原題網址：https://www.lintcode.com/problem/cosine-similarity/description

描述

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]).

樣例

給出 A = [1, 2, 3], B = [2, 3 ,4].

返回 0.9926.

給出 A = [0], B = [0].

返回 2.0000

思路：直接按照公式計算就好。註意余弦相似度無效的情況，分母等於0或者空數組。

PS：一開始提交的代碼沒考慮到空數組以及數組全0的情況，只排除了樣例中的無效情況……汗

AC代碼：

class Solution {
public:
    /*
     * @param A: An integer array
     * @param B: An integer array
     * @return: Cosine similarity
     */
    double cosineSimilarity(vector<int> &A, vector<int> &B) {
        // write your code here
 

    int n=A.size();
    if (n==0)
    {
        return 2.0;
    }
    double x=0.0,sumA=0.0,sumB=0.0;
    for (int i=0;i<n;i++)
    {
        x=x+A[i]*B[i];
        sumA=sumA+A[i]*A[i];
        sumB=sumB+B[i]*B[i];
    }
    sumA=sqrt(sumA);
    sumB=sqrt(sumB);
    if (sumA==0||sumB==0)
    {
        return 2.0;
    }
    double result=x/(sumA*sumB);
    return result;
    
    }
};

445 余弦相似度