I fumbled the first few minutes because I wasn't sure if the compartments were inclusive or exclusive on the boundaries.
Clarify the problem: we need to count the number of elements within each query range [L, R] inclusive. Since the array is static, precompute a prefix sum array where each element is 1 (or the value if counting specific items), then answer each query in O(1) by subtracting prefix[R] - prefix[L-1]. This yields O(n + q) time and O(n) space, which is optimal for large inputs.
Pro tip: Always discuss edge cases like empty ranges, out-of-bounds indices, and negative numbers if the array can contain them. Mention that for very large arrays, a prefix sum array is more memory-efficient than a segment tree when only range sum queries are needed.
Confirm that queries are inclusive of both boundaries, that the array is static, and that we need to count all items (or specific items) within each range. Ask about input size and constraints to choose the right approach.
For static arrays with many range sum queries, a prefix sum array is ideal. If the array is dynamic or queries are more complex, consider a Fenwick tree or segment tree.
Build a prefix sum array where prefix[i] = sum of elements from index 0 to i-1 (or 1 to i depending on indexing). This takes O(n) time and allows O(1) range sum queries.
For each query [L, R], compute the count as prefix[R+1] - prefix[L] (for 0-based indexing) or prefix[R] - prefix[L-1] (for 1-based indexing). Handle edge cases like L > R or out-of-bounds indices.
State that preprocessing is O(n) and each query is O(1), giving O(n + q) total time. Discuss space O(n) and potential optimizations like using a Fenwick tree if memory is a concern or if updates are needed.
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