2419. Subarray With Elements Greater Than Varying Threshold

Hard
Array
Stack
Union Find
Monotonic Stack

Description

You are given an integer array nums and an integer threshold.

Find any subarray of nums of length k such that every element in the subarray is greater than threshold / k.

Return the size of any such subarray. If there is no such subarray, return -1.

A subarray is a contiguous non-empty sequence of elements within an array.

 

Example 1:

Input: nums = [1,3,4,3,1], threshold = 6
Output: 3
Explanation: The subarray [3,4,3] has a size of 3, and every element is greater than 6 / 3 = 2.
Note that this is the only valid subarray.

Example 2:

Input: nums = [6,5,6,5,8], threshold = 7
Output: 1
Explanation: The subarray [8] has a size of 1, and 8 > 7 / 1 = 7. So 1 is returned.
Note that the subarray [6,5] has a size of 2, and every element is greater than 7 / 2 = 3.5. 
Similarly, the subarrays [6,5,6], [6,5,6,5], [6,5,6,5,8] also satisfy the given conditions.
Therefore, 2, 3, 4, or 5 may also be returned.

 

Constraints:

  • 1 <= nums.length <= 105
  • 1 <= nums[i], threshold <= 109

Hints

Hint 1
For all elements to be greater than the threshold/length, the minimum element in the subarray must be greater than the threshold/length.
Hint 2
For a given index, could you find the largest subarray such that the given index is the minimum element?
Hint 3
Could you use a monotonic stack to get the next and previous smallest element for every index?

Statistics

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