Maximize Movie Ratings Without Skipping Two in a Row

Problem Statement

You are given an array of integers ratings representing the critic scores of a list of movies in their original release order. Movie ratings can be positive, negative, or zero.

You want to curate a list of movies to maximize the sum of their ratings. However, to maintain continuity in your catalog, you cannot skip two consecutive movies from the original list. In other words, for every adjacent pair of movies at indices i and i + 1, at least one of them must be included in your selection.

Additionally, you must select at least one movie.

Return the maximum possible sum of ratings for a valid selection.

Function Signature

def max_movie_ratings(ratings: list[int]) -> int:
    pass

Input & Output Format

• Input: A list of integers ratings of length n.
• Output: An integer representing the maximum total rating sum achievable.

Constraints

• 1 <= ratings.length <= 1_000_000
• -10^9 <= ratings[i] <= 10^9
• Time complexity should be O(n) and auxiliary space should be O(1).

Examples

Example 1

Input: ratings = [9, -1, -3, 4, 5]
Output: 17
Explanation:
We cannot skip both -1 and -3 because they are consecutive. 
To maximize the sum, we pick 9, pick -1, skip -3, pick 4, and pick 5.
Total sum = 9 + (-1) + 4 + 5 = 17.

Example 2

Input: ratings = [-5, -2, -3]
Output: -2
Explanation:
All ratings are negative. We can skip index 0 (-5), pick index 1 (-2), and skip index 2 (-3).
No two consecutive movies are skipped, and the sum is -2.

Example 3

Input: ratings = [-10]
Output: -10
Explanation:
At least one movie must be selected, so we must pick the single movie with rating -10.