{ "data": { "question": { "questionId": "3313", "questionFrontendId": "3077", "categoryTitle": "Algorithms", "boundTopicId": 2674662, "title": "Maximum Strength of K Disjoint Subarrays", "titleSlug": "maximum-strength-of-k-disjoint-subarrays", "content": "

You are given a 0-indexed array of integers nums of length n, and a positive odd integer k.

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The strength of x subarrays is defined as strength = sum[1] * x - sum[2] * (x - 1) + sum[3] * (x - 2) - sum[4] * (x - 3) + ... + sum[x] * 1 where sum[i] is the sum of the elements in the ith subarray. Formally, strength is sum of (-1)i+1 * sum[i] * (x - i + 1) over all i's such that 1 <= i <= x.

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You need to select k disjoint subarrays from nums, such that their strength is maximum.

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Return the maximum possible strength that can be obtained.

\n\n

Note that the selected subarrays don't need to cover the entire array.

\n\n

 

\n

Example 1:

\n\n
\nInput: nums = [1,2,3,-1,2], k = 3\nOutput: 22\nExplanation: The best possible way to select 3 subarrays is: nums[0..2], nums[3..3], and nums[4..4]. The strength is (1 + 2 + 3) * 3 - (-1) * 2 + 2 * 1 = 22.\n
\n\n

Example 2:

\n\n
\nInput: nums = [12,-2,-2,-2,-2], k = 5\nOutput: 64\nExplanation: The only possible way to select 5 disjoint subarrays is: nums[0..0], nums[1..1], nums[2..2], nums[3..3], and nums[4..4]. The strength is 12 * 5 - (-2) * 4 + (-2) * 3 - (-2) * 2 + (-2) * 1 = 64.\n
\n\n

Example 3:

\n\n
\nInput: nums = [-1,-2,-3], k = 1\nOutput: -1\nExplanation: The best possible way to select 1 subarray is: nums[0..0]. The strength is -1.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "K 个不相交子数组的最大能量值", "translatedContent": "

给你一个长度为 n 下标从 0 开始的整数数组 nums 和一个 正奇数 整数 k 。

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x 个子数组的能量值定义为 strength = sum[1] * x - sum[2] * (x - 1) + sum[3] * (x - 2) - sum[4] * (x - 3) + ... + sum[x] * 1 ，其中 sum[i] 是第 i 个子数组的和。更正式的，能量值是满足 1 <= i <= x 的所有 i 对应的 (-1)i+1 * sum[i] * (x - i + 1) 之和。

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你需要在 nums 中选择 k 个 不相交子数组 ，使得 能量值最大 。

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请你返回可以得到的 最大能量值 。

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注意，选出来的所有子数组 不 需要覆盖整个数组。

\n\n

 

\n\n

示例 1：

\n\n
\n输入：nums = [1,2,3,-1,2], k = 3\n输出：22\n解释：选择 3 个子数组的最好方式是选择：nums[0..2] ，nums[3..3] 和 nums[4..4] 。能量值为 (1 + 2 + 3) * 3 - (-1) * 2 + 2 * 1 = 22 。\n
\n\n

示例 2：

\n\n
\n输入：nums = [12,-2,-2,-2,-2], k = 5\n输出：64\n解释：唯一一种选 5 个不相交子数组的方案是：nums[0..0] ，nums[1..1] ，nums[2..2] ，nums[3..3] 和 nums[4..4] 。能量值为 12 * 5 - (-2) * 4 + (-2) * 3 - (-2) * 2 + (-2) * 1 = 64 。\n
\n\n

示例 3：

\n\n
\n输入：nums = [-1,-2,-3], k = 1\n输出：-1\n解释：选择 1 个子数组的最优方案是：nums[0..0] 。能量值为 -1 。\n
\n\n

 

\n\n

提示：

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exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec maximum_strength(Nums :: [integer()], K :: integer()) -> integer().\nmaximum_strength(Nums, K) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec maximum_strength(nums :: [integer], k :: integer) :: integer\n def maximum_strength(nums, k) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"2.2K\", \"totalSubmission\": \"5.2K\", \"totalAcceptedRaw\": 2176, \"totalSubmissionRaw\": 5219, \"acRate\": \"41.7%\"}", "hints": [ "Let dp[i][j][x == 0/1] be the maximum strength to select j disjoint subarrays from the original array’s suffix (nums[i..(n - 1)]), x denotes whether we select the element or not.", "Initially dp[n][0][0] == 0.", "We have \r\ndp[i][j][1] = nums[i] * get(j) + max(dp[i + 1][j - 1][0], dp[i + 1][j][1]) where get(j) = j if j is odd, otherwise -j.", "We can select nums[i] as a separate subarray or select at least nums[i] and nums[i + 1] as the first subarray.\r\ndp[i][j][0] = max(dp[i + 1][j][0], dp[i][j][1]).", "The answer is dp[0][k][0]." ], "solution": null, "status": null, "sampleTestCase": "[1,2,3,-1,2]\n3", "metaData": "{\n \"name\": \"maximumStrength\",\n \"params\": [\n {\n \"name\": \"nums\",\n \"type\": \"integer[]\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"k\"\n }\n ],\n \"return\": {\n \"type\": \"long\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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