums = [4,3,-1], k = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>10</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><code>nums</code>&nbsp;总共有 3 个长度为 2 的子序列：<code>[4,3]</code>&nbsp;，<code>[4,-1]</code>&nbsp;和&nbsp;<code>[3,-1]</code>&nbsp;。能量和为&nbsp;<code>|4 - 3| + |4 - (-1)| + |3 - (-1)| = 10</code>&nbsp;。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == nums.length &lt;= 50</code></li>\n\t<li><code>-10<sup>8</sup> &lt;= nums[i] &lt;= 10<sup>8</sup> </code></li>\n\t<li><code>2 &lt;= k &lt;= n</code></li>\n</ul>\n",
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