{ "data": { "question": { "questionId": "3316", "questionFrontendId": "3098", "boundTopicId": null, "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> </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 <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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= n == nums.length <= 50</code></li>\n\t<li><code>-10<sup>8</sup> <= nums[i] <= 10<sup>8</sup> </code></li>\n\t<li><code>2 <= k <= n</code></li>\n</ul>\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 100, "dislikes": 4, "isLiked": null, "similarQuestions": "[{\"title\": \"Number of Subsequences That Satisfy the Given Sum Condition\", \"titleSlug\": \"number-of-subsequences-that-satisfy-the-given-sum-condition\", \"difficulty\": \"Medium\", \"translatedTitle\": null}, {\"title\": \"Closest Subsequence Sum\", \"titleSlug\": \"closest-subsequence-sum\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]", "exampleTestcases": "[1,2,3,4]\n3\n[2,2]\n2\n[4,3,-1]\n2", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Array", "slug": "array", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Sorting", "slug": "sorting", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int sumOfPowers(vector<int>& nums, int k) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int sumOfPowers(int[] nums, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def sumOfPowers(self, nums, k):\n \"\"\"\n :type nums: List[int]\n :type k: int\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def sumOfPowers(self, nums: List[int], k: int) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "int sumOfPowers(int* nums, int numsSize, int k) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int SumOfPowers(int[] nums, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[]} nums\n * @param {number} k\n * @return {number}\n */\nvar sumOfPowers = function(nums, k) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function sumOfPowers(nums: number[], k: number): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[] $nums\n * @param Integer $k\n * @return Integer\n */\n function sumOfPowers($nums, $k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func sumOfPowers(_ nums: [Int], _ k: Int) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun sumOfPowers(nums: IntArray, k: Int): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int sumOfPowers(List<int> nums, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func sumOfPowers(nums []int, k int) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[]} nums\n# @param {Integer} k\n# @return {Integer}\ndef sum_of_powers(nums, k)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def sumOfPowers(nums: Array[Int], k: Int): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn sum_of_powers(nums: Vec<i32>, k: i32) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (sum-of-powers nums k)\n (-> (listof exact-integer?) exact-integer? exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec sum_of_powers(Nums :: [integer()], K :: integer()) -> integer().\nsum_of_powers(Nums, K) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec sum_of_powers(nums :: [integer], k :: integer) :: integer\n def sum_of_powers(nums, k) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"3.2K\", \"totalSubmission\": \"14K\", \"totalAcceptedRaw\": 3233, \"totalSubmissionRaw\": 14028, \"acRate\": \"23.0%\"}", "hints": [ "Sort <code>nums</code>.", "There are at most <code>n<sup>2</sup></code> distinct differences.", "For a particular difference <code>d</code>, let <code>dp[len][i][j]</code> be the number of subsequences of length <code>len</code> in the subarray <code>nums[0..i]</code> where the last element picked was at index <code>j</code>.", "For each index, we can check if it can be picked if <code>nums[i] - nums[j] <= d</code>." ], "solution": null, "status": null, "sampleTestCase": "[1,2,3,4]\n3", "metaData": "{\n \"name\": \"sumOfPowers\",\n \"params\": [\n {\n \"name\": \"nums\",\n \"type\": \"integer[]\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"k\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "enableTestMode": false, "enableDebugger": true, "envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 17 </code> using the latest C++ 20 standard, and <code>libstdc++</code> provided by GCC 11.</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>. 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