Problema
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.
Vincoli
1 ≤ length ≤ 1,000
-1,000 ≤ each value ≤ 1,000
Esempi
Input:
a = [1.0, 0.0]
b = [0.0, 1.0]
Output atteso:
expected = 0.0Input:
std::vector<double> a = {1.0, 0.0};
std::vector<double> b = {0.0, 1.0};
Output atteso:
double expected = 0.0;Input:
double[] a = new double[] {1.0, 0.0};
double[] b = new double[] {0.0, 1.0};
Output atteso:
double expected = 0.0;Spiegazione
The dot product is 0, so the vectors are perpendicular and the similarity is 0.
Input:
a = [1.0, 2.0, 3.0]
b = [2.0, 4.0, 6.0]
Output atteso:
expected = 1.0Input:
std::vector<double> a = {1.0, 2.0, 3.0};
std::vector<double> b = {2.0, 4.0, 6.0};
Output atteso:
double expected = 1.0;Input:
double[] a = new double[] {1.0, 2.0, 3.0};
double[] b = new double[] {2.0, 4.0, 6.0};
Output atteso:
double expected = 1.0;Spiegazione
b is a times 2: same direction, so the similarity is 1 even though the lengths differ.
Riferimenti
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