What is the optimal solution approach for Threshold Majority Queries?

The optimal approach involves using sqrt decomposition and efficient query sorting to minimize time complexity when processing multiple queries.

How do I handle overlapping subarrays in Threshold Majority Queries?

Use a sliding window technique along with frequency counting to efficiently manage overlapping subarrays, especially when combined with sqrt decomposition.

What is sqrt decomposition in the context of this problem?

Sqrt decomposition breaks the array into blocks of size sqrt(n) to reduce redundant calculations when processing multiple queries, optimizing the overall performance.

What happens if no element meets the threshold in a query?

If no element appears at least `thresholdi` times, return -1 for that query.

Can the problem be solved without sorting queries?

While it's possible to solve without sorting, not sorting the queries can lead to inefficient query handling, especially with large inputs.

#3636

Hard

auto_awesomeThreshold Majority Queries core interview pattern

LeetCode 题解工作台

查询超过阈值频率最高元素

给你一个长度为 n 的整数数组 nums 和一个查询数组 queries ，其中 queries[i] = [l i , r i , threshold i ] 。返回一个整数数组 ans ，其中 ans[i] 等于子数组 nums[l i ...r i ] 中出现至少 threshold i …

题目描述

给你一个长度为 n 的整数数组 nums 和一个查询数组 queries，其中 queries[i] = [l_i, r_i, threshold_i]。

返回一个整数数组 ans，其中 ans[i] 等于子数组 nums[l_i...r_i] 中出现至少 threshold_i 次的元素，选择频率最高的元素（如果频率相同则选择最小的元素），如果不存在这样的元素则返回 -1。

示例 1:

输入： nums = [1,1,2,2,1,1], queries = [[0,5,4],[0,3,3],[2,3,2]]

输出： [1,-1,2]

解释：

查询	子数组	阈值	频率表	答案
[0, 5, 4]	[1, 1, 2, 2, 1, 1]	4	1 → 4, 2 → 2	1
[0, 3, 3]	[1, 1, 2, 2]	3	1 → 2, 2 → 2	-1
[2, 3, 2]	[2, 2]	2	2 → 2	2

示例 2:

输入：nums = [3,2,3,2,3,2,3], queries = [[0,6,4],[1,5,2],[2,4,1],[3,3,1]]

输出：[3,2,3,2]

解释：

查询	子数组	阈值	频率表	答案
[0, 6, 4]	[3, 2, 3, 2, 3, 2, 3]	4	3 → 4, 2 → 3	3
[1, 5, 2]	[2, 3, 2, 3, 2]	2	2 → 3, 3 → 2	2
[2, 4, 1]	[3, 2, 3]	1	3 → 2, 2 → 1	3
[3, 3, 1]	[2]	1	2 → 1	2

提示：

1 <= nums.length == n <= 10⁴
1 <= nums[i] <= 10⁹
1 <= queries.length <= 5 * 10⁴
queries[i] = [l_i, r_i, threshold_i]
0 <= l_i <= r_i < n
1 <= threshold_i <= r_i - l_i + 1

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解题思路

方法一

1

2

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Focus on how the candidate handles the query sorting and efficient sliding window techniques.
question_mark
Look for an understanding of advanced query optimization methods like sqrt decomposition.
question_mark
Check if the candidate can identify and address the potential pitfalls in query overlapping and frequency counting.

warning

常见陷阱

外企场景

error
Failure to handle overlapping subarrays efficiently, leading to high time complexity.
error
Incorrectly selecting the smallest element in case of a frequency tie.
error
Not optimizing the solution with techniques like sqrt decomposition, resulting in poor performance on large inputs.

swap_horiz

进阶变体

外企场景

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Consider handling dynamic updates to the array, where elements can be changed between queries.
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Modify the problem to return the element with the highest frequency for all subarrays, not just those satisfying the threshold.
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Extend the problem to multiple thresholds for each query, requiring additional logic for comparison.

help

常见问题

外企场景

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Threshold Majority Queries core interview pattern

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