1003. Cosine Similarity Between Two Vectors

Medium · Math

Compute the cosine similarity between two vectors.

cos_sim(a, b) = (a · b) / (||a|| * ||b||)

Foundation of dense retrieval, RAG, and embedding-based search.

Input (stdin, JSON): { "a": [1, 2, 3], "b": [4, 5, 6] }

Output (stdout): the similarity rounded to 6 decimal places.

Edge cases: zero vector → output 0.0 (avoid div-by-zero).

Examples

Example 1
Input: {"a":[1,2,3],"b":[4,5,6]}
Output: 0.974632
Explanation: Highly similar direction.

Example 2
Input: {"a":[1,0],"b":[0,1]}
Output: 0.0
Explanation: Orthogonal.

Constraints

• Vectors have same length, 1..1000 elements.
• Components are integers or floats in [-1e6, 1e6].