Google search results: How to find the minimum window that contains all the search keywords?

Question

What is the complexity of the algorithm is that is used to find the smallest snippet that contains all the search key words?

Answer 1

Here's a solution using Java 8.

static Map.Entry documentSearch(Collection document, Collection query) {
    Queue queue = new ArrayDeque<>(query.size());
    HashSet words = new HashSet<>();

    query.stream()
        .forEach(words::add);

    AtomicInteger idx = new AtomicInteger();
    IndexPair interval = new IndexPair(0, Integer.MAX_VALUE);
    AtomicInteger size = new AtomicInteger();
    document.stream()
        .map(w -> new KeywordIndexPair(w, idx.getAndIncrement()))
        .filter(pair -> words.contains(pair.word)) // Queue.contains is O(n) so we trade space for efficiency
        .forEach(pair -> {
            // only the first and last elements are useful to the algorithm, so we don't bother removing
            // an element from any other index. note that removing an element using equality
            // from an ArrayDeque is O(n)
            KeywordIndexPair first = queue.peek();
            if (pair.equals(first)) {
                queue.remove();
            }
            queue.add(pair);
            first = queue.peek();
            int diff = pair.index - first.index;
            if (size.incrementAndGet() == words.size() && diff < interval.interval()) {
                interval.begin = first.index;
                interval.end = pair.index;
                size.set(0);
            }
        });

    return new AbstractMap.SimpleImmutableEntry<>(interval.begin, interval.end);
}

There are 2 static nested classes KeywordIndexPair and IndexPair, the implementation of which should be apparent from the names. Using a smarter programming language that supports tuples those classes wouldn't be necessary.

Test:

Document: apple, banana, apple, apple, dog, cat, apple, dog, banana, apple, cat, dog

Query: banana, cat

Interval: 8, 10