My first instinct was a self-join with a WHERE clause and I actually started writing it out before realizing that's exactly the O(n²) thing they were steering away from.
Use a window function to compute a running sum over the sorted values, which gives the cumulative sum for each row including ties. This avoids the O(n^2) correlated subquery and leverages efficient sorting and window aggregation in modern databases.
Pro tip: Mention that window functions are optimized in most databases and can handle large datasets efficiently, but be prepared to discuss fallback strategies like self-join with aggregation if window functions are not supported.
Restate the problem: for each row, compute the sum of all val entries less than or equal to that row's val, with ties fully included. Confirm that the output should include the original id and val along with the cumulative sum.
Recognize that a correlated subquery would be O(n^2) and inefficient. Instead, use a window function: SUM(val) OVER (ORDER BY val ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW) to get the running sum.
Ensure that ties are fully included by using the default RANGE BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW, which includes all rows with the same val. Alternatively, use ROWS if you want to include only rows up to the current row in the sort order, but that would not fully include ties.
Construct the query: SELECT id, val, SUM(val) OVER (ORDER BY val) AS cumulative_sum FROM table; This uses the default window frame that includes all rows with val <= current val.
Explain that window functions are efficient (O(n log n) due to sorting) and scale well. If window functions are unavailable, suggest a self-join with GROUP BY as a fallback, but note its higher complexity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.