Count Windows That Follow an Increase, Equal, Decrease Pattern

You are given an integer array numbers and an array pattern whose values are each 1, 0 or -1. Let m = len(pattern). A window of m + 1 consecutive elements, numbers[s] through numbers[s + m], follows the pattern when every step inside it has the direction that pattern gives for that step:

• pattern[k] == 1 means numbers[s + k + 1] > numbers[s + k]
• pattern[k] == 0 means numbers[s + k + 1] == numbers[s + k]
• pattern[k] == -1 means numbers[s + k + 1] < numbers[s + k]

Return the number of starting indices s whose window follows the pattern.

Function Signature

def count_pattern_windows(numbers: list[int], pattern: list[int]) -> int:

Rules

• A window must lie entirely inside numbers, so s ranges from 0 to len(numbers) - m - 1.
• Every one of the m conditions must hold; a single mismatched step disqualifies the window.
• Windows may overlap, and each matching starting index is counted once.
• Return 0 when no window matches.

Constraints

• 2 <= len(numbers) <= 10^5
• 1 <= len(pattern) < len(numbers)
• -10^9 <= numbers[i] <= 10^9
• every pattern[k] is 1, 0 or -1

Examples

Example 1

Input: numbers = [3, 7, 5, 5, 8, 7], pattern = [-1, 0, 1]
Output: 1

The only matching window starts at index 1: [7, 5, 5, 8] steps down from 7 to 5, stays equal from 5 to 5, then steps up from 5 to 8. Put differently, the elements 5, 5, 8 at indices 2 to 4 each compare with the element just before them as the pattern requires. The windows starting at index 0 ([3, 7, 5, 5], whose first step goes up) and index 2 ([5, 5, 8, 7], whose first step is equal) do not match.

Example 2

Input: numbers = [2, 2, 2, 2], pattern = [0, 0]
Output: 2

The windows starting at indices 0 and 1 both stay equal twice; overlapping windows are counted separately.

Example 3

Input: numbers = [5, 4, 5, 4, 5], pattern = [1, -1]
Output: 1

Only the window starting at index 1, [4, 5, 4], goes up and then down. The windows starting at indices 0 and 2 begin with a decrease.