{ "data": { "question": { "questionId": "2891", "questionFrontendId": "2779", "categoryTitle": "Algorithms", "boundTopicId": 2341205, "title": "Maximum Beauty of an Array After Applying Operation", "titleSlug": "maximum-beauty-of-an-array-after-applying-operation", "content": "
You are given a 0-indexed array nums
and a non-negative integer k
.
In one operation, you can do the following:
\n\ni
that hasn't been chosen before from the range [0, nums.length - 1]
.nums[i]
with any integer from the range [nums[i] - k, nums[i] + k]
.The beauty of the array is the length of the longest subsequence consisting of equal elements.
\n\nReturn the maximum possible beauty of the array nums
after applying the operation any number of times.
Note that you can apply the operation to each index only once.
\n\nA subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the order of the remaining elements.
\n\n\n
Example 1:
\n\n\nInput: nums = [4,6,1,2], k = 2\nOutput: 3\nExplanation: In this example, we apply the following operations:\n- Choose index 1, replace it with 4 (from range [4,8]), nums = [4,4,1,2].\n- Choose index 3, replace it with 4 (from range [0,4]), nums = [4,4,1,4].\nAfter the applied operations, the beauty of the array nums is 3 (subsequence consisting of indices 0, 1, and 3).\nIt can be proven that 3 is the maximum possible length we can achieve.\n\n\n
Example 2:
\n\n\nInput: nums = [1,1,1,1], k = 10\nOutput: 4\nExplanation: In this example we don't have to apply any operations.\nThe beauty of the array nums is 4 (whole array).\n\n\n
\n
Constraints:
\n\n1 <= nums.length <= 105
0 <= nums[i], k <= 105
给你一个下标从 0 开始的整数数组 nums
和一个 非负 整数 k
。
在一步操作中,你可以执行下述指令:
\n\n[0, nums.length - 1]
中选择一个 此前没有选过 的下标 i
。nums[i]
替换为范围 [nums[i] - k, nums[i] + k]
内的任一整数。数组的 美丽值 定义为数组中由相等元素组成的最长子序列的长度。
\n\n对数组 nums
执行上述操作任意次后,返回数组可能取得的 最大 美丽值。
注意:你 只 能对每个下标执行 一次 此操作。
\n\n数组的 子序列 定义是:经由原数组删除一些元素(也可能不删除)得到的一个新数组,且在此过程中剩余元素的顺序不发生改变。
\n\n\n\n
示例 1:
\n\n\n输入:nums = [4,6,1,2], k = 2\n输出:3\n解释:在这个示例中,我们执行下述操作:\n- 选择下标 1 ,将其替换为 4(从范围 [4,8] 中选出),此时 nums = [4,4,1,2] 。\n- 选择下标 3 ,将其替换为 4(从范围 [0,4] 中选出),此时 nums = [4,4,1,4] 。\n执行上述操作后,数组的美丽值是 3(子序列由下标 0 、1 、3 对应的元素组成)。\n可以证明 3 是我们可以得到的由相等元素组成的最长子序列长度。\n\n\n
示例 2:
\n\n\n输入:nums = [1,1,1,1], k = 10\n输出:4\n解释:在这个示例中,我们无需执行任何操作。\n数组 nums 的美丽值是 4(整个数组)。\n\n\n
\n\n
提示:
\n\n1 <= nums.length <= 105
0 <= nums[i], k <= 105
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