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 becausemin(3, 4) = 3 > max(1) = 1.[5, 3, 1, 4]is a bowl becausemin(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 <= 1051 <= nums[i] <= 109numsconsists 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.