3113. Find the Number of Subarrays Where Boundary Elements Are Maximum

3113. Find the Number of Subarrays Where Boundary Elements Are Maximum

Hard

You are given an array of positive integers nums.

Return the number of subarrays¹ of nums, where the first and the last elements of the subarray are equal to the largest element in the subarray.

Example 1:

• Input: nums = [1,4,3,3,2]
• Output: 6
• Explanation: There are 6 subarrays which have the first and the last elements equal to the largest element of the subarray:
  • subarray [1,4,3,3,2], with its largest element 1. The first element is 1 and the last element is also 1.
  • subarray [1,4,3,3,2], with its largest element 4. The first element is 4 and the last element is also 4.
  • subarray [1,4,3,3,2], with its largest element 3. The first element is 3 and the last element is also 3.
  • subarray [1,4,3,3,2], with its largest element 3. The first element is 3 and the last element is also 3.
  • subarray [1,4,3,3,2], with its largest element 2. The first element is 2 and the last element is also 2.
  • subarray [1,4,3,3,2], with its largest element 3. The first element is 3 and the last element is also 3.

Hence, we return 6.

Example 2:

• Input: [3,3,3]
• Output: 6

• Explanation:
  There are 6 subarrays which have the first and the last elements equal to the largest element of the subarray:

  • subarray [3,3,3], with its largest element 3. The first element is 3 and the last element is also 3.
  • subarray [3,3,3], with its largest element 3. The first element is 3 and the last element is also 3.
  • subarray [3,3,3], with its largest element 3. The first element is 3 and the last element is also 3.
  • subarray [3,3,3], with its largest element 3. The first element is 3 and the last element is also 3.
  • subarray [3,3,3], with its largest element 3. The first element is 3 and the last element is also 3.
  • subarray [3,3,3], with its largest element 3. The first element is 3 and the last element is also 3.

Hence, we return 6.

Example 3:

• Input: nums = [1]
• Output: 1
• Explanation: There is a single subarray of nums which is [1], with its largest element 1. The first element is 1 and the last element is also 1.

Hence, we return 1.

Constraints:

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

Constraints:

class Solution {

    /**
     * @param Integer[] $nums
     * @return Integer
     */
    function numberOfSubarrays($nums) {
        $stack = [];
        $res = 0;

        for ($r = 0; $r < count($nums); $r++) {
            while ($stack && $stack[count($stack) - 1][0] < $nums[$r]) {
                array_pop($stack);
            }

            if ($stack && $stack[count($stack) - 1][0] == $nums[$r]) {
                $stack[count($stack) - 1][1]++;
            } else {
                array_push($stack, [$nums[$r], 1]);
            }

            $res += $stack[count($stack) - 1][1];
        }

        return $res;
    }
}

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