3874. Valid Subarrays With Exactly One Peak - Practice Online

You are given an integer array nums of length n and an integer k.

An index i is a peak if:

A subarray [l, r] is valid if:

Return an integer denoting the number of valid subarrays in nums.

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

Example 1:

Input: nums = [1,3,2], k = 1

Output: 4

Explanation:

Index i = 1 is a peak because nums[1] = 3 is greater than nums[0] = 1 and nums[2] = 2.
Any valid subarray must include index 1, and the distance from the peak to both ends of the subarray must not exceed k = 1.
The valid subarrays are [3], [1, 3], [3, 2], and [1, 3, 2], so the answer is 4.

Example 2:

Input: nums = [7,8,9], k = 2

Output: 0

Explanation:

There is no index i such that nums[i] is greater than both nums[i - 1] and nums[i + 1].
Therefore, the array contains no peak. Thus, the number of valid subarrays is 0.

Example 3:

Input: nums = [4,3,5,1], k = 2

Output: 6

Explanation:

Index i = 2 is a peak because nums[2] = 5 is greater than nums[1] = 3 and nums[3] = 1.
Any valid subarray must contain this peak, and the distance from the peak to both ends of the subarray must not exceed k = 2.
The valid subarrays are [5], [3, 5], [5, 1], [3, 5, 1], [4, 3, 5], and [4, 3, 5, 1], so the answer is 6.

Constraints: