Count Length-k Windows That Are Strictly Increasing

Given an integer array `nums` and an integer `k`, count the contiguous windows of exactly `k` elements whose values are strictly increasing from left to right. Windows may overlap, and each starting position whose window qualifies is counted once. The candidate's report describes the test only as a monotonic condition on each window; this version fixes it as strict increase, defined exactly in Rules below. ### Function Signature ```python def count_increasing_windows(nums: list[int], k: int) -> int: ``` ### Rules - The windows are the slices `nums[i : i + k]` for every starting index `i` with `0 <= i <= len(nums) - k`, so there are `len(nums) - k + 1` of them. - A window qualifies when each of its elements is strictly less than the next element inside the window: `nums[j] < nums[j + 1]` for every `j` with `i <= j < i + k - 1`. Two equal neighbours break strict increase. - A window of length 1 contains no neighbouring pair and always qualifies. - Return the number of qualifying windows as a single integer. ### Constraints - `1 <= k <= len(nums) <= 2 * 10^5` - `-10^9 <= nums[i] <= 10^9` - `len(nums)` and `k` can both reach `2 * 10^5`, so checking each window from scratch exceeds the time limit; the expected solution runs in time linear in `len(nums)`. ### Examples **Example 1** ```text Input: nums = [1, 2, 3, 2, 4, 5, 6], k = 3 Output: 3 ``` The five windows are `[1, 2, 3]`, `[2, 3, 2]`, `[3, 2, 4]`, `[2, 4, 5]` and `[4, 5, 6]`. The first, fourth and fifth are strictly increasing. **Example 2** ```text Input: nums = [5, 5, 6, 7], k = 2 Output: 2 ``` `[5, 5]` does not qualify because its two values are equal; `[5, 6]` and `[6, 7]` do. **Example 3** ```text Input: nums = [4, -1, 3], k = 1 Output: 3 ``` Every window has length 1, so all three qualify.