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Refactoring for Complexity

MediumCoding00:00
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Your question is Refactoring for Complexity. Take a moment with it on the right.

Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).

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Problem

You're a software engineer at Ovyo working on catalog and viewership analytics for streaming partners. The three functions below run nightly over the full content catalog and viewing logs: finding duplicate titles that were accidentally ingested twice, finding viewers who watched two specific shows, and finding the most-watched genre. Against a small test catalog they're fine, but against Ovyo's real catalog (tens of thousands of titles) and a day's worth of viewing events, the nightly job now takes hours.

def find_duplicate_titles(catalog):
    duplicates = []
    for i in range(len(catalog)):
        for j in range(len(catalog)):
            if i != j and catalog[i]["title"] == catalog[j]["title"]:
                if catalog[i] not in duplicates:
                    duplicates.append(catalog[i])
    return duplicates

def common_viewers(show_a_viewers, show_b_viewers):
    common = []
    for viewer in show_a_viewers:
        if viewer in show_b_viewers:
            common.append(viewer)
    return common

def most_watched_genre(watch_events):
    genre_counts = []
    for event in watch_events:
        genre = event["genre"]
        found = False
        for entry in genre_counts:
            if entry["genre"] == genre:
                entry["count"] += 1
                found = True
                break
        if not found:
            genre_counts.append({"genre": genre, "count": 1})
    genre_counts.sort(key=lambda e: e["count"], reverse=True)
    return genre_counts[0]["genre"]

How would you refactor this piece of code to improve its time and space complexity? For each function, state its current complexity, why, and what you'd change it to.