Find the Number of Subarrays Where Boundary Elements Are Maximum

Problem Description

You are given an array of positive integers nums. Return the number of subarrays of nums, where the first and the last elements of the subarray are equal to the largest element in the subarray.

Key Insights

• A subarray is defined by a pair of indices (i, j) where i <= j.
• The first and last elements of the subarray must be the maximum value within that subarray.
• To efficiently find the count of valid subarrays, we can utilize a two-pointer technique or iterate through the array while keeping track of maximum values and their positions.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

We can solve this problem by iterating through the array while maintaining a count of the valid subarrays. Whenever we encounter a new maximum, we will count how many times this maximum appears consecutively and compute the number of valid subarrays formed by these maximums.

1. Traverse the array while keeping track of the maximum value found.
2. When we find a new maximum, calculate the number of valid subarrays formed by the previous maximums.
3. Reset the count for the new maximum and continue.

Code Solutions