mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-10 18:48:13 +08:00
182 lines
17 KiB
JSON
182 lines
17 KiB
JSON
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"title": "Find the Maximum Number of Elements in Subset",
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"content": "<p>You are given an array of <strong>positive</strong> integers <code>nums</code>.</p>\n\n<p>You need to select a <span data-keyword=\"subset\">subset</span> of <code>nums</code> which satisfies the following condition:</p>\n\n<ul>\n\t<li>You can place the selected elements in a <strong>0-indexed</strong> array such that it follows the pattern: <code>[x, x<sup>2</sup>, x<sup>4</sup>, ..., x<sup>k/2</sup>, x<sup>k</sup>, x<sup>k/2</sup>, ..., x<sup>4</sup>, x<sup>2</sup>, x]</code> (<strong>Note</strong> that <code>k</code> can be be any <strong>non-negative</strong> power of <code>2</code>). For example, <code>[2, 4, 16, 4, 2]</code> and <code>[3, 9, 3]</code> follow the pattern while <code>[2, 4, 8, 4, 2]</code> does not.</li>\n</ul>\n\n<p>Return <em>the <strong>maximum</strong> number of elements in a subset that satisfies these conditions.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,4,1,2,2]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We can select the subset {4,2,2}, which can be placed in the array as [2,4,2] which follows the pattern and 2<sup>2</sup> == 4. Hence the answer is 3.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,3,2,4]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We can select the subset {1}, which can be placed in the array as [1] which follows the pattern. Hence the answer is 1. Note that we could have also selected the subsets {2}, {4}, or {3}, there may be multiple subsets which provide the same answer. \n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"exampleTestcases": "[5,4,1,2,2]\n[1,3,2,4]",
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"code": "class Solution {\npublic:\n int maximumLength(vector<int>& nums) {\n \n }\n};",
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"code": "class Solution(object):\n def maximumLength(self, nums):\n \"\"\"\n :type nums: List[int]\n :rtype: int\n \"\"\"\n ",
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"code": "/**\n * @param {number[]} nums\n * @return {number}\n */\nvar maximumLength = function(nums) {\n \n};",
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"code": "class Solution {\n\n /**\n * @param Integer[] $nums\n * @return Integer\n */\n function maximumLength($nums) {\n \n }\n}",
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"code": "class Solution {\n func maximumLength(_ nums: [Int]) -> Int {\n \n }\n}",
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"code": "class Solution {\n fun maximumLength(nums: IntArray): Int {\n \n }\n}",
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"code": "# @param {Integer[]} nums\n# @return {Integer}\ndef maximum_length(nums)\n \nend",
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"code": "impl Solution {\n pub fn maximum_length(nums: Vec<i32>) -> i32 {\n \n }\n}",
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"code": "defmodule Solution do\n @spec maximum_length(nums :: [integer]) :: integer\n def maximum_length(nums) do\n \n end\nend",
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"stats": "{\"totalAccepted\": \"13.4K\", \"totalSubmission\": \"60K\", \"totalAcceptedRaw\": 13372, \"totalSubmissionRaw\": 60016, \"acRate\": \"22.3%\"}",
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"hints": [
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"We can select an odd number of <code>1</code>’s.",
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"Put all the values into a HashSet. We can start from each <code>x > 1</code> as the smallest chosen value and we can find the longest subset by checking the new values (which are the square of the previous value) in the set by brute force.",
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"Note when <code>x > 1</code>, <code>x<sup>2</sup></code>, <code>x<sup>4</sup></code>, <code>x<sup>8</sup></code>, … increases very fast, the longest subset with smallest value x cannot be very long. (The length is <code>O(log(log(10<sup>9</sup>)))</code>.",
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"Hence we can directly check all lengths less than <code>10</code> for all values of <code>x</code>."
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"envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 17 </code> using the latest C++ 20 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code>OpenJDK 21</code>. Using compile arguments: <code>--enable-preview --release 21</code></p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 11</code> using the gnu11 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n int id; /* we'll use this field as the key */\\r\\n char name[10];\\r\\n UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n struct hash_entry *s;\\r\\n HASH_FIND_INT(users, &user_id, s);\\r\\n return s;\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-12\\\" target=\\\"_blank\\\">C# 12</a> with .NET 8 runtime</p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 20.10.0</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use 5.3.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/tree/fb4fdb984834421279aeb081df7af624d17c2a03\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.1 version of <a href=\\\"https://github.com
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