3676. Count Bowl Subarrays

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You are given an integer array nums with distinct elements.

A subarray nums[l...r] of nums is called a bowl if:

  • The subarray has length at least 3. That is, r - l + 1 >= 3.
  • The minimum of its two ends is strictly greater than the maximum of all elements in between. That is, min(nums[l], nums[r]) > max(nums[l + 1], ..., nums[r - 1]).

Return the number of bowl subarrays in nums.

 

Example 1:

Input: nums = [2,5,3,1,4]

Output: 2

Explanation:

The bowl subarrays are [3, 1, 4] and [5, 3, 1, 4].

  • [3, 1, 4] is a bowl because min(3, 4) = 3 > max(1) = 1.
  • [5, 3, 1, 4] is a bowl because min(5, 4) = 4 > max(3, 1) = 3.

Example 2:

Input: nums = [5,1,2,3,4]

Output: 3

Explanation:

The bowl subarrays are [5, 1, 2], [5, 1, 2, 3] and [5, 1, 2, 3, 4].

Example 3:

Input: nums = [1000000000,999999999,999999998]

Output: 0

Explanation:

No subarray is a bowl.

 

Constraints:

  • 3 <= nums.length <= 105
  • 1 <= nums[i] <= 109
  • nums consists of distinct elements.

Hints

Hint 1
Use monotonic stacks to find nearest greater elements on both sides.
Hint 2
The bowl condition depends on comparing both ends with the maximum of the middle - avoid recomputing max by preprocessing.
Hint 3
Think in terms of "valid endpoints" rather than enumerating all subarrays.
Hint 4
There's symmetry: you can check both (left endpoint is smaller) and (right endpoint is smaller) cases separately.