Top-5 Most Similar Rows Using MSE Across Multiple Features

You are given two datasets (or tables) A and B. They share the same set of numeric feature columns (e.g., f1, f2, ..., fk) and each has a unique identifier column (e.g., id). For each row a in A, find the top 5 most similar rows in B, where similarity is measured by the mean squared error (MSE) across multiple features: [ MSE(a,b)=\frac{1}{k}\sum_{j=1}^{k}(a.f_j-b.f_j)^2 ] Requirements: For every A.id, output 5 rows: the matched B.id values and their corresponding MSE. Sort by increasing MSE. If there is a tie, use B.id as a deterministic secondary sort key (ascending). You may implement using SQL (e.g., window functions) or pandas. Constraints (state reasonable assumptions if not provided): |A| = n, |B| = m, number of features is k. All features are numeric (int/float) with no missing values (or specify how to handle missingness). Provide the query/code and briefly discuss complexity or scalability considerations for large datasets if needed. Example Input A: 1 0 0 2 1 1 B: 10 0 1 11 1 2 12 2 2 13 0 0 14 1 1 15 3 3 (features: f1 f2) Output For a_id=1 (0,0): b_id ranking by MSE -> 13(0),10(0.5),14(1),11(2.5),12(4) For a_id=2 (1,1): b_id ranking by MSE -> 14(0),10(0.5),11(0.5),13(1),12(1) (tie broken by b_id)