Mid/SeniorArray

Sum of Beauty in the Array

You are given a 0-indexed integer array nums. For each index i (1 <= i <= nums.length - 2), the beauty of nums[i] equals:

  • 2, if nums[j] < nums[i] < nums[k], for all 0 <= j < i and for all i < k <= nums.length - 1.
  • 1, if nums[i - 1] < nums[i] < nums[i + 1], and the previous condition is not satisfied.
  • 0, if none of the previous conditions holds.

Return the sum of beauty of all nums[i] where 1 <= i <= nums.length - 2.

Example 1
Inputnums = [1,2,3]
Output2
For the only valid index i = 1, the beauty of nums[1] equals 2.
Example 2
Inputnums = [2,4,6,4]
Output1
For valid indices i = 1 and i = 2, the beauties are 1 and 0, so the total is 1.

Constraints

  • 3 <= nums.length <= 10^5
  • 1 <= nums[i] <= 10^5

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