My first instinct was brute force the pair count each time, which is obviously bad.
Clarify the constraints and operation mix, then propose a hybrid approach: preprocess the static array into a frequency map and handle updates to the dynamic array by maintaining a frequency map that is updated in O(1). For each query, iterate over the smaller frequency map and look up the complement in the other, achieving O(min(distinct values)) per query. Discuss trade-offs and mention that if updates are frequent and queries are rare, a different strategy like recomputing might be better.
Pro tip: Always start by asking about the relative frequency of updates vs. queries and the value ranges; this shows you think about real-world performance and can lead to a more tailored solution. Also, mention that using a hash map for frequencies is often faster than sorting when values are sparse or updates are frequent.
Ask about array sizes, number of operations, value ranges, and whether updates and queries are interleaved. This determines the optimal data structures and algorithm.
Use frequency maps (hash maps) for both arrays to allow O(1) updates and fast lookups. Alternatively, if the static array is large and queries are many, consider sorting it and using binary search, but updates to the dynamic array would still require a frequency map.
For each query, iterate over the distinct values of the smaller frequency map, compute the complement (target - value), and add the product of frequencies if the complement exists in the other map. This yields O(min(distinct values)) per query.
When an update occurs, decrement the frequency of the old value and increment the frequency of the new value in the dynamic array's frequency map. This is O(1) per update.
State the time complexity: O(1) per update, O(min(distinct values)) per query. Discuss alternatives like recomputing from scratch if updates are very frequent and queries are rare, or using a Fenwick tree if values are bounded and we need to count pairs with sum target.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.