{ "data": { "question": { "questionId": "2888", "questionFrontendId": "2780", "categoryTitle": "Algorithms", "boundTopicId": 2341216, "title": "Minimum Index of a Valid Split", "titleSlug": "minimum-index-of-a-valid-split", "content": "

An element x of an integer array arr of length m is dominant if freq(x) * 2 > m, where freq(x) is the number of occurrences of x in arr. Note that this definition implies that arr can have at most one dominant element.

\n\n

You are given a 0-indexed integer array nums of length n with one dominant element.

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You can split nums at an index i into two arrays nums[0, ..., i] and nums[i + 1, ..., n - 1], but the split is only valid if:

\n\n\n\n

Here, nums[i, ..., j] denotes the subarray of nums starting at index i and ending at index j, both ends being inclusive. Particularly, if j < i then nums[i, ..., j] denotes an empty subarray.

\n\n

Return the minimum index of a valid split. If no valid split exists, return -1.

\n\n

 

\n

Example 1:

\n\n
\nInput: nums = [1,2,2,2]\nOutput: 2\nExplanation: We can split the array at index 2 to obtain arrays [1,2,2] and [2]. \nIn array [1,2,2], element 2 is dominant since it occurs twice in the array and 2 * 2 > 3. \nIn array [2], element 2 is dominant since it occurs once in the array and 1 * 2 > 1.\nBoth [1,2,2] and [2] have the same dominant element as nums, so this is a valid split. \nIt can be shown that index 2 is the minimum index of a valid split. 
\n\n

Example 2:

\n\n
\nInput: nums = [2,1,3,1,1,1,7,1,2,1]\nOutput: 4\nExplanation: We can split the array at index 4 to obtain arrays [2,1,3,1,1] and [1,7,1,2,1].\nIn array [2,1,3,1,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.\nIn array [1,7,1,2,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.\nBoth [2,1,3,1,1] and [1,7,1,2,1] have the same dominant element as nums, so this is a valid split.\nIt can be shown that index 4 is the minimum index of a valid split.
\n\n

Example 3:

\n\n
\nInput: nums = [3,3,3,3,7,2,2]\nOutput: -1\nExplanation: It can be shown that there is no valid split.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "合法分割的最小下标", "translatedContent": "

如果元素 x 在长度为 m 的整数数组 arr 中满足 freq(x) * 2 > m ,那么我们称 x 是 支配元素 。其中 freq(x) 是 x 在数组 arr 中出现的次数。注意,根据这个定义,数组 arr 最多 只会有 一个 支配元素。

\n\n

给你一个下标从 0 开始长度为 n 的整数数组 nums ,数据保证它含有一个支配元素。

\n\n

你需要在下标 i 处将 nums 分割成两个数组 nums[0, ..., i] 和 nums[i + 1, ..., n - 1] ,如果一个分割满足以下条件,我们称它是 合法 的:

\n\n\n\n

这里, nums[i, ..., j] 表示 nums 的一个子数组,它开始于下标 i ,结束于下标 j ,两个端点都包含在子数组内。特别地,如果 j < i ,那么 nums[i, ..., j] 表示一个空数组。

\n\n

请你返回一个 合法分割 的 最小 下标。如果合法分割不存在,返回 -1 。

\n\n

 

\n\n

示例 1:

\n\n
输入:nums = [1,2,2,2]\n输出:2\n解释:我们将数组在下标 2 处分割,得到 [1,2,2] 和 [2] 。\n数组 [1,2,2] 中,元素 2 是支配元素,因为它在数组中出现了 2 次,且 2 * 2 > 3 。\n数组 [2] 中,元素 2 是支配元素,因为它在数组中出现了 1 次,且 1 * 2 > 1 。\n两个数组 [1,2,2] 和 [2] 都有与 nums 一样的支配元素,所以这是一个合法分割。\n下标 2 是合法分割中的最小下标。
\n\n

示例 2:

\n\n
输入:nums = [2,1,3,1,1,1,7,1,2,1]\n输出:4\n解释:我们将数组在下标 4 处分割,得到 [2,1,3,1,1] 和 [1,7,1,2,1] 。\n数组 [2,1,3,1,1] 中,元素 1 是支配元素,因为它在数组中出现了 3 次,且 3 * 2 > 5 。\n数组 [1,7,1,2,1] 中,元素 1 是支配元素,因为它在数组中出现了 3 次,且 3 * 2 > 5 。\n两个数组 [2,1,3,1,1] 和 [1,7,1,2,1] 都有与 nums 一样的支配元素,所以这是一个合法分割。\n下标 4 是所有合法分割中的最小下标。
\n\n

示例 3:

\n\n
输入:nums = [3,3,3,3,7,2,2]\n输出:-1\n解释:没有合法分割。\n
\n\n

 

\n\n

提示:

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