leetcode-problemset/leetcode-cn/originData/the-number-of-beautiful-subsets.json

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        "question": {
            "questionId": "2696",
            "questionFrontendId": "2597",
            "categoryTitle": "Algorithms",
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            "title": "The Number of Beautiful Subsets",
            "titleSlug": "the-number-of-beautiful-subsets",
            "content": "<p>You are given an array <code>nums</code> of positive integers and a <strong>positive</strong> integer <code>k</code>.</p>\n\n<p>A subset of <code>nums</code> is <strong>beautiful</strong> if it does not contain two integers with an absolute difference equal to <code>k</code>.</p>\n\n<p>Return <em>the number of <strong>non-empty beautiful </strong>subsets of the array</em> <code>nums</code>.</p>\n\n<p>A <strong>subset</strong> of <code>nums</code> is an array that can be obtained by deleting some (possibly none) elements from <code>nums</code>. Two subsets are different if and only if the chosen indices to delete are different.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,4,6], k = 2\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The beautiful subsets of the array nums are: [2], [4], [6], [2, 6].\nIt can be proved that there are only 4 beautiful subsets in the array [2,4,6].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1], k = 1\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> The beautiful subset of the array nums is [1].\nIt can be proved that there is only 1 beautiful subset in the array [1].\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 20</code></li>\n\t<li><code>1 &lt;= nums[i], k &lt;= 1000</code></li>\n</ul>\n",
            "translatedTitle": "美丽子集的数目",
            "translatedContent": "<p>给你一个由正整数组成的数组 <code>nums</code> 和一个 <strong>正</strong> 整数 <code>k</code> 。</p>\n\n<p>如果 <code>nums</code> 的子集中，任意两个整数的绝对差均不等于 <code>k</code> ，则认为该子数组是一个 <strong>美丽</strong> 子集。</p>\n\n<p>返回数组 <code>nums</code> 中 <strong>非空</strong> 且 <strong>美丽</strong> 的子集数目。</p>\n\n<p><code>nums</code> 的子集定义为：可以经由 <code>nums</code> 删除某些元素（也可能不删除）得到的一个数组。只有在删除元素时选择的索引不同的情况下，两个子集才会被视作是不同的子集。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = [2,4,6], k = 2\n<strong>输出：</strong>4\n<strong>解释：</strong>数组 nums 中的美丽子集有：[2], [4], [6], [2, 6] 。\n可以证明数组 [2,4,6] 中只存在 4 个美丽子集。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [1], k = 1\n<strong>输出：</strong>1\n<strong>解释：</strong>数组 nums 中的美丽数组有：[1] 。\n可以证明数组 [1] 中只存在 1 个美丽子集。 \n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 20</code></li>\n\t<li><code>1 &lt;= nums[i], k &lt;= 1000</code></li>\n</ul>\n",
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                    "code": "class Solution {\npublic:\n    int beautifulSubsets(vector<int>& nums, int k) {\n        \n    }\n};",
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                    "code": "class Solution(object):\n    def beautifulSubsets(self, nums, k):\n        \"\"\"\n        :type nums: List[int]\n        :type k: int\n        :rtype: int\n        \"\"\"",
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                    "code": "/**\n * @param {number[]} nums\n * @param {number} k\n * @return {number}\n */\nvar beautifulSubsets = function(nums, k) {\n\n};",
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                    "code": "# @param {Integer[]} nums\n# @param {Integer} k\n# @return {Integer}\ndef beautiful_subsets(nums, k)\n\nend",
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                    "code": "defmodule Solution do\n  @spec beautiful_subsets(nums :: [integer], k :: integer) :: integer\n  def beautiful_subsets(nums, k) do\n\n  end\nend",
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            "hints": [
                "Sort the array nums and create another array cnt of size nums[i].",
                "Use backtracking to generate all the beautiful subsets. If cnt[nums[i] - k] is positive, then it is impossible to add nums[i] in the subset, and we just move to the next index. Otherwise, it is also possible to add nums[i] in the subset, in this case, increase cnt[nums[i]], and move to the next index.",
                "Bonus: Can you solve the problem in O(n log n)?"
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