leetcode-problemset/leetcode-cn/originData/find-the-median-of-the-uniqueness-array.json

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        "question": {
            "questionId": "3362",
            "questionFrontendId": "3134",
            "categoryTitle": "Algorithms",
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            "title": "Find the Median of the Uniqueness Array",
            "titleSlug": "find-the-median-of-the-uniqueness-array",
            "content": "<p>You are given an integer array <code>nums</code>. The <strong>uniqueness array</strong> of <code>nums</code> is the sorted array that contains the number of distinct elements of all the <span data-keyword=\"subarray-nonempty\">subarrays</span> of <code>nums</code>. In other words, it is a sorted array consisting of <code>distinct(nums[i..j])</code>, for all <code>0 &lt;= i &lt;= j &lt; nums.length</code>.</p>\n\n<p>Here, <code>distinct(nums[i..j])</code> denotes the number of distinct elements in the subarray that starts at index <code>i</code> and ends at index <code>j</code>.</p>\n\n<p>Return the <strong>median</strong> of the <strong>uniqueness array</strong> of <code>nums</code>.</p>\n\n<p><strong>Note</strong> that the <strong>median</strong> of an array is defined as the middle element of the array when it is sorted in non-decreasing order. If there are two choices for a median, the <strong>smaller</strong> of the two values is taken.<!-- notionvc: 7e0f5178-4273-4a82-95ce-3395297921dc --></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]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The uniqueness array of <code>nums</code> is <code>[distinct(nums[0..0]), distinct(nums[1..1]), distinct(nums[2..2]), distinct(nums[0..1]), distinct(nums[1..2]), distinct(nums[0..2])]</code> which is equal to <code>[1, 1, 1, 2, 2, 3]</code>. The uniqueness array has a median of 1. Therefore, the answer is 1.</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 = [3,4,3,4,5]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The uniqueness array of <code>nums</code> is <code>[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3]</code>. The uniqueness array has a median of 2. Therefore, the answer is 2.</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 = [4,3,5,4]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The uniqueness array of <code>nums</code> is <code>[1, 1, 1, 1, 2, 2, 2, 3, 3, 3]</code>. The uniqueness array has a median of 2. Therefore, the answer is 2.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "找出唯一性数组的中位数",
            "translatedContent": "<p>给你一个整数数组 <code>nums</code> 。数组 <code>nums</code> 的<strong> 唯一性数组</strong> 是一个按元素从小到大排序的数组，包含了 <code>nums</code> 的所有<span data-keyword=\"subarray-nonempty\">非空子数组中</span>不同元素的个数。</p>\n\n<p>换句话说，这是由所有 <code>0 &lt;= i &lt;= j &lt; nums.length</code> 的 <code>distinct(nums[i..j])</code> 组成的递增数组。</p>\n\n<p>其中，<code>distinct(nums[i..j])</code> 表示从下标 <code>i</code> 到下标 <code>j</code> 的子数组中不同元素的数量。</p>\n\n<p>返回 <code>nums</code> <strong>唯一性数组 </strong>的 <strong>中位数 </strong>。</p>\n\n<p><strong>注意</strong>，数组的 <strong>中位数 </strong>定义为有序数组的中间元素。如果有两个中间元素，则取值较小的那个。<!-- notionvc: 7e0f5178-4273-4a82-95ce-3395297921dc --></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><strong>输入：</strong><span class=\"example-io\">nums = [1,2,3]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">1</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><code>nums</code> 的唯一性数组为 <code>[distinct(nums[0..0]), distinct(nums[1..1]), distinct(nums[2..2]), distinct(nums[0..1]), distinct(nums[1..2]), distinct(nums[0..2])]</code>，即 <code>[1, 1, 1, 2, 2, 3]</code> 。唯一性数组的中位数为 1 ，因此答案是 1 。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">nums = [3,4,3,4,5]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><code>nums</code> 的唯一性数组为 <code>[1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3]</code> 。唯一性数组的中位数为 2 ，因此答案是 2 。</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 = [4,3,5,4]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><code>nums</code> 的唯一性数组为 <code>[1, 1, 1, 1, 2, 2, 2, 3, 3, 3]</code> 。唯一性数组的中位数为 2 ，因此答案是 2 。</p>\n</div>\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;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                    "code": "class Solution {\npublic:\n    int medianOfUniquenessArray(vector<int>& nums) {\n        \n    }\n};",
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                    "code": "class Solution(object):\n    def medianOfUniquenessArray(self, nums):\n        \"\"\"\n        :type nums: List[int]\n        :rtype: int\n        \"\"\"",
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                "Binary search over the answer.",
                "For a given <code>x</code>, you need to check if <code>x</code> is the median, to the left of the median, or to the right of the media. You can do that by counting the number of sub-arrays <code>nums[i…j]</code> such that <code>distinct(num[i…j]) <= x</code>.",
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