問題
Cosine similarity compares the direction of two vectors and ignores their length. Semantic search uses it to find texts with similar embeddings:
cos(a, b) = (a · b) / (|a| × |b|), where |a| = √(a₁² + a₂² + … + aₙ²)
The result is 1 for the same direction, 0 for perpendicular vectors and -1 for opposite directions. If either vector is all zeros, return 0.
Implement cosine_similarity(a, b).
Input
a, b: Two lists of numbers with the same length.
Output
Return the cosine similarity as a decimal number.
制約
1 ≤ length ≤ 1,000
-1,000 ≤ each value ≤ 1,000
例
例 1
入力：
a = [1.0, 0.0]
b = [0.0, 1.0]
期待される出力：
expected = 0.0入力：
std::vector<double> a = {1.0, 0.0};
std::vector<double> b = {0.0, 1.0};
期待される出力：
double expected = 0.0;入力：
double[] a = new double[] {1.0, 0.0};
double[] b = new double[] {0.0, 1.0};
期待される出力：
double expected = 0.0;解説
The dot product is 0, so the vectors are perpendicular and the similarity is 0.
例 2
入力：
a = [1.0, 2.0, 3.0]
b = [2.0, 4.0, 6.0]
期待される出力：
expected = 1.0入力：
std::vector<double> a = {1.0, 2.0, 3.0};
std::vector<double> b = {2.0, 4.0, 6.0};
期待される出力：
double expected = 1.0;入力：
double[] a = new double[] {1.0, 2.0, 3.0};
double[] b = new double[] {2.0, 4.0, 6.0};
期待される出力：
double expected = 1.0;解説
b is a times 2: same direction, so the similarity is 1 even though the lengths differ.
参考資料
この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。