Cosine Similarity

Cosine similarity is a measure of similarity between two vectors of an inner product space that measures the cosine of the angle between them. The cosine of 0° is 1, and it is less than 1 for any other angle.

See wiki: Cosine Similarity

Here is the formula:

Given two vectors A and B with the same size, calculate the cosine similarity.

Return 2.0000 if cosine similarity is invalid (for example A = [0] and B = [0]).

Example

Given A = [1, 2, 3], B = [2, 3 ,4].

Return 0.9926.

Given A = [0], B = [0].

Return 2.0000

分析：

按照公式算就可以了。需要考虑invalid case.

class Solution {
    /**
     * @param A: An integer array.
     * @param B: An integer array.
     * @return: Cosine similarity.
     */
    public double cosineSimilarity(int[] A, int[] B) {
        
        if (A == null || B == null || A.length == 0 || B.length == 0 || A.length != B.length) return 2.0;
        double nA = norm(A);
        double nB = norm(B);
        double  m = 0;
        if (nA == 0 || nB == 0) return 2.0;
        for (int i = 0; i < A.length; ++i) {
            m += A[i] * B[i];
        }
        return m / (nA * nB);
    }
    double norm(int[] V) {
        int res = 0;
        for (int i = 0; i < V.length; ++i) {
            res += V[i] * V[i];
        }
        return Math.sqrt(res);
    }
}