sum-of-beauty-in-the-array

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2012. Sum of Beauty in the Array (Medium)

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 all0 <= j < i and for alli < 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:

Input: nums = [1,2,3] Output: 2 Explanation: For each index i in the range 1 <= i <= 1: - The beauty of nums[1] equals 2. 

Example 2:

Input: nums = [2,4,6,4] Output: 1 Explanation: For each index i in the range 1 <= i <= 2: - The beauty of nums[1] equals 1. - The beauty of nums[2] equals 0. 

Example 3:

Input: nums = [3,2,1] Output: 0 Explanation: For each index i in the range 1 <= i <= 1: - The beauty of nums[1] equals 0. 

 

Constraints:

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

Related Topics

[Array]

Hints

Hint 1

Use suffix/prefix arrays.

Hint 2

prefix[i] records the maximum value in range (0, i - 1) inclusive.

Hint 3

suffix[i] records the minimum value in range (i + 1, n - 1) inclusive.