Solution Explanation: Sorting Features by Popularity

This problem requires sorting a list of features based on their popularity derived from user responses. The popularity of a feature is the number of responses containing that feature (each feature is counted only once per response, even if it appears multiple times). Features with the same popularity should maintain their original order from the input features array.

Approach:

The most efficient approach uses a hash table (or dictionary) to count the occurrences of each feature and then sorts the features based on their counts and original indices.

1. Count Feature Occurrences: We iterate through the responses array. For each response, we split it into words and use a Set (or similar data structure to avoid duplicate counts within a single response) to track the unique features present. Then, we update a count in the hash table (cnt) for each unique feature found.

2. Sort Features: We sort the features array using a custom comparison function. This function first compares the popularity (count) of two features. If their popularity is different, the feature with higher popularity comes first. If their popularity is the same, we use the original index of the features in the input array to maintain the original order. This ensures stability in the sorting process.

Time Complexity Analysis:

• Counting feature occurrences: The nested loops iterate through the responses and words. The total number of words is roughly proportional to the total length of all responses. Thus, this step has a time complexity of O(R), where R is the total number of words in all responses.

• Sorting features: The sorting algorithm (typically merge sort or quicksort) has a time complexity of O(F log F), where F is the number of features.

Therefore, the overall time complexity is dominated by the sorting step, resulting in O(F log F + R). In most practical scenarios, the number of features (F) is likely to be smaller than the total number of words in responses (R), so we can approximate it as O(R) if R is significantly larger than F.

Space Complexity Analysis:

The hash table (cnt) stores the counts of each feature, requiring O(F) space, where F is the number of features. The auxiliary space used during sorting depends on the specific sorting algorithm, but is typically O(F) or O(F log F) in the worst case. The Set used to track unique features within a response also consumes space proportional to the number of unique features in that response. Thus, the overall space complexity is O(F + R), but again can be approximated as O(R) if R is significantly larger than F.

Code Examples:

The provided code examples demonstrate this approach in multiple programming languages. The core logic remains consistent across all languages. Note that the Python solution leverages the Counter object for concise counting, and the other languages use HashMaps or similar structures to achieve the same functionality. The sorting logic (using a lambda function or comparator) differs slightly depending on the language syntax but performs the same comparison logic described above.