Find the Number of Subarrays Where Boundary Elements Are Maximum - Problem

You are given an array of positive integers nums.

Return the number of subarrays of nums where the first and last elements of the subarray are equal to the largest element in the subarray.

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

Input & Output

Example 1 — Basic Case
$ Input: nums = [1,4,3,3,2]
Output: 6
💡 Note: Valid subarrays: [1] (first=last=max=1), [4] (first=last=max=4), [3] at index 2, [3] at index 3, [3,3] (first=last=max=3), [2] (first=last=max=2)
Example 2 — All Same Elements
$ Input: nums = [3,3,3]
Output: 6
💡 Note: All elements equal, so all subarrays are valid: [3], [3], [3], [3,3], [3,3], [3,3,3]
Example 3 — Single Element
$ Input: nums = [1]
Output: 1
💡 Note: Only one subarray [1] where first=last=max=1

Constraints

  • 1 ≤ nums.length ≤ 105
  • 1 ≤ nums[i] ≤ 109

Visualization

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Find Subarrays Where Boundary Elements Are MaximumInput: [1, 4, 3, 3, 2]14332[1] ✓[4] ✓[3] ✓[3] ✓[2] ✓[3,3] ✓Valid subarrays: first == last == maximum elementOutput: 6 subarrays[1], [4], [3], [3], [2], [3,3]
Understanding the Visualization
1
Input
Array with positive integers
2
Process
Find subarrays where first == last == max
3
Output
Count of valid subarrays
Key Takeaway
🎯 Key Insight: A subarray is valid only when its boundary elements are both equal to the maximum element in that subarray
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