Maximize Movie Ratings Without Skipping Two in a Row

Question

The question asks the candidate to devise an algorithm that maximizes movie ratings without selecting two consecutive movies.

Codemia · Accepted Answer

To solve the problem of maximizing movie ratings without selecting two consecutive movies, we can use a dynamic programming approach. The main idea is to maintain a record of the maximum ratings that can be achieved up to each movie while adhering to the constraint of not picking two consecutive movies.

We can define a dynamic programming array `dp` where `dp[i]` represents the maximum rating we can achieve by considering movies up to index `i`. The recurrence relation will be:

- If we choose the current movie `i`, we add its rating to `dp[i-2]` (the maximum rating up to the movie before the last one).
- If we skip the current movie, we take the maximum rating up to the previous movie `dp[i-1]`.

Thus, the relation can be defined as:

```python
  dp[i] = max(dp[i-1], ratings[i] + (dp[i-2] if i > 1 else 0))
```

The complete algorithm can be implemented as follows:

```python
def maximize_ratings(ratings):
    n = len(ratings)
    if n == 0:
        return 0
    if n == 1:
        return ratings[0]

dp = [0] * n
    dp[0] = ratings[0]
    dp[1] = max(ratings[0], ratings[1])

for i in range(2, n):
        dp[i] = max(dp[i-1], ratings[i] + dp[i-2])

return dp[-1]
```
This algorithm runs in O(n) time and uses O(n) space.

The time complexity of this solution is O(n) because we iterate through the list of ratings once. The space complexity is also O(n) due to the additional array used for dynamic programming. However, we can optimize the space complexity to O(1) by only storing the last two results instead of the entire array.

We should consider edge cases such as:
- An empty list of ratings, which should return 0.
- A list with only one movie, which should return that movie's rating. 
- A list where all ratings are negative, where the algorithm should still function correctly and return the maximum rating (which could be 0 if we choose not to select any movies).

Maximize Movie Ratings Without Skipping Two in a Row

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